Find the rate of change for each linear function.

Can someone help me figure out the answer?

Ahat [919]

Answer:

You will break even on the car wash when you buy 13.5 gallons. As long as you buy that or more, it is cheaper to get the car wash.

Step-by-step explanation:

In order to find this, we need to create equations for both situations. If we let x equal the amount of gallons purchased, we can model the first equation as:

f(x) = 3.35x

And the second equation as:

f(x) = 3.05x + 4.05

Then to find when they equal each other, we can set the two equations equal to each other and solve for x.

3.35x = 3.05x + 4.05

0.30x = 4.05

x = 13.5

This means once you buy 13.5 gallons, the prices will be the same. Any amount over that and the car wash will be cheaper

6 0

2 years ago

What is the solution to 3-3x + 9| = -18?

solmaris [256]

Answer:

x = 5 or x = 1

Step-by-step explanation:

Absolute Value Equation entered :

3|3x-9|=18

Step by step solution :

Step 1: Rearrange this Absolute Value Equation

Absolute value equalitiy entered

3|3x-9| = 18

Step 2: Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is 3|3x-9|

For the Negative case we'll use -3(3x-9)

For the Positive case we'll use 3(3x-9)

Step 3: Solve the Negative Case

-3(3x-9) = 18

Multiply

-9x+27 = 18

Rearrange and Add up

-9x = -9

Divide both sides by 9

-x = -1

Multiply both sides by (-1)

x = 1

Which is the solution for the Negative Case

Step 4: Solve the Positive Case

(3x-9) = 18

Multiply

9x-27 = 18

Rearrange and Add up

9x = 45

Divide both sides by 9

x = 5

Which is the solution for the Positive Case

Step 5: Wrap up the solution

x=1

x=5

Solutions on the Number Line

Two solutions were found :

x=5

x=1

8 0

1 year ago

What is the sum, difference, product, and quotient of 7/12

True [87]

Answer:

7 plus 12 equals 19.

7 minus 12 equals -5.

7 times 12 equals 84.

7 divided by 12 equals 0,583...

7 0

2 years ago

Read 2 more answers

Write each expression in simplified radical form PLEASE HELP ITS DUE FRIDAY AND I DONT UNDERSTAND THIS AT ALL REALLY BAD TEACHER

Nonamiya [84]

Answer:

1) The simplified radical form is $\sqrt{36x^2}=6x$

2) The simplified radical form is $\sqrt{72x^3}=6x\sqrt{2x}$

3) The simplified radical form is $\sqrt{15x^8}=\sqrt{15}x^4$

4) The simplified radical form is $\sqrt{36x^7}=6x^3\sqrt{x}$

Step-by-step explanation:

1) Given expression is $\sqrt{36x^2}$

To find the simplified radical form of the given expression :

$\sqrt{36x^2}$

$=\sqrt{36\times x^2}$

$=\sqrt{36}\times \sqrt{x^2}$

$=\sqrt{6\times 6}\times \sqrt{x\times x}$

$=6\times x$

$\sqrt{36x^2}=6x$

Therefore the simplified radical form is $\sqrt{36x^2}=6x$

2)Given expression is $\sqrt{72x^3}$

To find the simplified radical form of the given expression :

$\sqrt{72x^3}$

$=\sqrt{72\times x^3}$

$=\sqrt{72}\times \sqrt{x^3}$

$=\sqrt{9\times 8}\times \sqrt{x\times x\times x}$

$=\sqrt{9}\times \sqrt{8}\times x\sqrt{x}$

$=3\times 2\sqrt{2}\times x\sqrt{x}$

$\sqrt{72x^3}=6x\sqrt{2x}$

Therefore the simplified radical form is $\sqrt{72x^3}=6x\sqrt{2x}$

3) Given expression is $\sqrt{15x^8}$

To find the simplified radical form of the given expression :

$\sqrt{15x^8}$

$=\sqrt{15\times x^8}$

$=\sqrt{15}\times \sqrt{x^8}$

$=\sqrt{5\times 3}\times \sqrt{x^4\times x^4}$

$=\sqrt{15}\times x^4$

$\sqrt{15x^8}=\sqrt{15}x^4$

Therefore the simplified radical form is $\sqrt{15x^8}=\sqrt{15}x^4$

4) Given expression is $\sqrt{36x^7}$

To find the simplified radical form of the given expression :

$\sqrt{36x^7}$

$=\sqrt{36\times x^7}$

$=\sqrt{36}\times \sqrt{x^7}$

$=\sqrt{6\times 6}\times \sqrt{x^3\times x^3\times x}$

$=6\times x^3\sqrt{x}$

$\sqrt{36x^7}=6x^3\sqrt{x}$

Therefore the simplified radical form is $\sqrt{36x^7}=6x^3\sqrt{x}$

3 0

2 years ago

C={ 4,6 }, determine n(C)=

Arte-miy333 [17]

we have given that $C={4,6}$

where $n(C)$ represents the number of elements in C.

where we have 4 and 6 which have two elements.

so $n(C)=2 .$

4 0

2 years ago