# Graphs, Equations, and Inequalities

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Graphs, Equations, and Inequalities
Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc. All rights reserved. Chapter 1 Graphs, Equations, and Inequalities

Find the distance between the d(P1, P2) between the points P1(–4, –1) and P2(5, –4).

Find the distance between the d(P1, P2) between the points P1(–4, –1) and P2(5, –4).

Find the midpoint of the line segment joining points P1(0. 3, 0
Find the midpoint of the line segment joining points P1(0.3, 0.9) and P2(1.7, 1.4). a. (1.15, 1) b. (1, 1.15) c. (0.7, 0.25) d. (0.25, 0.7)

Find the midpoint of the line segment joining points P1(0. 3, 0
Find the midpoint of the line segment joining points P1(0.3, 0.9) and P2(1.7, 1.4). a. (1.15, 1) b. (1, 1.15) c. (0.7, 0.25) d. (0.25, 0.7)

Graph y = 3x - 9. a. b. c. d.

Graph y = 3x - 9. a. b. c. d.

Graph 3x2 –2y = 56 using a graphing utility.
b. c. d.

Graph 3x2 –2y = 56 using a graphing utility.
b. c. d.

List the intercepts of the graph.
x List the intercepts of the graph. a. (–4, 0), (0, –4), (0, 1), (0, –5) b. (–4, 0), (0, 4), (0, 1), (0, 5) c. (–4, 0), (1, 0), (–5, 0), (0, –4) d. (4, 0), (1, 0), (5, 0), (0, –4)

List the intercepts of the graph.
x List the intercepts of the graph. a. (–4, 0), (0, –4), (0, 1), (0, –5) b. (–4, 0), (0, 4), (0, 1), (0, 5) c. (–4, 0), (1, 0), (–5, 0), (0, –4) d. (4, 0), (1, 0), (5, 0), (0, –4)

Use a graphing utility to approximate the intercepts rounded to two decimal places for the equation 3x2 – 5y = 34. a. (0, –6.8), (3.37, 0) b. (0, –6.8), (–3.36, 0), (3.36, 0) c. (0, 6.8), (–3.37, 0), (3.37, 0) d. (0, –6.8), (–3.37, 0), (3.37, 0)

Use a graphing utility to approximate the intercepts rounded to two decimal places for the equation 3x2 – 5y = 34. a. (0, –6.8), (3.37, 0) b. (0, –6.8), (–3.36, 0), (3.36, 0) c. (0, 6.8), (–3.37, 0), (3.37, 0) d. (0, –6.8), (–3.37, 0), (3.37, 0)

Use a graphing utility to approximate the real solutions, if any, rounded to two decimal places of the equation x4 – 3x2 + 4x + 15 = 0. a. {–0.84, –1.93} b. {2.11, –2.60} c. {3.94, –1.27} d. No real solutions

Use a graphing utility to approximate the real solutions, if any, rounded to two decimal places of the equation x4 – 3x2 + 4x + 15 = 0. a. {–0.84, –1.93} b. {2.11, –2.60} c. {3.94, –1.27} d. No real solutions

Solve. a. b. c. d.

Solve. a. b. c. d.

Solve. a. b. c. d. No solution

Solve. a. b. c. d. No solution

Going into the final exam, which will count as three tests, Jerome has test scores of 61, 72, 59, 75, and 77. What score does Jerome need on the final in order to earn a C, which requires an average of 70? a b. 72 c d. 76

Going into the final exam, which will count as three tests, Jerome has test scores of 61, 72, 59, 75, and 77. What score does Jerome need on the final in order to earn a C, which requires an average of 70? a b. 72 c d. 76

Solve. a. b. c. d.

Solve. a. b. c. d.

Solve the equation by square root method.
c. {–4, 1} d. {0, 1}

Solve the equation by square root method.
c. {–4, 1} d. {0, 1}

Solve the equation by completing the square.
a. b. c. d.

Solve the equation by completing the square.
a. b. c. d.

Solve the equation by using the quadratic formula.
a b. c d. No solution

Solve the equation by using the quadratic formula.
a b. c d. No solution

A ball is thrown vertically upward from the top of a building 128 feet tall with an initial velocity of 112 feet per second. The distance s (in feet) of the ball form the ground after t seconds is s = t – 16t2 . After how many seconds will the ball pass the top of the building on its way down? a. 9 sec b. 128 sec c. 6 sec d. 7 sec

A ball is thrown vertically upward from the top of a building 128 feet tall with an initial velocity of 112 feet per second. The distance s (in feet) of the ball form the ground after t seconds is s = t – 16t2 . After how many seconds will the ball pass the top of the building on its way down? a. 9 sec b. 128 sec c. 6 sec d. 7 sec

Multiply. (4 + 6i)(2 – 7i) a. – i b i c. 50 – 16i d. –42i2 – 16i + 8

Multiply. (4 + 6i)(2 – 7i) a. – i b i c. 50 – 16i d. –42i2 – 16i + 8

Given z = 4 – 9i, evaluate a. –65 b. 16 – 81i2 c. 97 d. 16 – 81i

Given z = 4 – 9i, evaluate a. –65 b. 16 – 81i2 c. 97 d. 16 – 81i

Solve the equation in the complex number system.
d.

Solve the equation in the complex number system.
d.

Find the real solutions of the equation.
b. c. d. No real solution

Find the real solutions of the equation.
b. c. d. No real solution

Find the real solutions of the equation.
b. c. d.

Find the real solutions of the equation.
b. c. d.

Solve the equation. a. b. c. d.

Solve the equation. a. b. c. d.

Solve the equation. a. b. c. d.

Solve the equation. a. b. c. d.

A bank loaned out \$65,000, part of it at a rate of 12% per year and the rest at a rate of 6% per year. If the interest received was \$5580, how much was loaned at 12%? a. \$28,000 b. \$37,000 c. \$29,000 d. \$36,000

A bank loaned out \$65,000, part of it at a rate of 12% per year and the rest at a rate of 6% per year. If the interest received was \$5580, how much was loaned at 12%? a. \$28,000 b. \$37,000 c. \$29,000 d. \$36,000

How many gallons of a 30% alcohol solution must be mixed with 60 gallons of a 14% solution to obtain a solution that is 20% alcohol? a. 27 gal b. 36 gal c. 7 gal d. 12 gal

How many gallons of a 30% alcohol solution must be mixed with 60 gallons of a 14% solution to obtain a solution that is 20% alcohol? a. 27 gal b. 36 gal c. 7 gal d. 12 gal

A freight train leaves a station traveling at 32 km/h
A freight train leaves a station traveling at 32 km/h. Two hours later, a passenger train leaves the same station traveling in the same direction at 52 km/h. How long does it take the passenger train to catch up to the freight train? a. 5.2 hr b. 4.2 hr c. 3.2 hr d. 2.2 hr

A freight train leaves a station traveling at 32 km/h
A freight train leaves a station traveling at 32 km/h. Two hours later, a passenger train leaves the same station traveling in the same direction at 52 km/h. How long does it take the passenger train to catch up to the freight train? a. 5.2 hr b. 4.2 hr c. 3.2 hr d. 2.2 hr

BJ can overhaul a boat’s diesel inboard engine in 20 hours
BJ can overhaul a boat’s diesel inboard engine in 20 hours. His apprentice takes 60 hours to do the same job. How long would it take them working together assuming no gain or loss in efficiency? a. 12 hr b. 6 hr c. 80 hr d. 15 hr

BJ can overhaul a boat’s diesel inboard engine in 20 hours
BJ can overhaul a boat’s diesel inboard engine in 20 hours. His apprentice takes 60 hours to do the same job. How long would it take them working together assuming no gain or loss in efficiency? a. 12 hr b. 6 hr c. 80 hr d. 15 hr

Express the graph shown using interval notation and as an inequality involving x.
[ ) –8 –6 –4 –2 2 4 a. [–7, –1); –7 ≤ x < –1 b. (–7, –1); –7 < x < –1 c. [–7, –1]; –7 ≤ x ≤ –1 d. (–7, –1]; –7 < x ≤ –1

Express the graph shown using interval notation and as an inequality involving x.
[ ) –8 –6 –4 –2 2 4 a. [–7, –1); –7 ≤ x < –1 b. (–7, –1); –7 < x < –1 c. [–7, –1]; –7 ≤ x ≤ –1 d. (–7, –1]; –7 < x ≤ –1

Solve –5(2x + 13) < –15x – 35. Express your answer in interval notation.
b. (–∞, 6) c. (–∞, 4) d. (–∞, 20)

Solve –5(2x + 13) < –15x – 35. Express your answer in interval notation.
b. (–∞, 6) c. (–∞, 4) d. (–∞, 20)

Solve –27 ≤ –5x – 2 ≤ –12. Express your answer in interval notation.
b. [2, 5] c. [–5, –2] d. (–5, –2)

Solve –27 ≤ –5x – 2 ≤ –12. Express your answer in interval notation.
b. [2, 5] c. [–5, –2] d. (–5, –2)

Solve |x – 6| + 7 ≤ 16. Express your answer in interval notation.
b. (–3, 15) c. [–3, 15] d.

Solve |x – 6| + 7 ≤ 16. Express your answer in interval notation.
b. (–3, 15) c. [–3, 15] d.