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Precalculus: A Graphing Approach

Ron Larson, Robert P. Hostetler, Bruce H. Edwards

Chapter 2

Solving Equations and Inequalities - all with Video Answers

Educators

Section 1

Linear Equations and Problem Solving

05:27

Problem 1

Determine whether each value of $x$ is a solution of the equation.
Equation
$\frac{5}{2 x}-\frac{4}{x}=3$
Values
(a) $x=-\frac{1}{2}$
(b) $x=4$
(c) $x=0$
(d) $x=\frac{1}{4}$

Oluwaseyitan Balogun
Oluwaseyitan Balogun
Numerade Educator
01:26

Problem 2

Determine whether each value of $x$ is a solution of the equation.
Equation
$\frac{x}{2}+\frac{6 x}{7}=\frac{19}{14}$
Values
(a) $x=-2$
(b) $x=1$
(c) $x=\frac{1}{2}$
(d) $x=7$

Clay Rehmel
Clay Rehmel
Numerade Educator
02:27

Problem 3

Determine whether each value of $x$ is a solution of the equation.
Equation
$3+\frac{1}{x+2}=4$
Values
(a) $x=-1$
(b) $x=-2$
(c) $x=0$
(d) $x=5$

AG
Ankit Gupta
Numerade Educator
05:27

Problem 4

Determine whether each value of $x$ is a solution of the equation.
Equation
$\frac{(x+5)(x-3)}{2}=24$
Values
(a) $x=-3$
(b) $x=-2$
(c) $x=7$
(d) $x=9$

Oluwaseyitan Balogun
Oluwaseyitan Balogun
Numerade Educator
01:26

Problem 5

Determine whether each value of $x$ is a solution of the equation.
Equation
$\frac{\sqrt{x+4}}{6}+3=4$
Values
(a) $x=-3$
(b) $x=0$
(c) $x=21$
(d) $x=32$

Clay Rehmel
Clay Rehmel
Numerade Educator
01:57

Problem 6

Determine whether each value of $x$ is a solution of the equation.
Equation
$\frac{\sqrt[3]{x-8}}{3}=-\frac{2}{3}$
Values
(a) $x=-16$
(b) $x=0$
(c) $x=9$
(d) $x=16$

Clay Rehmel
Clay Rehmel
Numerade Educator
00:27

Problem 7

Determine whether the equation is an identity or a conditional equation.
$2(x-1)=2 x-2$

AG
Ankit Gupta
Numerade Educator
01:29

Problem 8

Determine whether the equation is an identity or a conditional equation.
$-7(x-3)+4 x=3(7-x)$

Stephanie Carter
Stephanie Carter
Numerade Educator
00:36

Problem 9

Determine whether the equation is an identity or a conditional equation.
$x^2-8 x+5=(x-4)^2-11$

AG
Ankit Gupta
Numerade Educator
00:55

Problem 10

Determine whether the equation is an identity or a conditional equation.
$x^2+2(3 x-2)=x^2+6 x-4$

AG
Ankit Gupta
Numerade Educator
00:54

Problem 11

Determine whether the equation is an identity or a conditional equation.
$3+\frac{1}{x+1}=\frac{4 x}{x+1}$

AG
Ankit Gupta
Numerade Educator
00:43

Problem 12

Determine whether the equation is an identity or a conditional equation.
$\frac{5}{x}+\frac{3}{x}=24$

AG
Ankit Gupta
Numerade Educator
02:39

Problem 13

Solve the equation using two methods. Then explain which method is easier.
$\frac{3 x}{8}-\frac{4 x}{3}=4$

Clay Rehmel
Clay Rehmel
Numerade Educator
02:14

Problem 14

Solve the equation using two methods. Then explain which method is easier.
$\frac{3 z}{8}-\frac{z}{10}=6$

Clay Rehmel
Clay Rehmel
Numerade Educator
02:40

Problem 15

Solve the equation using two methods. Then explain which method is easier.
$\frac{2 x}{5}+5 x=\frac{4}{3}$

Clay Rehmel
Clay Rehmel
Numerade Educator
02:40

Problem 16

Solve the equation using two methods. Then explain which method is easier.
$\frac{4 y}{3}-2 y=\frac{16}{5}$

Clay Rehmel
Clay Rehmel
Numerade Educator
00:15

Problem 17

Solve the equation (if possible).
$3 x-5=2 x+7$

AG
Ankit Gupta
Numerade Educator
00:18

Problem 18

Solve the equation (if possible).
$5 x+3=6-2 x$

AG
Ankit Gupta
Numerade Educator
00:36

Problem 19

Solve the equation (if possible).
$4 y+2-5 y=7-6 y$

Grace Muhihu
Grace Muhihu
Numerade Educator
04:04

Problem 20

Solve the equation (if possible).
$5 y+1=8 y-5+6 y$

Stephanie Carter
Stephanie Carter
Numerade Educator
00:28

Problem 21

Solve the equation (if possible).
$3(y-5)=3+5 y$

AG
Ankit Gupta
Numerade Educator
02:36

Problem 22

Solve the equation (if possible).
$5(z-4)+4 z=5-6 z$

Clay Rehmel
Clay Rehmel
Numerade Educator
00:40

Problem 23

Solve the equation (if possible).
$\frac{x}{5}-\frac{x}{2}=3$

AG
Ankit Gupta
Numerade Educator
01:38

Problem 24

Solve the equation (if possible).
$\frac{5 x}{4}+\frac{1}{2}=x-\frac{1}{2}$

Clay Rehmel
Clay Rehmel
Numerade Educator
01:19

Problem 25

Solve the equation (if possible).
$\frac{3}{2}(z+5)-\frac{1}{4}(z+24)=0$

AG
Ankit Gupta
Numerade Educator
00:40

Problem 26

Solve the equation (if possible).
$\frac{3 x}{2}+\frac{1}{4}(x-2)=10$

AG
Ankit Gupta
Numerade Educator
02:51

Problem 27

Solve the equation (if possible).
$\frac{2(z-4)}{5}+5=10 z$

Clay Rehmel
Clay Rehmel
Numerade Educator
00:28

Problem 28

Solve the equation (if possible).
$\frac{5}{3}+2(y+1)=\frac{10}{3}$

AG
Ankit Gupta
Numerade Educator
02:21

Problem 29

Solve the equation (if possible).
$\frac{100-4 u}{3}=\frac{5 u+6}{4}+6$

Clay Rehmel
Clay Rehmel
Numerade Educator
00:40

Problem 30

Solve the equation (if possible).
$\frac{17+y}{y}+\frac{32+y}{y}=100$

AG
Ankit Gupta
Numerade Educator
00:45

Problem 31

Solve the equation (if possible).
$\frac{5 x-4}{5 x+4}=\frac{2}{3}$

AG
Ankit Gupta
Numerade Educator
00:32

Problem 32

Solve the equation (if possible).
$\frac{10 x+3}{5 x+6}=\frac{1}{2}$

AG
Ankit Gupta
Numerade Educator
01:24

Problem 33

Solve the equation (if possible).
$\frac{1}{x-3}+\frac{1}{x+3}=\frac{10}{x^2-9}$

AG
Ankit Gupta
Numerade Educator
01:35

Problem 34

Solve the equation (if possible).
$\frac{1}{x-2}+\frac{3}{x+3}=\frac{4}{x^2+x-6}$

AG
Ankit Gupta
Numerade Educator
00:44

Problem 35

Solve the equation (if possible).
$\frac{7}{2 x+1}-\frac{8 x}{2 x-1}=-4$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:45

Problem 36

Solve the equation (if possible).
$\frac{x}{x+4}+\frac{4}{x+4}+2=0$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:09

Problem 37

Solve the equation (if possible).
$\frac{1}{x}+\frac{2}{x-5}=0$

AG
Ankit Gupta
Numerade Educator
00:53

Problem 38

Solve the equation (if possible).
$3=2+\frac{2}{z+2}$

AG
Ankit Gupta
Numerade Educator
01:27

Problem 39

Solve the equation (if possible).
$\frac{3}{x^2-3 x}+\frac{4}{x}=\frac{1}{x-3}$

AG
Ankit Gupta
Numerade Educator
01:36

Problem 40

Solve the equation (if possible).
$\frac{6}{x}-\frac{2}{x+3}=\frac{3(x+5)}{x(x+3)}$

AG
Ankit Gupta
Numerade Educator
00:29

Problem 41

Solve for the indicated variable.
Area of a Triangle
Solve for $h: A=\frac{1}{2} b h$

AG
Ankit Gupta
Numerade Educator
00:49

Problem 42

Solve for the indicated variable.
Area of a Trapezoid
Solve for $b: A=\frac{1}{2}(a+b) h$

AG
Ankit Gupta
Numerade Educator
00:37

Problem 43

Solve for the indicated variable.
Investment at Compound Interest
Solve for $P: A=P\left(1+\frac{r}{n}\right)^{\text {nt }}$

AG
Ankit Gupta
Numerade Educator
00:33

Problem 44

Solve for the indicated variable.
Investment at Simple Interest
Solve for $r: A=P+P r t$

AG
Ankit Gupta
Numerade Educator
00:57

Problem 45

Solve for the indicated variable.
Geometric Progression
Solve for $r: S=\frac{r L-a}{r-1}$

Victor Salazar
Victor Salazar
Numerade Educator
00:38

Problem 46

Solve for the indicated variable.
Arithmetic Progression
Solve for $n: L=a+(n-1) d$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:32

Problem 47

Solve for the indicated variable.
Volume of an Oblate Spheroid
Solve for $b: V=\frac{4}{3} \pi a^2 b$

AG
Ankit Gupta
Numerade Educator
06:25

Problem 48

Solve for the indicated variable.
Volume of a Spherical Segment
Solve for $r: V=\frac{1}{3} \pi h^2(3 r-h)$

Puneet Prajapati
Puneet Prajapati
Numerade Educator
00:34

Problem 49

Solve for the indicated variable.
Perimeter of a Rectangle
Solve for $w: P=2 l+2 w$

Emily Himsel
Emily Himsel
Numerade Educator
00:49

Problem 50

Solve for the indicated variable.
Sum of a Convergent Geometric Series
Solve for $r: S=\frac{a}{1-r}$

Ramzi Deek
Ramzi Deek
Numerade Educator
00:38

Problem 51

Solve for the indicated variable.
Volume of a Right Circular Cylinder
Solve for $h: V=\pi r^2 h$

AG
Ankit Gupta
Numerade Educator
00:34

Problem 52

Solve for the indicated variable.
Volume of a Right Circular Cone
Solve for $h: V=\frac{1}{3} \pi r^2 h$

AG
Ankit Gupta
Numerade Educator
00:58

Problem 53

Solve for the indicated variable.
Lateral Surface Area of a Right Circular Cylinder
Solve for $r: S=2 \pi r h$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:39

Problem 54

Solve for the indicated variable.
Velocity of a Free-Falling Object
Solve for $t: v=-g t+v_0$

Kian Manafi
Kian Manafi
Numerade Educator
01:00

Problem 55

Solve for the indicated variable.
Ideal Gas Law
Solve for $R: P V=n R T$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:56

Problem 56

Solve for the indicated variable.
Resistors in Parallel
Solve for $R_1: \frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}$

Ryan Swift
Ryan Swift
Numerade Educator
02:58

Problem 58

Use the following information. The relationship between the length of an adult's femur (thigh bone) and the height of the adult can be approximated by the linear equations
$$
\begin{array}{ll}
y=0.432 x-10.44 & \text { Female } \\
y=0.449 x-12.15 & \text { Male }
\end{array}
$$
where $y$ is the length of the femur in inches and $x$ is the height of the adult in inches (see figure).
(FIGURE CAN'T COPY)
From the foot bones of an adult human male, an anthropologist estimates that the person's height was 69 inches. A few feet away from the site where the foot bones were discovered, the anthropologist discovers a male adult femur that is 19 inches long. Is it likely that both the foot bones and the thigh bone came from the same person?

Anna Jones
Anna Jones
Numerade Educator
03:42

Problem 59

Geometry A room is 1.5 times as long as it is wide, and its perimeter is 25 meters.
(a) Draw a diagram that gives a visual representation of the problem. Identify the length as $l$ and the width as $w$.
(b) Write $l$ in terms of $w$ and write an equation for the perimeter in terms of $w$.
(c) Find the dimensions of the room.

AG
Ankit Gupta
Numerade Educator
03:07

Problem 60

Geometry A picture frame has a total perimeter of 3 meters. The height of the frame is $\frac{2}{3}$ times its width.
(a) Draw a diagram that gives a visual representation of the problem. Identify the width as $w$ and the height as $h$.
(b) Write $h$ in terms of $w$ and write an equation for the perimeter in terms of $w$.
(c) Find the dimensions of the picture frame.

AG
Ankit Gupta
Numerade Educator
04:20

Problem 61

Course Grade To get an A in a course, you must have an average of at least 90 on four tests of 100 points each. The scores on your first three tests were 87,92 , and 84 .
(a) Write a verbal model for the test average for the course.
(b) What must you score on the fourth test to get an A for the course?

Anna Jones
Anna Jones
Numerade Educator
04:20

Problem 62

Course Grade You are taking a course that has four tests. The first three tests are 100 points each and the fourth test is 200 points. To get an $\mathrm{A}$ in the course, you must have an average of at least $90 \%$ the four tests. Your scores on the first three tests were 87,92 , and 84 . What must you score on the fourth test to get an A for the course?

Anna Jones
Anna Jones
Numerade Educator
02:24

Problem 63

Travel Time You are driving on a Canadian freeway to a town that is 300 kilometers from your home. After $30 \mathrm{~min}$ utes you pass a freeway exit that you know is 50 kilometers from your home. Assuming that you continue at the same constant speed, how long will it take for the entire trip?

AG
Ankit Gupta
Numerade Educator
04:43

Problem 64

Travel Time On the first part of a 317-mile trip, a salesperson averaged 58 miles per hour. The salesperson averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. The total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speeds.

AG
Ankit Gupta
Numerade Educator
03:58

Problem 65

Average Speed A truck driver traveled at an average speed of 55 miles per hour on a 200-mile trip to pick up a load of freight. On the return trip (with the truck fully loaded), the average speed was 40 miles per hour. Find the average speed for the round trip.

AG
Ankit Gupta
Numerade Educator
05:37

Problem 66

Wind Speed An executive flew in the corporate jet to a meeting in a city 1500 kilometers away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300 kilometers to go. The air speed of the plane was 600 kilometers per hour. How fast was the wind blowing?(Assume that the wind direction was parallel to the flight path and constant all day.)

AG
Ankit Gupta
Numerade Educator
02:46

Problem 67

Height To obtain the height of a barn silo, you measure the silo's shadow and find that it is 80 feet long. You also measure the shadow of a four-foot stake and find that it is $3 \frac{1}{2}$ feet long.
(a) Draw a diagram that illustrates the problem. Let $h$ represent the height of the silo.
(b) Find the height of the silo.

AG
Ankit Gupta
Numerade Educator
04:26

Problem 68

Height A person who is 6 feet tall walks away from a flagpole toward the tip of the shadow of the flagpole. When the person is 30 feet from the flagpole, the tips of the person's shadow and the shadow cast by the flagpole coincide at a point 5 feet in front of the person.
(a) Draw a diagram that illustrates the problem. Let $h$ represent the height of the flagpole.
(b) Find the height of the flagpole.

Anna Jones
Anna Jones
Numerade Educator
02:18

Problem 69

Simple Interest Find the interest on a $\mathbf{5 0 0 0}$ bond that pays an annual percentage rate of $6 \frac{1}{2} \%$ for 6 years.

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
01:47

Problem 70

Simple Interest A certificate of deposit with an initial deposit of $$\$ 8000$$ accumulates $$\$ 400$$ interest in 2 years. Find the annual interest rate.

Amber Leann
Amber Leann
Numerade Educator
04:20

Problem 71

Investment You plan to invest $$\$ 2,000$$ in two funds paying $4 \frac{1}{2} \%$ and $5 \%$ imple interest. (There is more risk in the $5\%$ fund.) Your goal is to obtain a total annual interest income of $$\$ 560$$ from the investments. What is the smallest amount you can invest in the $5 \%$ fund in order to meet your objective?

Amber Leann
Amber Leann
Numerade Educator
04:20

Problem 72

Investment You plan to invest $$\$ 5,000$$ in two funds paying 3 sind $4 \frac{1}{2} \%$ Simple interest. (There is more risk in the $4 \frac{1}{2} \%$ fund.) Your goal is to obtain a total annual interest income of $$\$ 000$$ from the investments. What is the smallest amount you can invest in the $4 \frac{1}{2} \%$ fund in order to meet your objective?

Amber Leann
Amber Leann
Numerade Educator
03:47

Problem 73

Inventory A store has $\mathbf{5 0 , 0 0 0}$ of inventory in DVD players and VCRs. The profit on a DVD player is 30 and the profit on a VCR is 25\%The profit on the entire stock is $29 \%$ How much is invested in DVD players and how much is invested in VCRs?

Amber Leann
Amber Leann
Numerade Educator
01:12

Problem 74

Inventory A store has $$\$45 0 0$$ of inventory in $8 \times 1$ picture frames and $5 \times 7$ picture frames. The profit on an $8 \times 10$ frame is $25 \%$ and the profit on a $5 \times$ 7 Frame is $22 \%$ The profit on the entire stock is $24 \%$ How much is invested in the $8 \times 10$ picture frames and how much is invested in the $5 \times 7$ picture frames?

Nick Johnson
Nick Johnson
Numerade Educator
05:19

Problem 75

Mixture Problem A grocer mixes peanuts that cost $$\$ .49$$ per pound and walnuts that cost $$\$ .89$$ per pound to make 100 pounds of a mixture that costs $$\$ .19$$ per pound. How much of each kind of nut is put into the mixture?

Anna Jones
Anna Jones
Numerade Educator
06:10

Problem 76

Mixture Problem A forester mixes gasoline and oil to make 2 gallons of mixture for his two-cycle chainsaw engine. This mixture is 32 parts gasoline and 1 part oil. How much gasoline must be added to bring the mixture to 40 parts gasoline and 1 part oil?

AG
Ankit Gupta
Numerade Educator
02:08

Problem 77

Height A triangular sail has an area of 182.25 square feet. The sail has a base of 13.5 feet. Find the height of the sail.

AG
Ankit Gupta
Numerade Educator
02:15

Problem 78

Area The figure shows three squares. The perimeter of square I is 20 inches and the perimeter of square II is 32 inches. Find the area of square III.
(FIGURE CAN'T COPY)

AG
Ankit Gupta
Numerade Educator
05:13

Problem 79

Geometry The volume of a rectangular package is 2304 cubic inches. The length of the package is 3 times its width, and the height is $1 \frac{1}{2}$ times its width.
(a) Draw a diagram that illustrates the problem. Label the height, width, and length accordingly.
(b) Find the dimensions of the package.

Anna Jones
Anna Jones
Numerade Educator
02:29

Problem 80

Geometry The volume of a globe is about $47,712.94$ cubic centimeters. Use a graphing utility to find the radius of the globe. Round your result to two decimal places.

Amber Leann
Amber Leann
Numerade Educator
04:38

Problem 81

Meteorology The line graph shows the temperatures (in degrees Fahrenheit) on a summer day in Buffalo, New York from 1000 A.M. to 600 P.M. Create a new line graph showing the temperatures throughout the day in degrees Celsius.
(FIGURE CAN'T COPY)

Mukesh Devi
Mukesh Devi
Numerade Educator
00:41

Problem 82

Meteorology The average daily temperature in San Francisco, California is $57.3^{\circ} \mathrm{F}$. What is San Francisco's average daily temperature in degrees Celsius? (U.S. National Oceanic and Atmospheric Administration)
(FIGURE CAN'T COPY)

Matthew Biollo
Matthew Biollo
Numerade Educator
01:11

Problem 83

You have a uniform beam of length $L$ with a fulcrum $x$ feet from one end (see figure). Objects with weights $W_1$ and $W_2$ are placed at opposite ends of the beam. The beam will balance when
$$
W_1 x=W_2(L-x) .
$$
Find $x$ such that the beam will balance.
(FIGURE CAN'T COPY)
Two children weighing 50 pounds and 75 pounds are going to play on a seesaw that is 10 feet long.

Matthew Biollo
Matthew Biollo
Numerade Educator
01:18

Problem 84

You have a uniform beam of length $L$ with a fulcrum $x$ feet from one end (see figure). Objects with weights $W_1$ and $W_2$ are placed at opposite ends of the beam. The beam will balance when
$$
W_1 x=W_2(L-x) .
$$
Find $x$ such that the beam will balance.
(FIGURE CAN'T COPY)
A person weighing 200 pounds is attempting to move a 550 -pound rock with a bar that is 5 feet long.

Matthew Biollo
Matthew Biollo
Numerade Educator
00:52

Problem 85

True or False? Determine whether the statement is true or false. Justify your answer.
The equation
$$
x(3-x)=10
$$
is a linear equation.

AG
Ankit Gupta
Numerade Educator
02:13

Problem 86

True or False? Determine whether the statement is true or false. Justify your answer.
The volume of a cube with a side length of 9.5 inches is greater than the volume of a sphere with a radius of 5.9 inches.

AG
Ankit Gupta
Numerade Educator
01:55

Problem 87

Write a linear equation that has the given solution.
$x=-3$

AG
Ankit Gupta
Numerade Educator
01:44

Problem 88

Write a linear equation that has the given solution.
$x=\frac{1}{4}$

AG
Ankit Gupta
Numerade Educator
01:58

Problem 89

Think About It What is meant by equivalent equations? Give an example of two equivalent equations.

Vinnu M
Vinnu M
Numerade Educator
01:04

Problem 90

Writing In your own words, describe how to clear an equation of fractions.

Emily Himsel
Emily Himsel
Numerade Educator
02:25

Problem 91

Think About It Find $c$ such that $x=3$ is a solution to the linear equation $2 x-5 c=10+3 c-3 x$.

Anna Jones
Anna Jones
Numerade Educator
01:16

Problem 92

Think About It Find $c$ such that $x=2$ is a solution to the linear equation $5 x+2 c=12+4 x-2 c$.

AG
Ankit Gupta
Numerade Educator
02:28

Problem 93

Sketch the graph of the equation by hand. Verify using a graphing utility.
$y=\frac{5}{8} x-2$

Anna Jones
Anna Jones
Numerade Educator
01:29

Problem 94

Sketch the graph of the equation by hand. Verify using a graphing utility.
$y=\frac{3 x-5}{2}+2$

AG
Ankit Gupta
Numerade Educator
02:32

Problem 95

Sketch the graph of the equation by hand. Verify using a graphing utility.
$y=(x-3)^2+7$

Amber Leann
Amber Leann
Numerade Educator
01:55

Problem 96

Sketch the graph of the equation by hand. Verify using a graphing utility.
$y=\frac{1}{3} x^2-4$

Amber Leann
Amber Leann
Numerade Educator
01:32

Problem 97

Sketch the graph of the equation by hand. Verify using a graphing utility.
$y=-\frac{1}{2}|x+4|-1$

AG
Ankit Gupta
Numerade Educator
01:35

Problem 98

Sketch the graph of the equation by hand. Verify using a graphing utility.
$y=|x-2|+10$

AG
Ankit Gupta
Numerade Educator
01:42

Problem 99

Evaluate the combination of functions for $f(x)=-x^2+4$ and $g(x)=6 x-5$.
$(f+g)(-3)$

Anna Jones
Anna Jones
Numerade Educator
01:57

Problem 100

Evaluate the combination of functions for $f(x)=-x^2+4$ and $g(x)=6 x-5$.
$(g-f)(-1)$

Anna Jones
Anna Jones
Numerade Educator
03:44

Problem 101

Evaluate the combination of functions for $f(x)=-x^2+4$ and $g(x)=6 x-5$.
$(f g)(8)$

Anna Jones
Anna Jones
Numerade Educator
02:07

Problem 102

Evaluate the combination of functions for $f(x)=-x^2+4$ and $g(x)=6 x-5$.
$\left(\frac{f}{g}\right)\left(\frac{1}{2}\right)$

Anna Jones
Anna Jones
Numerade Educator
01:44

Problem 103

Evaluate the combination of functions for $f(x)=-x^2+4$ and $g(x)=6 x-5$.
$(f \circ g)(4)$

Anna Jones
Anna Jones
Numerade Educator
01:10

Problem 104

Evaluate the combination of functions for $f(x)=-x^2+4$ and $g(x)=6 x-5$.
$(g \circ f)(2)$

Anna Jones
Anna Jones
Numerade Educator
01:03

Problem 5757

Use the following information. The relationship between the length of an adult's femur (thigh bone) and the height of the adult can be approximated by the linear equations
$$
\begin{array}{ll}
y=0.432 x-10.44 & \text { Female } \\
y=0.449 x-12.15 & \text { Male }
\end{array}
$$
where $y$ is the length of the femur in inches and $x$ is the height of the adult in inches (see figure).
(FIGURE CAN'T COPY)
An anthropologist discovers a femur belonging to an adult human female. The bone is 16 inches long. Estimate the height of the female.

Anna Jones
Anna Jones
Numerade Educator