Ask question

Ask question

All categories

lorasvet [3.4K]

3 years ago

14

Jonah is purchasing a car that is on sale for 15% off. He knows the function that represents the sale price of his car is c(p) =

0.85p, where p is the original price of the car. He also knows he has to pay 9% sale's tax on the car. The price of the car with tax is f(c) = 1.09c, where c is the sale price of the car. Determine the composite function that can be used to calculate the final price of Jonah's car by solving for f[c(p)].
answers
A.f [c(p)] = 0.9265cp
B. f[c(p)] = 0.9265p
C. f [c(p)} = 1.94cp
D. f [c(p)] = 1.94p

1 answer:

nika2105 [10]3 years ago

7 0

The answer is b, f[c(p)]=0.9265p.

f[c(p)]=f(0.85p)=1.09(0.85p)=0.9265p

You might be interested in

Intersection point of Y=logx and y=1/2log(x+1)

GalinKa [24]

Answer:

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

The Problem:

What is the intersection point of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ ?

Step-by-step explanation:

To find the intersection of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ , we will need to find when they have a common point; when their $x$ and $y$ are the same.

Let's start with setting the $y$ 's equal to find those $x$ 's for which the $y$ 's are the same.

$\log(x)=\frac{1}{2}\log(x+1)$

By power rule:

$\log(x)=\log((x+1)^\frac{1}{2})$

Since $\log(u)=\log(v)$ implies $u=v$ :

$x=(x+1)^\frac{1}{2}$

Squaring both sides to get rid of the fraction exponent:

$x^2=x+1$

This is a quadratic equation.

Subtract $(x+1)$ on both sides:

$x^2-(x+1)=0$

$x^2-x-1=0$

Comparing this to $ax^2+bx+c=0$ we see the following:

$a=1$

$b=-1$

$c=-1$

Let's plug them into the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$x=\frac{1 \pm \sqrt{1+4}}{2}$

$x=\frac{1 \pm \sqrt{5}}{2}$

So we have the solutions to the quadratic equation are:

$x=\frac{1+\sqrt{5}}{2}$ or $x=\frac{1-\sqrt{5}}{2}$ .

The second solution definitely gives at least one of the logarithm equation problems.

Example: $\log(x)$ has problems when $x \le 0$ and so the second solution is a problem.

So the $x$ where the equations intersect is at $x=\frac{1+\sqrt{5}}{2}$ .

Let's find the $y$ -coordinate.

You may use either equation.

I choose $y=\log(x)$ .

$y=\log(\frac{1+\sqrt{5}}{2})$

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

6 0

3 years ago

Order the following numbers from least to greatest <br> -9/2<br> 0<br> 1 3/5<br> 9/7<br> 2/3

marysya [2.9K]

$\frac{-9}{2}$

0

$\frac{2}{3}$

$\frac{9}{7}$

1 $\frac{3}{5}$

3 0

3 years ago

Read 2 more answers

A 26-foot long ladder is leaning against a building

xxTIMURxx [149]

Answer:

13

Step-by-step explanation:

cos(60) =building height / 26

8 0

3 years ago

Read 2 more answers

The sum of all the ages of Dylan and Renee is 57 years . 9 yrs ago , Dylans age was 2 times Renee's age. How old is Dylan now?

Ugo [173]

Answer:

Step-by-step explanation:

let present age of

Dylan=x

Renee=y

x+y=57

9 years ago

x-9=2(y-9)=2y-18

x=2y-18+9=2y-9

so 2y-9+y=57

3y=57+9=66

y=66/3=22

x+22=57

x=57-22=35

Dylan's present age=35 years

3 0

3 years ago

Ron and Ben had a total of 700 playing cards. After Ron gave away 40% of his playing cards and Ben gave away 20% of his playing

allsm [11]

Ron had 140 picture cards more than Ben

5 0

3 years ago