Quantitative Reasoning Exam Solutions - 840 Verified Questions

Quantitative Reasoning Exam Solutions

Course Introduction

Quantitative Reasoning is a course designed to develop students ability to analyze, interpret, and draw logical conclusions from quantitative information encountered in real-world contexts. Through a focus on problem-solving and critical thinking, the course covers topics such as data interpretation, basic probability, statistical reasoning, mathematical modeling, and financial literacy. Students learn to apply quantitative methods to everyday situations, make informed decisions using data, and effectively communicate their reasoning. The skills acquired in Quantitative Reasoning are essential for academic success across disciplines as well as for responsible citizenship in an increasingly data-driven world.

Recommended Textbook

Elementary and Intermediate Algebra 4th Edition by Mark Dugopolski Emeritus

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32 Chapters

840 Verified Questions

840 Flashcards

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Chapter 1: Section 1: Real Numbers and Their Properties

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Sample Questions

Q1) Write the interval of real numbers in interval notation. The set of real numbers less than -6

A) [-6, )

B) (- , -6]

C) (- , -6)

D) (-6, )

Answer: C

Q2) A large industrial plant produces one ton of concrete every 0.80 minutes. At what rate is the facility producing concrete in tons per hour? Round to the nearest thousandth of a ton per hour.

A) 84.523 tons/hr

B) 61.112 tons/hr

C) 0.021 tons/hr

D) 75.000 tons/hr

Answer: D

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Chapter 1: Section 2: Real Numbers and Their Properties

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Sample Questions

Q1) T.L. and Quina plan to add a 9-inch thick layer of gravel to their driveway. The driveway is 29 yards long and 3 yards wide. What volume of gravel in cubic yards is required? Assume that the driveway layer is in the shape of a rectangular slab.

Answer: 11ea9079_e301_cd11_aec7_8d887fb183cb_TB3543_11 yd³

Q2) Evaluate: (6 - 2)(5 - 12)

Answer: -28

Q3) Evaluate: (5)(10)

Answer: 50

Q4) Use the commutative and associative properties of multiplication and exponential notation to rewrite the given product. v²(v·13)(vw)

Answer: 13v⁴w

Q5) Use the distributive property to factor the expression. -35p + 20

Answer: 5(-7p + 4)

Q6) Simplify: 2(m - 4) - 3(-m - 7)

Answer: 5m + 13

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Chapter 2: Section 1: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. s + 6s = 7s

A) Ø, inconsistent

B) All real numbers, identity

C) {0}, conditional

Answer: B

Q2) Solve and write your solution in interval notation. -21 < 33 - 9x \(\le\) -3

A) [4, 6)

B) Ø

C) [2, 6)

D) (2, 6]

Answer: A

Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. v - 11 = v + 11

A) Ø, inconsistent

B) All real numbers, identity

C) {0}, conditional

Answer: A

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Chapter 2: Section 2: Linear Equations and Inequalities in

One Variable

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Sample Questions

Q1) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. p - 8 = p + 8

Q2) Write the appropriate inequality symbol in the blank so that the two inequalities are equivalent.

-55 \(\ge\) 5y

-11 _____ y

Q3) Solve.

0.2n + 2.4 = 0.6n

Q4) Graph the inequality: -2 < x < 3

Q5) Solve for x.

4(x - a) - (26b - x) = a - b

Q6) Find an algebraic expression for the underlined quantity. The distance, given that the rate is x miles per hour and the time is 8 hours.

Q7) Find y given that x = -7 and y = -4x + 5.

Q8) Lori built a dog lot for her dog, Chollie, by fencing in a rectangular area of her yard. If Chollie's lot required 60 feet of fence and the length is 10 feet longer than the width, then what are the length and width of Chollie's dog lot?

Q9) Find three consecutive integers whose sum is 216. Page 6

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Page 7

Chapter 3: Section 1: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) If s varies inversely as x and s = 4 when x = -4, then find s when x = 2.

A) -8

B) 4

C) -16

D) -2

Q2) Does the point (2, 14) satisfy the inequality y \(\le\) 2x - 2?

A)True

B)False

Q3) Complete the ordered pair so that it satisfies the given equation. y = 7x - 13: (4, ___)

A) (4, 16)

B) (4, 28)

C) (4, 15)

D) (4, 41)

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Chapter 3: Section 2: Linear Equations and Inequalities in

Two Variables

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Sample Questions

Q1) Gotham City's budget deficit was $4.5 million in 1991 and $4.6 million in 2000. Find the slope of the line through (1991, 4.5) and (2000, 4.6) and interpret your result.

Q2) The time to drive from Gotham City to Farmville varies inversely with the average speed. If the drive takes 5.0 hours at 49 mph, then how long will it take at 70 mph? Round to the nearest tenth of an hour.

Q3) Graph the line through (-1, 3) with slope -2.

Q4) Find the x- and y-intercepts of x + 3y + 2 = 0 and use these intercepts to graph the equation.

Q5) Line l goes through (1, 3) and is parallel to the line through (4, 3) and (-3, 1). Find the slope of l.

Q6) Graph the equation y = -3x + 1.

Q7) Write a formula that expresses the relationship described below. P varies jointly as x and y and P = -8 when x = -2 and y = 7

Q8) Find the equation (in standard form) of the line through (2, 0) and (4, -1).

Q9) Find the slope of the line that contains the points (-11,2) and (8,-12).

Q10) Does the point (-4, -1) satisfy the inequality y \(\le\) 6x - 5?

A)True

B)False Page 9

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Page 10

Chapter 4: Section 1: Exponents and Polynomials

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Sample Questions

Q1) Simplify. (-5)⁰

A) -5

B) 5

C) -1

D) 1

Q2) Find the product. -5y⁷·2y²

A) -10y⁹

B) -10y¹⁴

C) -5y⁷.2y²

D) -3y⁹

Q3) Find the product. (x + 2)(x - 3)(x + 6)

A) x³+ 15x² + 12x - 36

B) x³+ 5x² + 12x + 36

C) x³+ 11x² + 36x + 36

D) x³+ 5x² - 12x - 36

Q4) Perform the indicated operation. (2p + 5) + (p² - 8p + 7)

A) p² + 10p + 12

B) p² + 2p + 12

C) -5p² + 12

D) p² - 6p + 12

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Chapter 4: Section 2: Exponents and Polynomials

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Sample Questions

Q1) Multiply. (5x - 6)²

Q2) Simplify. -(11)⁰

Q3) Expand the binomial. (n - 2)³

Q4) Find the quotient and the remainder. (x⁴ - x³ + 5) \(\div\) (x² + 2)

Q5) Write in scientific notation. 957 \(\times\)10³

Q6) What is the coefficient of x³ in the polynomial -11x³ + 13x²?

Q7) Perform the computation. (3 \(\times\)10^-14)²

Q8) Perform the indicated operation. (t - 5) - (5t - 8)

Q9) The edges of a triangular homesite have lengths of 3x + 4, x, and x - 1. Write an expression for the perimeter of the property.

Q10) Simplify. (xy³)³ Page 12

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Chapter 5: Section 1: Factoring

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Sample Questions

Q1) Factor the given polynomial completely. If the polynomial is prime, say so. x³+ xy + 2x² + 2y

A) The polynomial is prime.

B) (x + 2)(x² + y)

C) (x + 2)(x + y)

D) (x² + 2)(x + y)

Q2) Factor the given polynomial completely. z⁶ - 8z³ + 7

A) The polynomial is prime.

B) (z³ - 7)(z - 1)(z² - z - 1)

C) (z³ - 7)(z - 1)(z² + z + 1)

D) (z³ + 7)(z + 1)(z² + z + 1)

Q3) Factor the given polynomial completely. c⁴+ d⁴

A) c²d²(c²- d²)

B) (c - d)²(c + d)²

C) The polynomial is prime.

D) (c - d)(c + d)(c²+ d²)

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Page 14

Chapter 5: Section 2: Factoring

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Sample Questions

Q1) Factor.

tu + 5u - 7t - 35

Q2) Factor.

8x³ - 27

Q3) Factor the given polynomial completely. If the polynomial is prime, say so. n² - 2n

Q4) Factor the given polynomial completely. z⁶ + 2z³ - 3

Q5) Find the prime factorization.

115

Q6) Find the greatest common factor of the given terms. 8qr, 28rs, 12qs

Q7) Factor the given polynomial completely. If the polynomial is prime, say so. 7w² - 24w - 16

Q8) Factor the given polynomial completely. If the polynomial is prime, say so. c³+ cd + 3c² + 3d

Q9) Solve the given equation. x³ + 5x² - 2x - 24 = 0

Q10) Factor.

uvw + 9u + 5vw + 45 Page 15

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Page 16

Chapter 6: Section 1: Rational Expressions

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Sample Questions

Q1) A large pump can fill a 73,000 gallon reservoir in 7 hours. Working together, the large pump and a smaller one can fill the reservoir in 6 hours. How long would it take the smaller pump to fill the reservoir by itself?

A) 41 hours

B) 42 hours

C) 44 hours

D) 43 hours

Q2) Among 100 college students, 45 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?

A) 9 to 11

B) 20 to 11

C) 9 to 20

D) 11 to 9

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Chapter 6: Section 2: Rational Expressions

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Sample Questions

Q1) Among 100 college students, 40 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?

Q2) A large pump can fill a 78,000 gallon reservoir in 8 hours. Working together, the large pump and a smaller one can fill the reservoir in 6 hours. How long would it take the smaller pump to fill the reservoir by itself?

Q3) David hires a septic system contractor to dig trenches for his new septic tank. The cost to hire the contractor is a fixed cost of $250 plus an additional $80 per hour. Write an expression which describes the average cost of an x-hour job.

Q4) Jimbo biked 50 miles at x mph. He then increased his speed by 5 mph and biked another 40 miles. Write a rational expression for Jimbo's total travel time.

Q5) Find the least common multiple of the given terms. q² + 7q - 30, q² + 20q + 100

Q6) Chris prepares a 10-pound mixture of cashews and peanuts. He paid $18 for the cashews and $14 for the peanuts. If cashews cost three times more than peanuts, then how many pounds of cashews did he use?

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Chapter 7: Section 1: Systems of Linear Equations

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Sample Questions

Q1) Solve the system of equations.

2x - 3y + z = 4

8x - 12y + 4z = 16

-4x + 6y - 2z = -8

A) {(-3, 6, 7)}

B) {(-4, -2, -1)}

C) {\(\varnothing\)}

D) {(x, y, z) | 2x - 3y + z = 4}

Q2) Solve the system of equations.

-x + y - z = 8

4x - 2y + 5z = -28

2x - 2y + 2z = -14

A) {(0, 4, -4)}

B) {\(\varnothing\)}

C) {(x, y, z) | -x + y - z = 8}

D) {(x, y, z) | 4x - 2y + 5z = -28}

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Chapter 7: Section 2: Systems of Linear Equations

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Sample Questions

Q1) Solve the system of linear equations by the substitution method.

-5x = -2y + 9

5x + 5y = -30

Q2) Solve the system of equations.

-3.5x + 3y = -5.375

-0.875x - 0.5y = 0.53125

Q3) Solve the system of equations.

-x + 5y - 3z = 31

-4x - 5y + 4z = 6

3x - 15y + 9z = -91

Q4) For Monday morning's staff meeting, Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $9.00 (excluding sales tax). For Friday's meeting, he bought 4 bags of bagels and 2 packages of cream cheese and paid $10.00 (again, excluding sales tax). How much do bags of bagels and packages of cream cheese cost?

Q5) Solve the system of linear equations by the substitution method. Then, state whether the system is independent, dependent, or inconsistent.

4x - 3y = 4

12x - 9y = 12

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Chapter 8: Section 1: More on Inequalities

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Sample Questions

Q1) Determine whether the absolute value inequality is equivalent to the inequality following it: |4 - x| < 14, 4 - x < 14 and -(4 - x) < 14

A)True

B)False

Q2) Solve: -4 - |-11 - x| = -10

A) {-19, -3}

B) {-17, -5}

C) {-16, -2}

D) {-16, -4}

Q3) Trisha needs to adjust her cholesterol level to a target value of 150. She recalls that her cholesterol level differed from her target value by 16 units, but does not recall whether she is above or below the target value. Use an absolute value equation to find the possible values for Trisha's cholesterol level.

A) 118 or 134

B) 129 or 161

C) 134 or 166

D) 144 or 176

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Chapter 8: Section 2: More on Inequalities

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Sample Questions

Q1) Determine whether the absolute value inequality is equivalent to the inequality following it:

|-2 - x| < 14, -2 - x < 14 and -(-2 - x) < 14

A)True

B)False

Q2) The Belew's Creek Volunteer Fire Department is having a community chicken dinner in order to raise funds. Patrons have a choice between two sizes of dinners. The small dinner costs $2.50 and comes with one piece of chicken and two rolls. The large dinner costs $4.00 and comes with two pieces of chicken and three rolls. The department has a total of 568 rolls and 300 pieces of chicken. How many of each type of dinners need to be sold to maximize the fire department's revenue?

Q3) Trisha needs to adjust her cholesterol level to a target value of 170. She recalls that her cholesterol level differed from her target value by 6 units, but does not recall whether she is above or below the target value. Use an absolute value equation to find the possible values for Trisha's cholesterol level.

Q4) Write as a single interval if possible: [-1, \(\infty\))\(\cup\)(4, \(\infty\))

Q5) Solve: 12 - |-13 - x| = 2

Q6) Solve: |x - 5| = 3

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Chapter 9: Section 1: Radicals and Rational Exponents

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Sample Questions

Q1) Find the difference. (1 + 4i) - (-7 + 7i)

A) -6 - 3i

B) 8 + 11i

C) -6 + 11i

D) 8 - 3i

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Chapter 9: Section 2: Radicals and Rational Exponents

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Sample Questions

Q1) Find all real solutions. (s + 3)² - 5 = 0

Q2) Find all real solutions. (u - 2)^-1/3 = 1

Q3) The diagonal of a square measures 8 inches. What is the length of the sides?

Q4) Find the difference. (-5 - 10i) - (-7 - 3i)

Q5) Find all real solutions. -10(x - 3)³ = 0

Q6) Simplify.

49^2/3 \(\div\) 49^1/6

Q7) Evaluate. (27)^-4/3

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Chapter 10: Section 1: Quadratic Equations and Inequalities

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Sample Questions

Q1) Complete the ordered pair so that it satisfies the given equation. y = x²10x - 5, (-10, )

A) (-10, 195)

B) (-10, 194)

C) (-10, 200)

D) (-10, 196)

Q2) Find b² - 4ac and the number of real solutions for the given equation. x² + 3x + 4 = 0

A) -7, 2

B) 25, 0

C) -7, 0

D) 25, 2

Q3) Find all real solutions of the given equation. (x² + 1)²18(x² + 1) = -17

A) {5, 3}

B) {0, 5, 3}

C) {0, ±4}

D) {±16}

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25

Chapter 10: Section 2: Quadratic Equations and Inequalities

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Sample Questions

Q1) Find all real and imaginary solutions to the equation. t⁴ - 6561 = 0

Q2) Find the vertex for the graph of the parabola. f(x) = x² - 5

Q3) Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 7x² + 7x + 9

Q4) Solve: (q - 6)² = 36

Q5) A battery manufacturing plant spends C dollars per hour to produce "D"-size batteries. An efficiency consultant has determined that C is related to the number of batteries produced per hour, x, according to the equation C(x) = 0.02x² - 3x + 217.5. What number of batteries per hour minimizes the cost?

Q6) Graph the parabola. y = -x² + 4

Q7) Find all intercepts for the graph of the parabola. f(x) = 49 - x²

Q8) The monthly profit P in dollars that Carla makes on the sale of x automobiles is determined by the formula P = x² - 6x - 7. For what values of x is her profit positive?

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Chapter 11: Section 1: Functions

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Sample Questions

Q1) Determine whether the relation |6x| = |-7y| is a function.

A)True B)False

Q2) How are the graphs of f(x) = (x + 10)² and g(x) = -(x + 10)² related?

A) The graph of g(x) is the same as that of f(x), but reflected about the x-axis.

B) The graph of g(x) is the same as that of f(x), but translated upward by 10 units.

C) The graph of g(x) is the same as that of f(x), but translated 10 units to the left.

D) The graph of g(x) is the same as that of f(x), but translated 10 units to the right.

Q3) Determine whether f(x) = 5x and g(x) = 0.2x are inverses of each other.

A)True B)False

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27

Chapter 11: Section 2: Functions

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Q1) Determine whether f(x) = 2x and g(x) = 0.5x are inverses of each other.

A)True

B)False

Q2) Give the correct domain and range of the relation . {(-5, 4), (5, 4)}

Q3) A gas station charges $1.67 per gallon for regular gasoline. Write an expression for the cost c(g) as a function of the number of gallons g and use this function to determine c(13).

Q4) Determine whether the relation |2x| = |-8y| is a function.

A)True

B)False

Q5) How are the graphs of f(x) = (x + 4)² and g(x) = -(x + 4)² related?

Q6) How are the graphs of f(x) = x² and g(x) = x² + 7 related?

Q7) Let f(x) = -2x - 4 and g(x) = x² + 10x. Find (f ·g)(4).

Q8) For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. f(x) = x² + 2x - 3

Page 28

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Chapter 12: Section 1: Exponential and Logarithmic

Functions

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Q1) Write ln(r²) + ln(r⁴) + ln(r) as a single logarithm. Assume r represents numbers for which the logarithms are defined.

A) ln(r⁵)

B) ln(r⁷)

C) The logarithms cannot be combined.

D) ln(r⁸)

Q2) Solve log₇(x - 24) + log₇(x + 24) = 2.

A) {26}

B) {-25}

C) {25}

D) {27}

Q3) Solve -8^-6-^x = -64.

A) {-8}

B) {0}

C) {-6}

D) {-7}

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Chapter 12: Section 2: Exponential and Logarithmic Functions

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Q1) Write log₇(36) - log₇(6) as a single logarithm.

Q2) Write log(64) in terms of log(4).

Q3) Write log₆216 = 3 as an exponential equation.

Q4) Solve log(x) = -4.

Q5) Write ln(s⁵) + ln(s⁶) + ln(s) as a single logarithm. Assume s represents numbers for which the logarithms are defined.

Q6) Solve log₁₂(x - 35) + log₁₂(x + 35) = 2.

Q7) Simplify ln(e⁹).

Q8) Write 3⁶ = 729 as a logarithmic equation.

Q9) Rewrite log(75) in terms of log(3) and log(5).

Q10) Solve log₂(x² - 2) = 2 + log₂(x² + 8).

Q11) If $10,000 is deposited in an account paying 7% compounded quarterly, then what amount will be in the account after 8 years?

Q13) Solve -7^-5-^x = -49. Page 30

Q12) Evaluate log_1/5(6). Round to four decimal places.

Q14) Solve e^x^{+ 2} = 5.

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Page 31

Chapter 13: Section 1: Nonlinear Systems and the Conic Sections

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Sample Questions

Q1) Solve the given system of equations. x² + y² = 625

Y = x² - 25

A) {(0, -25)}

B) {(-7, 24), (7, 24)}

C) {(0,-25), (-7, 26), (7, 26)}

D) {(0, -25), (-7, 24), (7, 24)}

Q2) Find two complex numbers that have a sum of 12 and a product of 72.

A) 6 - 7i and 6 + 5i

B) 6 - 7i and 6 + 7i

C) 6 - 6i and 6 + 6i

D) 6 and 6

Q3) Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius. x² - 2x + y² + 2y - 98 = 0

A) (x + 1)² + (y - 1)² = 10; (-1, 1); 10

B) (x - 1)² + (y + 1)² = 10; (1, -1); 10

C) (x - 1)² + (y + 1)² = 100; (1, -1); 10

D) (x + 1)² + (y - 1)² = 100; (-1, 1); 10

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Page 32

Chapter 13: Section 2: Nonlinear Systems and the Conic Sections

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Sample Questions

Q1) Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection.

y = 1 - x² x² + 4y² = 4

Q2) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.

(x + 9)² - y² = 1

Q3) Solve the given system of equations.

y = x² + 4

-7x + y = -6

Q4) Pump A can either fill or empty a tank in the same amount of time. If pump A and pump B are working together, the tank can be filled in 36 minutes. When pump A is draining the tank while pump B is filling it, the tank fills in 180 minutes. How long would it take either pump working alone to fill the tank?

Q5) Write the standard equation for the circle with the given radius and center. Center (8, -5), radius 12

Q6) Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola.

(x + 5)² + y² = 1

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Chapter 14: Section 1: Sequences and Series Available

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Sample Questions

Q1) Use the binomial theorem to write out the first four terms of the given binomial. (x² + 1)¹⁷

A) x¹⁷ + 17x¹⁶ + 136x¹⁵ + 680x¹⁴

B) x³⁴ + 17x³² + 136x³⁰ + 680x²⁸

C) x¹⁷ + 17x³³ + 136x³² + 680x³¹

D) x³⁴ + 17x³³ + 136x³² + 680x³¹

Q2) Use the binomial theorem to expand the given binomial. (t + 2)⁴

A) t⁴ + 8t³ + 12t² + 8t + 2

B) t⁴ + 8t³ + 24t² + 32t + 16

C) 2t⁴ + 16t³ + 48t² + 16t + 2

D) t⁴ + 2t³ + 4t² + 8t + 16

Q3) Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -3 + (n - 2)(-3)

A) -6, -3, 0, 3, 6

B) 3, 0, -3, -6.0, -9

C) 3, 0, -3, -6, -9

D) 0, -3, -6, -9, -12

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Chapter 14: Section 2: Sequences and Series Available

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Q1) List all terms of the finite sequence a_n = 3n + 2 for 1 n 5.

Q2) List the first four terms of the given sequence and match your result to the correct answer below. c_n = (-1)ⁿ(-4n + 3)²

Q3) Each time an aluminum beverage can is recycled, some amount of the material is lost due to a variety of reasons. If each recycling step is 80% efficient, what percent of the original material remains if a can is recycled 3 times? Round to the nearest tenth of a percent.

Q4) Write a formula for the general term of the given sequence and match your result to the correct answer below. -4, -3, -2, -1, 0, ...

Q5) Write a formula for the nth term of the given arithmetic sequence. 1, 7, 13, 19, 25, . . .

Q6) Write the given series in summation notation. Use the index i, and let i begin at 1. ln(6) + ln(7) + ln(8)

Q7) Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -1 + (n + 1)(2)

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Chapter 15: Mathematical Problem Set

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Q1) Solve the given equation. y² + 6y + 8 = 0

Q2) Factor completely. If the polynomial is prime, say so. 9q² + 8q + 2

Q3) Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 4x - x = 3x

Q4) A triangle has sides of length x inches, x + 1 inches, and x + 2 inches and its perimeter is given by x + (x + 1) + (x + 2) = 42 inches. Find the measures of the sides by solving the perimeter equation.

Q5) Factor.

125x³ + 27

Q6) Find the product. (3a + 7)(a + 9)

Q7) Solve and write your answer in interval notation. y + 6 < 7y - 36

Q8) Simplify: u - 0.03(u - 300)

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Q9) The length of a rectangular painting is 5 feet greater than the width. If the perimeter is 22 feet, then what are the length and the width?

Chapter 16: Algebraic Equations and Problem Solving

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Q1) Simplify: r - 0.1(r + 400)

A) 0.9r - 40

B) 1.1r + 40

C) 1.1r - 40

D) 0.9r + 40

Q2) Solve the given equation. x² + 10x + 24 = 0

A) 4, -6

B) -4, 6

C) -4, -6

D) 4, 6

Q3) Factor the given polynomial completely. If the polynomial is prime, say so. y³- 8y² - 9y + 72

A) y(y + 3)(y - 8)

B) (y - 3)(y + 3)(y - 8)

C) The polynomial is prime. D) (y - 3)²(y - 8)

Q4) Does the point (-15, 15) satisfy the inequality y \(\ge\) -12x + 8?

A)True

B)False

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Chapter 17: Algebra and Math Problems

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Q1) List all terms of the finite sequence a_n = n + 6 for 1 n 5.

Q2) Write a formula for the nth term of the given arithmetic sequence. 6, 10, 14, 18, 22, . . .

Q3) Which, if any, of the ordered pairs (1, 2), (-1, 4), (-1, -1), and (5, -3) satisfy the system of inequalities?

x - y > 0

4x² + y² 4

Q4) Solve.

(z - 8)^1/3 = -3

Q5) Find the midpoint and length of the line segment with the endpoints (2,2) and (12,26).

Q6) Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection. y = - x²

2x² - y² = 1

Q7) If $1,300 is deposited in an account paying 11% compounded continuously, then what amount will be in the account after 3 years?

Q8) Simplify: t - (6t + 7)

Q9) Graph the linear equation 3x - 2y = 6.

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Chapter 18: Algebraic Equation Practice

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Q1) For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. f(x) = x³ - 10x²

A) Crosses at (10, 0) and at (-10, 0) but does not cross at (0, 0)

B) Crosses at (10, 0) but does not cross at (0, 0)

C) Crosses at (10, 0)

D) Crosses at (10, 0) and at (0, 0)

Q2) The owner of a hobby store bought a case of 9-volt batteries for $24.00. He marked the price up such that his profit was $1.76 per battery. After selling 12 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?

A) 100 batteries

B) 110 batteries

C) 105 batteries

D) 95 batteries

Q3) Factor. 64y³ - 125z³

A) (4y + 5z)(16y² - 20yz + 25z²)

B) (4y - 5z)(16y² + 20yz + 25z²)

C) (4y - 5z)(4y² + 20yz + 5z²)

D) (4y - 5z)(16y² - 20yz + 25z²)

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