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3 years ago

6. Protein bars come in a 4-pack box or 12-pack

Mathematics

1 answer:

cricket20 [7]3 years ago

5 0

Answer:

The 12 pack has a better value.

Step-by-step explanation:

1. create a ratio table.

you want to know how much the 4 pack would cost if it was a 12 pack.

you can see the ratio table in the picture above.

As you can see, when the 4 pack equals $7.68, making it a 12 pack will equal $23.04.

Then, compare 23.04 to 22.32.

In conclusion, the 12 pack has a better value.

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A car travels 61 miles per hour. At this rate, how far will the car travel in 5 hours?

VMariaS [17]

Answer:

305 miles per hour

Step-by-step explanation:

61 miles per hour

61(5)= 305 miles/ hour

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3 years ago

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John is going on a trip and the country he is traveling to uses the Celsius scale. He is curious about converting Celsius temper

Setler79 [48]

Answer:

$f(x)=\dfrac{9}{5}x+32$ converts Celsius to Fahrenheit.

$g(x)=\dfrac{5(x-32)}{9}$ converts Fahrenheit to Celsius.

Step-by-step explanation:

Write given data in the table

$\begin{array}{cc}x&f(x)\\^{\circ}\text{C}&^{\circ}\text{F}\\20&68\\30&86\end{array}$

Let the expression for the function be

$f(x)=ax+b$

Note, that this equation is linear equation and it is well-known fact that the Celsius to Fahrenheit dependence is linear.

Substitute corresponding values into this expression:

$68=20a+b\\ \\86=30a+b$

Subtract these two equations:

$86-68=30a-20a\\ \\10a=18\\ \\a=\dfrac{9}{5}$

Substitute it into the first equation:

$68=20\cdot \dfrac{9}{5}+b\Rightarrow b=68-36=32$

So,

$f(x)=\dfrac{9}{5}x+32$

This is the function which converts Celsius to Fahrenheit.

And function

$g(x)=\dfrac{5(x-32)}{9}$ converts Fahrenheit to Celsius.

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2 years ago

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Consider function f.

tekilochka [14]

Given:

The function is:

$f(x)=\sqrt{7x-21}$

To find:

The steps of finding the inverse function $f^{-1}(x)$ .

Solution:

We have,

$f(x)=\sqrt{7x-21}$

The steps of finding the inverse function are:

Step 1: Substitute $f(x)=y$ .

$y=\sqrt{7x-21}$

Step 2: Interchange x and y.

$x=\sqrt{7y-21}$

Step 3: Taking square on both sides, we get

$x^2=7y-21$

Step 4: Adding 21 on both sides, we get

$x^2+21=7y$

Step 5: Divide both sides by 7.

$\dfrac{1}{7}x^2+3=y$

Step 6: Substitute $y=f^{-1}(x)$ .

$\dfrac{1}{7}x^2+3=f^{-1}(x)$ , where $x\geq 0$ .

Therefore, the inverse of the given function is $f^{-1}(x)=\dfrac{1}{7}x^2+3$ and the arrangement of steps is shown above.

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