# 3-6 Multiplying Matrices. Determine whether each matrix product is defined. If so, state the dimensions of the product. 1. ANSWER: ANSWER: undefined

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

Download "3-6 Multiplying Matrices. Determine whether each matrix product is defined. If so, state the dimensions of the product. 1. ANSWER: ANSWER: undefined"

## Transcription

1 Determine whether each matrix product is defined. If so, state the dimensions of the product Undefined Find each product, if possible CCSS SENSE-MAKING The table shows the number of people registered for aerobics for the first quarter. Quinn s Gym charges the following registration fees: class-by-class, \$165; 11-class pass, \$110; unlimited pass, \$ Undefined Write a matrix for the registration fees and a matrix for the number of students. b. Find the total amount of money the gym received from aerobics and step aerobic registrations. esolutions Manual - Powered by Cognero Page 1

2 and 12. CCSS SENSE-MAKING The table shows the number of people registered for aerobics for the first quarter. Quinn s Gym charges the following registration fees: class-by-class, \$165; 11-class pass, \$110; unlimited pass, \$239. Determine whether each matrix product is defined. If so, state the dimensions of the product. 15. P 2 3 Q A 5 5 B 5 5 Write a matrix for the registration fees and a matrix for the number of students. b. Find the total amount of money the gym received from aerobics and step aerobic registrations. b. \$22,955 Use determine whether the following equations are true for the given matrices. 13. XY YX No; to M 3 1 N X 2 6 Y J 2 1 K S 5 2 T Find each product, if possible. 14. X(YZ) (XY)Z and 21. [ 26 ] 22. Determine whether each matrix product is defined. If so, state the dimensions of the product. 15. P 2 3 Q 3 4 esolutions Manual - Powered by Cognero Page

3 TRAVEL The Wolf family owns three bed and breakfasts in a vacation spot. A room with a single bed is \$220 a night, a room with two beds is \$250 a night, and a suite is \$ Undefined Write a matrix for the number of each type of room at each bed and breakfast. Then write a roomcost matrix. b. Write a matrix for total daily income, assuming that all the rooms are rented. c. What is the total daily income from all three bed and breakfasts, assuming that all the rooms are rented? b. 27. c. \$5060 Use, and k 2 to determine whether the following equations are true for the given matrices k(pq) P(kQ) 29. TRAVEL The Wolf family owns three bed and breakfasts in a vacation spot. A room with a single bed is \$220 a night, a room with two beds is \$250 a night, and a suite is \$ PQR RQP No; 32. PR + QR (P + Q)R esolutions Manual - Powered by Cognero Page 3

4 31. PQR RQP 3-6 Multiplying No; Matrices 32. PR + QR (P + Q)R \$ b. \$ c. \$ AUTO SALES A car lot has four sales associates. At the end of the year, each sales associate gets a bonus of \$1000 for every new car they have sold and \$500 for every used car they have sold. 33. R(P + Q) PR + QR No; 34. CCSS SENSE-MAKING Student Council is selling flowers for Mother s Day. They bought 200 roses, 150 daffodils, and 100 orchids for the purchase prices shown. They sold all of the flowers for the sales prices shown. Use a matrix to determine which sales associate earned the most money. b. What is the total amount of money the car lot spent on bonuses for the sales associates this year? Organize the data in two matrices, and use matrix multiplication to find the total amount that was spent on the flowers. b. Write two matrices, and use matrix multiplication to find the total amount the student council received for the flower sale. c. Use matrix operations to find how much money the student council made on their project. \$ b. \$ c. \$ AUTO SALES A car lot has four sales associates. At the end of the year, each sales associate gets a bonus of \$1000 for every new car they have sold and \$500 for every used car they have sold. b. \$187,500 Use matrices to find each of the following. If the matrix does not exist, write. 36. XY 37. YX Use a matrix to determine which sales associate earned the most money. b. What is the total amount of money the car lot 38. ZY 39. YZ esolutions Manual - Powered by Cognero Page 4

5 46. REASONING If the product matrix AB has 38. ZY 3-6 Multiplying Matrices 39. YZ 43. (XX)Z 44. CAMERAS Prices of digital cameras depend on features like optical zoom, digital zoom, and megapixels. 40. (YX)Z 41. (XZ)X 42. X(ZZ) 43. (XX)Z The 10-mp cameras are on sale for 20% off, and the other models are 10% off. Write a new matrix for these changes. b. Write a new matrix allowing for a 6.25% sales tax on the discounted prices. c. Describe what the differences in these two matrices represent. b. 44. CAMERAS Prices of digital cameras depend on features like optical zoom, digital zoom, and megapixels. c. sales tax 45. BUSINESS The Kangy Studio has packages available for senior portraits. The 10-mp cameras are on sale for 20% off, and the other models are 10% off. Write a new matrix for these changes. b. Write a new matrix allowing for a 6.25% sales tax on the discounted prices. c. Describe what the differences in these two matrices represent. Use matrices to determine the total cost of each package. b. The studio offers an early bird discount of 15% off any package. Find the early bird price for each package. A: \$421; B: \$274; C: \$150; D: \$68 b. A: \$357.85; B: \$232.90; C: \$127.50; D: \$57.80 esolutions Manual - Powered by Cognero Page 5

6 b. c. sales tax 45. BUSINESS The Kangy Studio has packages available for senior portraits. b. Use matrices to determine the total cost of each package. b. The studio offers an early bird discount of 15% off any package. Find the early bird price for each package. A: \$421; B: \$274; C: \$150; D: \$68 b. A: \$357.85; B: \$232.90; C: \$127.50; D: \$57.80 c. 46. REASONING If the product matrix AB has dimensions 5 8, and A has dimensions 5 6, what are the dimensions of matrix B? CCSS ARGUMENTS Show that each property of matrices. Scalar Distributive Property b. Matrix Distributive Property c. Associative Property of Multiplication d. Associative Property of Scalar Multiplication d. c(ab) c Substi Distri b. esolutions Manual - Powered by Cognero Page 6 (ca)b Substi

7 Distri (ca)b Substi c(ab) c Subst Distri Com A(cB) Substi 48. OPEN ENDED Write two matrices A and B such that AB BA. a 2, b 1, c 3, d WRITING IN MATH Use the data on Lisa Leslie found at the beginning of the lesson to explain how matrices can be used in sports statistics. Describe a matrix that represents the total number of points she has scored during her career and an example of a sport in which different point values are used in scoring. Sports statistics are often listed in columns and matrices. In this case, you can find the total number of points scored by multiplying the point value matrix, which does not change, by the scoring matrix, which changes after each season. The total number of points for her career can be found by multiplying the scoring matrix S by the point matrix P. Basketball and wrestling use different point values in scoring. 51. GRIDDED RESPONSE The average (arithmetic mean) of r, w, x, and y is 8, and the average of x and y is 4. What is the average of r and w? Carla, Meiko, and Kayla went shopping to get ready for college. Their purchases and total amounts spent are shown in the table below. Sample Answer: 49. CHALLENGE Find the missing values in a 2, b 1, c 3, d WRITING IN MATH Use the data on Lisa Leslie found at the beginning of the lesson to explain how matrices can be used in sports statistics. Describe a matrix that represents the total number of points she has scored during her career and an example of a sport in which different point values are used in scoring. Assume that all of the shirts were the same price, all of the pants were the same price, and all of the shoes were the same price. What was the price of each item? A shirt, \$12.95; pants, \$15.99; shoes, \$23.49 B shirt, \$15.99; pants, \$12.95; shoes, \$23.49 C shirt, \$15.99; pants, \$23.49; shoes, \$12.95 D shirt, \$23.49; pants, \$15.99; shoes, \$12.95 A 53. GEOMETRY Rectangle LMNQ has diagonals that intersect at point P. Which of the following represents point P? Sports statistics are often listed in columns and matrices. In this case, you can find the total number of points scored by multiplying the point value matrix, esolutions Manual - Powered by Cognero Page 7

8 C shirt, \$15.99; pants, \$23.49; shoes, \$12.95 D shirt, \$23.49; pants, \$15.99; shoes, \$ Multiplying Matrices A 53. GEOMETRY Rectangle LMNQ has diagonals that intersect at point P. Which of the following represents point P? 57. F (2, 2) G (1, 1) H (0, 0) J ( 1, 1) H 58. Solve each system of equations. ( 2, 5, 7) 54. SAT/ACT What are the dimensions of the matrix that results from the multiplication shown? 59. (8, 3, 1) 55. A 1 4 B 3 3 C 3 1 D 4 1 E 4 3 D Perform the indicated operations. If the matrix does not exist, write impossible. 60. ( 3, 2, 6) 61. MEDICINE The graph shows how much Americans spent on doctors visits in some recent years and a prediction for Find a regression equation for the data without the predicted value. b. Use your equation to predict the expenditures for c. Compare your prediction to the one given in the graph Sample answer: y x - 231, b. Sample answer: \$ billion esolutions Manual - Powered by Cognero Page 8

9 Multiplying Matrices ( 3, 2, 6) 61. MEDICINE The graph shows how much Americans spent on doctors visits in some recent years and a prediction for Find a regression equation for the data without the predicted value. b. Use your equation to predict the expenditures for c. Compare your prediction to the one given in the graph. 64. Translated 3 units to the left and 5 units down and stretched vertically Translated 2 units to the left and 6 units down. Sample answer: y x - 231, b. Sample answer: \$ billion c. The value predicted by the equation is significantly lower than the one given in the graph. 62. How many different ways can the letters of the word MATHEMATICS be arranged? 4,989,600 Describe the transformation in each function. Then graph the function. 63. Translated 4 units to the right and 3 units up. 64. esolutions Manual - Powered by Cognero Page 9 Translated 3 units to the left and 5 units down and stretched vertically..

### 0-5 Systems of Linear Equations and Inequalities

1. Solve each system of equations by graphing. Graph each equation in the system. The lines intersect at the point (1, 3). This ordered pair is the solution of the system. CHECK esolutions Manual - Powered

### Study Guide and Review - Chapter 8

Study Guide Review - Chapter 8 Solve each equation. Check your solutions. 41. 6x 2 = 12x Factor the trinomial using the Zero Product Property. 43. 3x 2 = 5x Factor the trinomial using the Zero Product

### The graphs coincide. Therefore, the trinomial has been factored correctly. The factors are (x + 2)(x + 12).

8-6 Solving x^ + bx + c = 0 Factor each polynomial. Confirm your answers using a graphing calculator. 1. x + 14x + 4 In this trinomial, b = 14 and c = 4, so m + p is positive and mp is positive. Therefore,

### 3-1 Solving Systems of Equations. Solve each system of equations by using a table. 2. SOLUTION: Write each equation in slope-intercept form.

Solve each system of equations by using a table. 2. Write each equation in slope-intercept form. Also: Make a table to find a solution that satisfies both equations. Therefore, the solution of the system

### 8-1 Adding and Subtracting Polynomials

Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial. 1. 7ab + 6b 2 2a 3 yes; 3; trinomial 2. 2y 5 +

### 8-8 Differences of Squares. Factor each polynomial. 1. x 9 SOLUTION: 2. 4a 25 SOLUTION: 3. 9m 144 SOLUTION: 4. 2p 162p SOLUTION: 5.

Factor each polynomial. 1.x 9 SOLUTION:.a 5 SOLUTION:.9m 1 SOLUTION:.p 16p SOLUTION: 5.u 81 SOLUTION: Page 1 5.u 81 SOLUTION: 6.d f SOLUTION: 7.0r 5n SOLUTION: 8.56n c SOLUTION: Page 8.56n c SOLUTION:

### 8-2 The Pythagorean Theorem and Its Converse. Find x.

Find x. 1. of the hypotenuse. The length of the hypotenuse is 13 and the lengths of the legs are 5 and x. 2. of the hypotenuse. The length of the hypotenuse is x and the lengths of the legs are 8 and 12.

### Here are some examples of combining elements and the operations used:

MATRIX OPERATIONS Summary of article: What is an operation? Addition of two matrices. Multiplication of a Matrix by a scalar. Subtraction of two matrices: two ways to do it. Combinations of Addition, Subtraction,

1. Simplify. 4. 9i 2. 5. 1 3. (4i)( 3i) 6. 12 i esolutions Manual - Powered by Cognero Page 1 7. Solve each equation. Find the values of a and b that make each equation true. 9. 3a + (4b + 2)i = 9 6i Set

### State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence. 1. x + 5x + 6 is an example of a prime polynomial. The statement is false. A

1. Determine whether each quadrilateral is a Justify your answer. 3. KITES Charmaine is building the kite shown below. She wants to be sure that the string around her frame forms a parallelogram before

### 8-3 Multiplying Polynomials. Find each product. 1. (x + 5)(x + 2) SOLUTION: 2. (y 2)(y + 4) SOLUTION: 3. (b 7)(b + 3) SOLUTION:

Find each product. 1. (x + 5)(x + ). (y )(y + 4) 3. (b 7)(b + 3) 4. (4n + 3)(n + 9) 5. (8h 1)(h 3) 6. (a + 9)(5a 6) 7. FRAME Hugo is designing a frame as shown. The frame has a width of x inches all the

### 7-1 Multiplication Properties of Exponents

Determine whether each expression is a monomial. Write yes or no. Explain your reasoning. 1. 15 15 is a monomial. It is a constant and all constants are monomials.. 3a 3a is not a monomial. There is subtraction

### 11-1 Areas of Parallelograms and Triangles. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary.

Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 2. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. Each pair of opposite

### 5-2 Dividing Polynomials. Simplify. SOLUTION: ANSWER: 4y + 2x (3a 2 b 6ab + 5ab 2 )(ab) 1 SOLUTION: ANSWER: 3a + 5b (x 2 6x 20) (x + 2)

1. Simplify. 4. (2a 2 4a 8) (a + 1) 4y + 2x 2 2. (3a 2 b 6ab + 5ab 2 )(ab) 1 3a + 5b 6 5. (3z 4 6z 3 9z 2 + 3z 6) (z + 3) 3. (x 2 6x 20) (x + 2) esolutions Manual - Powered by Cognero Page 1 6. (y 5 3y

### 7-2 Solving Exponential Equations and Inequalities. Solve each equation y 3 = 4 y + 1 SOLUTION:

Solve each equation. 2. 16 2y 3 = 4 y + 1 4. 49 x + 5 = 7 8x 6 6. A certificate of deposit (CD) pays 2.25% annual interest compounded biweekly. If you deposit \$500 into this CD, what will the balance be

### 4-1 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240.

ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.

### 5-2 Dividing Polynomials. Simplify. 2. (3a 2 b 6ab + 5ab 2 )(ab) 1 SOLUTION: 4. (2a 2 4a 8) (a + 1) SOLUTION: 6. (y 5 3y 2 20) (y 2) SOLUTION:

Simplify. 2. (3a 2 b 6ab + 5ab 2 )(ab) 1 4. (2a 2 4a 8) (a + 1) 6. (y 5 3y 2 20) (y 2) esolutions Manual - Powered by Cognero Page 1 Simplify. 8. (10x 2 + 15x + 20) (5x + 5) 10. 12. Simplify esolutions

### 3-3 Rate of Change and Slope. Find the rate of change represented in each table or graph.

Find the rate of change represented in each table or graph. To find the rate of change, use the coordinates (3, 6) and (0, 2). So, the rate of change is. To find the rate of change, use the coordinates

### The difference between terms is not constant. Therefore, it is not an arithmetic sequence.

Determine whether each sequence is an arithmetic sequence. Write yes or no. Explain. 18, 16, 15, 13, An arithmetic sequence is a numerical pattern that increases or decreases at a constant rate called

### 10-1 Sequences as Functions. Determine whether each sequence is arithmetic no. 1. 8, 2, 12, 22

10-1 Sequences as Functions Determine whether each sequence is arithmetic no. 1. 8, 2, 12, 22 3. 1, 2, 4, 8, 16 Subtract each term from the term directly after it. Subtract each term from the term directly

### 10-5 The Normal Distribution

A normal distribution has a mean of 416 and a standard deviation of 55. 1. Find the range of values that represent the middle 99.7% of the distribution. The middle 99.7% of data in a normal distribution

### State the assumption you would make to start an indirect proof of each statement.

1. State the assumption you would make to start an indirect proof of each statement. Identify the conclusion you wish to prove. The assumption is that this conclusion is false. 2. is a scalene triangle.

### Math 1314 Lesson 8 Business Applications: Break Even Analysis, Equilibrium Quantity/Price

Math 1314 Lesson 8 Business Applications: Break Even Analysis, Equilibrium Quantity/Price Three functions of importance in business are cost functions, revenue functions and profit functions. Cost functions

### 6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.

ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 3. PROOF Write a two-column proof to prove that if ABCD is a rhombus with diagonal. 1. If, find. A rhombus is a parallelogram with all

### Therefore, x is 3. To find BC. find 2x or 2(3) = 6. Thus, BC is Linear Measure

Find the length of each line segment or object. 1. Refer to Page 18. The ruler is marked in centimeters. The tail of the fish starts at the zero mark of the ruler and the mouth appears to end 7 tenth marks

### 2-2 Linear Relations and Functions. So the function is linear. State whether each function is a linear function. Write yes or no. Explain.

1. 2. 3. 4. State whether each function is a linear function. Write yes or no. Explain. The function written as. is linear as it can be + b. cannot be written in the form f (x) = mx So the function is

### This is a function because no vertical line can be drawn so that it intersects the graph more than once.

Determine whether each relation is a function. Explain. A function is a relation in which each element of the domain is paired with exactly one element of the range. So, this relation is a function. A

### 2-5 Solving Equations Involving Absolute Value. Evaluate each expression if f = 3, g = 4, and h = 5. Solve each equation. Then graph the solution set.

Evaluate each expression if f = 3, g = 4, and h = 5 Solve each equation Then graph the solution set The solution set is { 2, 12} Page 1 The solution set is { 2, 12} The solution set is {4, 2} means the

### 2-1 Writing Equations. Translate each sentence into an equation. Three times r less than 15 equals 6.

Translate each sentence into an equation. Three times r less than 15 equals 6. Rewrite the verbal sentence so it is easier to translate. Three times r less than 15 equals 6 is the same as 15 minus 3 times

### 4-6 Regression and Median-Fit Lines. a. Write an equation of the regression line and find the correlation coefficient.

a. Write an equation of the regression line and find the correlation coefficient. b. Graph the residual plot and determine if the regression line models the data well. Use a calculator to find the equation

### 5-6 The Remainder and Factor Theorems

Use synthetic substitution to find f (4) and f ( 2) for each function. 1. f (x) = 2x 3 5x 2 x + 14 Divide the function by x 4. The remainder is 58. Therefore, f (4) = 58. Divide the function by x + 2.

### 0-5 Systems of Linear Equations and Inequalities

21. Solve each system of equations. Eliminate one variable in two pairs of the system. Add the first equation and second equations to eliminate x. Multiply the first equation by 3 and add it to the second

### 6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.

ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. A rhombus is a parallelogram with all four sides congruent. So, Then, is an isosceles triangle. Therefore, If a parallelogram

### Study Guide and Review - Chapter 4

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. 1. The y-intercept is the y-coordinate of the point where the graph crosses the y-axis. The

### Use the graph to determine whether each system is consistent or inconsistent and if it is independent or dependent.

Use the graph to determine whether each system is consistent or inconsistent and if it is independent or dependent. y = 2x 1 y = 2x + 3 The lines y = 2x 1 and y = 2x + 3 intersect at exactly one point

Solve each inequality. Then graph the solution set on a number line. 1. 7. 2. 8. 3. 4. 5. 9. YARD WORK Tara is delivering bags of mulch. Each bag weighs 48 pounds, and the push cart weighs 65 pounds. If

### Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.

Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. 1. measures less than By the Exterior Angle Inequality Theorem, the exterior angle ( ) is larger than

### 8-1 Multiplying and Dividing Rational Expressions. Simplify each expression. SOLUTION: SOLUTION: 3. MULTIPLE CHOICE Identify all values of x for which

Simplify each expression. 1. 2. 3. MULTIPLE CHOICE Identify all values of x for which is undefined. A 7, 4 B 7, 4 C 4, 7, 7 D 4, 7 The function is undefined when the denominator tends to 0. The correct

### Practice Test - Chapter 1

Determine whether the given relation represents y as a function of x. 1. y 3 x = 5 2. When x = 1, y = ±. Therefore, the relation is not one-to-one and not a function. The graph passes the Vertical Line

### 2-4 Writing Linear Equations. Write an equation in slope-intercept form for the line described. 2. passes through ( 2, 3) and (0, 1) SOLUTION:

Write an equation in slope-intercept form for the line described 2 passes through ( 2, 3) and (0, 1) Substitute m = 1 and in the point slope form 4 passes through ( 8, 2); Substitute m = and (x, y) = (

### Each pair of opposite sides of a parallelogram is congruent to each other.

Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite

### Section 1.5 Linear Models

Section 1.5 Linear Models Some real-life problems can be modeled using linear equations. Now that we know how to find the slope of a line, the equation of a line, and the point of intersection of two lines,

### 10-7 Special Segments in a Circle. Find x. Assume that segments that appear to be tangent are tangent. 1. SOLUTION: ANSWER: 2 SOLUTION: ANSWER:

Find x. Assume that segments that appear to be tangent are tangent. 1. 3. 2 5 2. 4. 6 13 esolutions Manual - Powered by Cognero Page 1 5. SCIENCE A piece of broken pottery found at an archaeological site

### Practice Test - Chapter 1

Determine whether the given relation represents y as a function of x. 1. y 3 x = 5 When x = 1, y = ±. Therefore, the relation is not one-to-one and not a function. not a function 2. The graph passes the

### 2-2 Logic. SOLUTION: is a disjunction. A disjunction is true if at least

Use the following statements to write a compound statement for each conjunction or disjunction. Then find its truth value. Explain your reasoning. p : A week has seven days. q: There are 20 hours in a

### 2-4 Writing Linear Equations. Write an equation in slope-intercept form for the line described.

Write an equation in slope-intercept form for the line described 1 slope 15, passes through (0, 5) m = 15 (x, y) = (0, 5) in the equation y = mx + b 3 passes through (3, 5); m = 2 m = 2 (x, y) = (3, 5)

### A floor is a flat surface that extends in all directions. So, it models a plane. 1-1 Points, Lines, and Planes

1-1 Points, Lines, and Planes Use the figure to name each of the following. 1. a line containing point X 5. a floor A floor is a flat surface that extends in all directions. So, it models a plane. Draw

### 2-4 Solving Equations with the Variable on Each Side. Solve each equation. Check your solution. 13x + 2 = 4x Check: Check: Page 1

Solve each equation. Check your solution. 13x + 2 = 4x + 38 Page 1 6(n + 4) = 18 7 = 11 + 3(b + 5) Page 2 6(n + 4) = 18 7 = 11 + 3(b + 5) 5 + 2(n + 1) = 2n Page 3 5 + 2(n + 1) = 2n Since, this equation

### 4-7 Inverse Linear Functions. Find the inverse of each relation. {(4, 15), ( 8, 18), ( 2, 16.5), (3, 15.25)}

Find the inverse of each relation. {(4, 15), (8, 18), (2, 16.5), (3, 15.25)} To find the inverse, exchange the coordinates of the ordered pairs. (4, (8, 18, 8) (2, 16.5, 2) (3, 15.25, 3) The inverse is

### 2-2 Solving One-Step Equations. Solve each equation. Check your solution. g + 5 = 33. Check: 104 = y. Check: Check: Page 1

Solve each equation. Check your solution. g + 5 = 33 104 = y 67 4 +Manual t = 7- Powered by Cognero esolutions Page 1 4+t= 7 a + 26 = 35 6 + c = 32 1.5 = y ( 5.6) Page 2 1.5 = y ( 5.6) Page 3 Page 4 Page

### 4-5 Matrix Inverses and Solving Systems. Warm Up Lesson Presentation Lesson Quiz

Warm Up Lesson Presentation Lesson Quiz Holt Holt Algebra 2 2 Warm Up Find the determinant and the inverse. Warm Up Find the determinant. How To Find the Inverse Matrix Warm Up Find the inverse. 1. Find

### 3-2 Solving Systems of Inequalities by Graphing. Solve each system of inequalities by graphing. ANSWER: ANSWER: ANSWER:

1. Solve each system of inequalities by graphing. 4. CCSS REASONING The most Kala can spend on hot dogs and buns for her cookout is \$35. A package of 10 hot dogs costs \$3.50. A package of buns costs \$2.50

### 7-8 Recursive Formulas. Find the first five terms of each sequence. 1. SOLUTION: Use a 1. = 16 and the recursive formula to find the next four terms.

Find the first five terms of each sequence. 1. Use a 1 = 16 and the recursive formula to find the next four terms. The first five terms are 16, 13, 10, 7, and 4. esolutions Manual - Powered by Cognero

### 7-1 Ratios and Proportions

1. PETS Out of a survey of 1000 households, 460 had at least one dog or cat as a pet. What is the ratio of pet owners to households? The ratio of per owners to households is 23:50. 2. SPORTS Thirty girls

### 8-5 Using the Distributive Property. Use the Distributive Property to factor each polynomial. 1. 21b 15a SOLUTION:

Use the Distributive Property to factor each polynomial. 1. 1b 15a The greatest common factor in each term is 3.. 14c + c The greatest common factor in each term is c. 3. 10g h + 9gh g h The greatest common

1. Simplify each expression. 10. MULTIPLE CHOICE Which expression is equivalent to? A 2. 3. 4. 5. 12 10 11. B C D D Simplify each expression. 6. 120 12. 7. 13. 8. 9. 14. esolutions Manual - Powered by

### 6-5 Operations with Radical Expressions. CCSS PRECISION Simplify. SOLUTION: SOLUTION: SOLUTION: esolutions Manual - Powered by Cognero Page 1

2. CCSS PRECISION Simplify. 4. 6. esolutions Manual - Powered by Cognero Page 1 8. 10. 12. esolutions Manual - Powered by Cognero Page 2 14. 16. esolutions Manual - Powered by Cognero Page 3 Simplify.

### 4-6 The Quadratic Formula and the Discriminant. Solve each equation by using the Quadratic Formula.

2. Solve each equation by using the Quadratic Formula. Write the equation in the form ax 2 + bx + c = 0 and identify a, b, and c. Substitute these values into the Quadratic Formula and simplify. esolutions

### We can use the last column to set up an equation involving total price in order to solve for x.

FOOD Tasha ordered soup and salad for lunch. The soup cost 15 cents per ounce, and the salad cost 20 cents per ounce. If Tasha ordered 10 ounces of soup for lunch and the total cost was \$3.30, how many

### Warm-Up 1. 1. What is the least common multiple of 6, 8 and 10?

Warm-Up 1 1. What is the least common multiple of 6, 8 and 10? 2. A 16-page booklet is made from a stack of four sheets of paper that is folded in half and then joined along the common fold. The 16 pages

### Math 1314 Lesson 8: Business Applications: Break Even Analysis, Equilibrium Quantity/Price

Math 1314 Lesson 8: Business Applications: Break Even Analysis, Equilibrium Quantity/Price Cost functions model the cost of producing goods or providing services. Examples: rent, utilities, insurance,

### 11-5 Dividing Polynomials. Find each quotient. 1. (8a a) 4a ANSWER: 2a (4z 3 + 1) 2z ANSWER: 3. (12n 3 6n ) 6n ANSWER:

Find each quotient. 1. (8a 2 + 20a) 4a 2a + 5 9. (4y 2 + 8y + 3) (y + 2) 2. (4z 3 + 1) 2z 10. (4h 3 + 6h 2 3) (2h + 3) 3. (12n 3 6n 2 + 15) 6n 11. (9n 3 13n + 8) (3n 1) 4. (t 2 + 5t + 4) (t + 4) t + 1

### 7-2 Solving Exponential Equations and Inequalities. Solve each equation. 1. 3 5x = 27 2x 4 SOLUTION:

7-2 Solving Exponential Equations and Inequalities Solve each equation. 1. 3 5x = 27 2x 4 3. 2 6x = 32 x 2 12 2. 16 2y 3 = 4 y + 1 10 4. 49 x + 5 = 7 8x 6 3. 2 6x = 32 x 2 5. SCIENCE Mitosis is a process

### Study Guide and Review - Chapter 5

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. Set-builder notation is a less concise way of writing a solution set. The statement is false.

### Math 1324 Exam 3 Review (Spring 2011) (covers sections 2.1, 2.2, 2.3, 2.4, 3.1, 3.2, 3.3)

c Dr. Patrice Poage, March 30, 011 1 Math 134 Exam 3 Review (Spring 011) (covers sections.1,.,.3,.4, 3.1, 3., 3.3) 1. A = [ -15 - -1-38 B= 4-1 5 8-1 C= [ -3 h 4 p 6 Using the above matrices, find the value

### 1.1 Practice Worksheet

Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)

### Rotation Matrices and Homogeneous Transformations

Rotation Matrices and Homogeneous Transformations A coordinate frame in an n-dimensional space is defined by n mutually orthogonal unit vectors. In particular, for a two-dimensional (2D) space, i.e., n

### C A R I B B E A N E X A M I N A T I O N S C O U N C I L REPORT ON CANDIDATES WORK IN THE SECONDARY EDUCATION CERTIFICATE EXAMINATION MAY/JUNE 2011

C A R I B B E A N E X A M I N A T I O N S C O U N C I L REPORT ON CANDIDATES WORK IN THE SECONDARY EDUCATION CERTIFICATE EXAMINATION MAY/JUNE 2011 MATHEMATICS GENERAL PROFICIENCY EXAMINATION Copyright

### CONVERTING PERCENTS TO DECIMALS a) replace the % with x0.01 b) multiply by 0.01, i.e., move decimal point TWO PLACES TO LEFT

Chapter 6 Percents and Their Fraction and Decimal Forms N% = N per hundred Ratio = (this form I use most of the time) 70% 23.4%. 00% CONVERTING PERCENTS TO FRACTIONS 32% 90% 75% 0.06%.. 75% 50% 66 % CONVERTING

### 1-7 Inverse Relations and Functions

Graph each function using a graphing calculator, and apply the horizontal line test to determine whether its inverse function exists. Write yes or no. 3. f (x) = x 10x + 5 1. f (x) = x + 6x + 9 The graph

### 10-7 Special Segments in a Circle. Find x. Assume that segments that appear to be tangent are tangent. 1. SOLUTION: 2. SOLUTION: 3.

Find x. Assume that segments that appear to be tangent are tangent. 1. 2. 3. esolutions Manual - Powered by Cognero Page 1 4. 5. SCIENCE A piece of broken pottery found at an archaeological site is shown.

### Drew needs to add more than 27, or at least 28, comic books to have a larger collection than Connor. So, the correct choice is C.

Solve each inequality. Then graph it on a number line. x 9 < 4 The solution set is {x x < 5}. 6p 5p 3 The solution set is {p p 3}. Drew currently has 31 comic books in his collection. His friend Connor

### Use the graph shown to determine whether each system is consistent or inconsistent and if it is independent or dependent.

Use the graph shown to determine whether each system is consistent or inconsistent and if it is independent or dependent. y = 3x + 1 y = 3x + 1 The two equations intersect at exactly one point, so they

### Thursday, January 12 / Friday, January 13. Student Objective (Obj. 3c) TSW identify and justify the congruency of two figures.

Course: 7 th Grade Math Student Objective (Obj. 3c) TSW identify and justify the congruency of two figures. DETAIL LESSON PLAN Thursday, January 12 / Friday, January 13 Lesson 7-5 Congruent Figures Textbook

### Negative Integer Exponents

7.7 Negative Integer Exponents 7.7 OBJECTIVES. Define the zero exponent 2. Use the definition of a negative exponent to simplify an expression 3. Use the properties of exponents to simplify expressions

### 4-3 Writing Equations in Point-Slope Form

Write an equation in point-slope form for the line that passes through the given point with the slope provided. Then graph the equation. 1. ( 2, 5), slope 6 Write the equation in point-slope form. To graph

### To Evaluate an Algebraic Expression

1.5 Evaluating Algebraic Expressions 1.5 OBJECTIVES 1. Evaluate algebraic expressions given any signed number value for the variables 2. Use a calculator to evaluate algebraic expressions 3. Find the sum

### Lesson 1: Introduction to Equations

Solving Equations Lesson 1: Introduction to Equations Solving Equations Mentally Key to Solving Equations Solving Equations Lesson 2: Solving Addition Equations Golden Rule for Solving Equations: In order

### 2. SOLUTION: The members of the domain are the x-values of the relation while the members of the range are the y-values.

CCSS STRUCTURE State the domain and range of each relation. Then determine whether each relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither. 2. The members

### 12. The equations of two lines are and. What is the value of x in the solution for this system of equations?

Name: Period: Solving systems of equations word problems worksheet For all problems, define variables, write the system of equations and solve for all variables. The directions are from TAKS so do all

### SOLUTION: Since this is an isosceles triangle, two sides are congruent. Here, FG is 2a units long. Draw

and Codinate Proof Position and label each triangle on the codinate plane 1 right with legs and so that is 2a units long and leg is 2b units long Since this is a right triangle, two sides can be located

### December 4, 2013 MATH 171 BASIC LINEAR ALGEBRA B. KITCHENS

December 4, 2013 MATH 171 BASIC LINEAR ALGEBRA B KITCHENS The equation 1 Lines in two-dimensional space (1) 2x y = 3 describes a line in two-dimensional space The coefficients of x and y in the equation

### Math 210 Lecture Notes: Chapter Matrix Product Inverse Matrix

Math 210 Lecture Notes: Chapter 2.5 2.6 Matrix Product Inverse Matrix Richard Blecksmith Dept. of Mathematical Sciences Northern Illinois University 1. Matrix Product A B Step 1. The Initial Matrices Step

### 6-1 Angles of Polygons

Find the sum of the measures of the interior angles of each convex polygon. 1. decagon A decagon has ten sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures.

### Benchmark Assessment Test 2005 Math Grade 5 Test 1 Interpretive Guide

Benchmark Assessment Test 2005 Math Grade 5 Test 1 Interpretive Guide STRAND A MAA122 Compare relative size and order of whole numbers, fractions, decimals and percents 1 2 Comparing common fractions with

### Muscle Mania and Healthy Heart Gym

Muscle Mania and Healthy Heart Gym Allie Algebra and her friend Carly Coefficient wanted to get in shape. Allie Algebra joined the Muscle Mania Gym. To get a membership to the Muscle Mania Gym she had

### Applied Finite Mathematics Second Edition. Rupinder Sekhon De Anza College Cupertino, California. Page 1

Applied Finite Mathematics Second Edition Rupinder Sekhon De Anza College Cupertino, California Page 1 Author: Rupinder Sekhon Associate Editors: Jessica and Vijay Sekhon Rupinder Sekhon has been teaching

### Solving Two-Step and Multi-Step Equations

-3 Solving Two-Step and Multi-Step Equations Objective Solve equations in one variable that contain more than one operation. Why learn this? Equations containing more than one operation can model real-world

### CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.

TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has

### 1-8 Interpreting Graphs of Functions

CCSS SENSE-MAKING Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and

### 10-4 Inscribed Angles. Find each measure. 1.

Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semi-circle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what

### This lesson plan is from the Council for Economic Education's publication:

This lesson plan is from the Council for Economic Education's publication: Focus: Middle School Economics To purchase Focus: Middle School Economics, visit: http://store.councilforeconed.org/focmidschool.html

### Unit 1 Equations, Inequalities, Functions

Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1-100 Overview: This unit models real-world situations by using one- and two-variable linear equations. This unit will further expand upon pervious

### Finding the Measure of Segments Examples

Finding the Measure of Segments Examples 1. In geometry, the distance between two points is used to define the measure of a segment. Segments can be defined by using the idea of betweenness. In the figure

### Exam. Name. Solve the system of equations by graphing. 1) 2x y 5 3x y 6. Solve the system of equations by substitution.

Exam Name Solve the system of equations by graphing. 1) 2x y 5 3x y 6 10 y 1) 5-10 -5 5 10 x -5-10 Var: 50 Objective: (4.1) Solve Systems of Linear Equations by Graphing Solve the system of equations by

### Math 1314 Lesson 8: Business Applications: Break Even Analysis, Equilibrium Quantity/Price

Math 1314 Lesson 8: Business Applications: Break Even Analysis, Equilibrium Quantity/Price Cost functions model the cost of producing goods or providing services. Examples: rent, utilities, insurance,