Carnegie Learning Algebra I Student Text Volume 1 3rd Edition Chapter 3 Linear Functions
Page 188 Problem 1 Answer
Given the normal temperature for the human body is 98.6oF
we have to find the temperature is that in degrees Celsius. Use the formula to convert degrees Fahrenheit to degrees Celsius.
Formula is C=5/9(F−32)
SubstituteF=98.6
C=5/9(98.6−32)
=5/9×66.6
=37
Hence, the temperature is37oC.
The temperature is 37oC.
Page 188 Problem 2 Answer
Given the directions on a box of cake batter tells you to bake your cake at 177oC
we have to find the temperature is that in degrees Fahrenheit.
Use the formula to convert degrees Celsius to degrees Fahrenheit.
Formula is C=5/9(F−32)
SubstituteC=177
177=5/9(F−32)
177×9/5=F−32
318.6=F−32
F=350.6
Hence, the temperature is 350.6oF.
The temperature is 350.6oF.
Page 189 Problem 3 Answer
GivenC=5/9(F−32)
Here we have to tell is there a more efficient way to determine degrees Fahrenheit than the method you used in Question 3
To determine degrees Fahrenheit more efficient way you can solve literal Equations C=5/9(F−32)
for F And then substituteC=177 to find the temperature in degrees Fahrenheit.
Solve literal Equations C=5/9(F−32) for F and then substituteC=177 to find the temperature in degrees Fahrenheit.
Page 189 Problem 4 Answer
Given C=5/9(F−32)
We have to convert the given formula to determine degrees Fahrenheit and show and explain our work.
Solve literal Equations C=5/9(F−32) for F.
Given C=5/9(F−32)
We have to convert the given formula to determine degrees Fahrenheit
So, multiply 9/5 on both sides
C×9/5=F−32
Add 32 on both sides
9C/5+32=F
The formula to determine degrees Fahrenheit is F=9C/5+32
Page 189 Problem 5 Answer
Given the hottest temperature ever recorded on Earth occurred in Africa in 1922. It was recorded as 57.8oC.
we have to find the temperature is that in degrees Fahrenheit.Use the formula to convert degrees Celsius to degrees Fahrenheit.
Formula is F=9C/5+32
SubstituteC=57.8
F=9(57.8)/5+32
=104.04+32
=136.04
Hence, the temperature is136.04oF
The temperature is 136.04oF.
Page 189 Problem 6 Answer
Given dry ice melts at−78oC.
we have to find the temperature in degrees Fahrenheit does dry ice melt
Use the formula to convert degrees Celsius to degrees Fahrenheit.
Formula is F=9C/5+32
SubstituteC=−78
F=9(−78)/5+32
=−140.4+32
=−108.4
Hence, the temperature is −108.4oF.
The temperature in degrees Fahrenheit does dry ice melt is −108.4oF
Page 190 Problem 7 Answer
Given in the original equations, the coefficients 9/5 and 5/9 as well as the constant 32 had meaning based on temperature.
We have to find what do the coefficients, 9 and 5 and the constant 160 represent in Carlos’s and Mikala’s equations. In the original equations, the coefficients 9/5 and 5/9
were slope of so they gave the rate of change in temperature and was a y-intercept so it gave the temperature when C=0 in F=9/5 C+32.
The coefficients, 9 and 5, and the constant 160 do not represent any things because they do not represent slope or y-intercept.
The coefficients, 9 and 5 and the constant 160 do not represent any things in Carlos’s and Mikala’s equations.
Page 191 Problem 8 Answer
Given the equation 6x+5y=20
We have to identify the Slope-intercept form and show our work.Solve the equation for y.
Given 6x+5y=20
We have to identify the Slope-intercept form
Subtract 6x on both side
5y=20−6x
Divide both sides by 5
y=−6/5x+4
Hence, the Slope-intercept form is y=−6/5x+4.
The Slope-intercept form of 6x+5y=20 is y=−6/5x+4.
Page 191 Problem 9 Answer
Given the equation6x+5y=20
We have to identify the x-intercept and show we work.
Solve the equation for x and substitutey=0.
Given the equation6x+5y=20
The x-intercept is the point where the function graph meets the x-axis.
then at x-axis y=0 Substitute y=0 in equation
6x+5(0)=20
6x=20
x=10/3
Hence, the x-intercept is x=10/3.
The x-intercept form of6x+5y=20
Is x=10/3.
Page 191 Problem 10 Answer
Given the equation6x+5y=20
We have to identify the y-intercept and show our work.Solve the equation for y and substitutex=0.
Given the equation6x+5y=20
The y-intercept is the point where the function graph meets the y-axis.
then at y-axis x=0 substitutex=0 in equation 6(0)+5y=20
5y=20
y=4
Hence, the y-intercept is y=4.
The y-intercept form of 6x+5y=20 is y=4.
Page 191 Problem 11 Answer
Given the equation 6x+5y=20
We have to identify the slope and show we work.Compare this equation with y=mx+c.
Given the equation6x+5y=20 and from previews part slope-intercept form is y=−6/5x+4
Compare this equation withy=mx+c
Thus m=−6/5
Hence, the slope is −6/5.
The slope of 6x+5y=20 is−6/5
Page 191 Problem 12 Answer
Given the equation y=−2/3x+10
We have to identify the standard form and show our work.
First, get rid of the factor and x and y on one side and constant on the other.
Giveny=−2/3x+10
We have to identify the standard form
Multiply both sides by 3.
3×y=3(−2/3x+10)
3y=−2x+30
3y−2x=30.
Hence, the standard form is 3y−2x=30.
The standard form ofy=−2/3x+10 is 3y−2x=30.
Page 191 Problem 13 Answer
Given the equationy=−2/3x+10
We have to identify the x-intercept and show we work.
Solve the equation for x and substitute y=0.
Given the equation y=−2/3x+10
The x-intercept is the point where the function graph meets the x-axis.
then at x-axis y=0 Substitute y=0
0=−2/3x+10/2/3
x=10
x=30/2
x=15
Hence, the x-intercept is x=15.
The x-intercept form ofy=−2/3x+10 is x=15.
Page 191 Problem 14 Answer
Given the equation y=−2/3x+10
We have to identify the y-intercept and show our work.
Solve the equation for y and substitute x=0.
Given the equation y=−2/3x+10
The y-intercept is the point where the function graph meets the y-axis.
then at y-axis x=0 substitutex=0
y=−2/3(0)+10
y=10
Hence, the y-intercept is y=10.
The y-intercept form of y=−2/3x+10 is y=10.
Page 191 Problem 15 Answer
Given the equation y=−2/3x+10
We have to identify the slope and show we work.
Compare this equation with y=mx+c
Given the equation y=−2/3x+10
Compare this equation with y=mx+c
Thus m=−2/3
Hence, the slope is−2/3.
The slope ofy=−2/3x+10 is−2/3.
Page 192 Problem 16 Answer
Given the equation Ax+By=C
We have to identify the Slope-intercept form and show our work.Solve the equation for y.
Given on both side Ax+By=C
We have to identify the Slope-intercept form
Subtract Ax on both side
By=C−Ax
Divide both sides by B
y=−A/Bx+C/B
Hence, the Slope-intercept form is y=−A/Bx+C/B
The Slope-intercept form of Ax+By=C is y=−A/Bx+C/B.
Page 192 Problem 17 Answer
Given the equation Ax+By=C
We have to identify the x-intercept and show we work.
Solve the equation for x and substitute y=0.
Given the equation Ax+By=C
The x-intercept is the point where the function graph meets the x-axis.
then at x-axis y=0 Substitute y=0 in equation
Ax+B(0)=C
Ax=C
x=C/A
Hence, the x-intercept is x=C/A.
The x-intercept form of Ax+By=C is x=C/A.
Page 192 Problem 18 Answer
Given the equation Ax+By=C
We have to identify the y-intercept and show our work.
Solve the equation for y and substitute y=0.
Given the equation Ax+By=C
The y-intercept is the point where the function graph meets the y-axis.
then at y-axis x=0
substitutex=0 in equation
A(0)+By=C
By=C
y=B/C
Hence, the y-intercept is y=B/C
The y-intercept form of Ax+By=C is y=B/C.
Page 192 Problem 19 Answer
Given the equation Ax+By=C
We have to identify the slope and show we work.
Compare this equation with y=mx+c.
Given the equationAx+By=C and from previews part slope-intercept form is y=−A/Bx+C/B
Compare this equation with y=mx+c
Thus, m=−A/B
Hence, the slope is−A/B
The slope of A x+By=C is−A/B.
Page 192 Problem 20 Answer
Here we have to tell if we want to determine the y-intercept of an equation, which form is more efficient, and explain our reasoning.
To determine the y-intercept of an equation slope-intercept form is more efficient.
Because in slope-intercept we can easily find the value of y-intercept is b by compare with y=mx+b.
To find y-intercept slope-intercept formy=mx+b is more efficient because the y-intercept is b.
Page 192 Problem 21 Answer
Here we have to tell if we wanted to graph an equation on a calculator, which form is more efficient, and explain our reasoning.
To graph, an equation on our calculator slope-intercept form is more efficient.
Because to graph equation must be solved for y and in slope-intercept form equation already solved for y.
To graph, an equation on our calculator slope-intercept form is more efficient Because to graph equation must be solved for y and in slope-intercept form equation already solved for y.
Page 193 Problem 22 Answer
Given Think Inside the Box is manufacturing new boxes for You Pack ‘Em, We Ship ‘Em (YPEWSE).
YPEWSE told Think Inside the Box that the boxes must have a specific volume and area.
However, YPEWSE did not specify a height for the boxes.
We have to write a literal equation to calculate the volume of a box.
We know the box has a cube shape.
So the formula of volume of a box is V=Bh where B is the area of the base and h is its height.
A literal equation to calculate the volume of a box is V=Bh where B is the area of the base and h is its height.
Page 193 Problem 23 Answer
Given the equation V=Bh
We have to convert the volume formula to solve for height.
Solve the equationV=Bh for h.
Given V=Bh
We have to convert the volume formula to solve for height
Divide both sides by B.
h=V/B
The volume formula to solve for height ish=V/B.
Page 193 Problem 24 Answer
Given YPEWSE specified the volume of the box must be 450 in 3 and the area of the base must be 75 in 2.
We have to use your formula to determine the height of the new boxes.
Substitute the value in formula.
The volume formula to solve for height is h=V/B
Substitute V=450 in 3 and B=75 in 2
h=450/75
h=6
Hence, the height of the new boxes is 6 in.
The height of the new boxes is 6 in.
Page 193 Problem 25 Answer
Given the volume of an ice cream cone is the measure of how much ice cream a cone can hold.
An ice cream cone company wants to make an ice cream cone with a larger radius that still holds the same amount of ice cream.
We have to write an equation to calculate the volume of a cone.
We know the ice cream has a cone shape.
So the formula of the cone is V=1/3πr2h
where r is the radius and h is the height.
An equation to calculate the volume of a cone is V=1/3πr2h.
Page 193 Problem 26 Answer
Given the equation V=1/3πr2h.we have to convert the equation to solve for the radius.
Solve the equation V=1/3πr2h for r.
Given V=1/3πr2h
We have to convert the volume formula to solve for radius.
multiply both sides by 3
3V=πr2/h
Divide both sides by πh
3V/πh=r2
Take square on both sides
r=√3V/πh
The equation to solve for the radius is r=√3V/πh.
Page 194 Problem 27 Answer
Given future value is the value of a sum of money at a specific date due to interest.
The formula A=P(1+rt) is used to determine future value.
The variable A is the future value, P is the principal, r is the interest rate, and t is the time.
A bank wants to know the interest rate of a customer’s account who earned a certain amount of future value.
We have to convert the equation to solve for rate.solve literal Equations for r
Given A=P(1+rt)
We have to convert the equation to solve for rate.
distribution P
A=P+Prt subtracting P on both sides
A−P=Prt
Divide both sides by Pt.
r=A−P/Pt
The equation to solve for rate is r=A−P/Pt.
Page 194 Problem 28 Answer
Given Jillian deposited $5000 in an account 10 years ago after her college graduation.
The money she deposited now has a value of $15,000 We have to determine the interest rate of Jillian’s account.
Substitute the value in the formula.
The equation to solve for rate is r=A−P/Pt.
Substitute P=5000, t=10 and A=15000
r=15000−5000/5000(10)
=10000/50000
=0.2
=20%.
The interest rate of Jillian’s account. Is 20%.