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yawa3891 [41]
2 years ago
11

Mark has already run 33.4 miles this week. He can run 2.5 miles in one hour. Construct an equation that represents the total num

ber of miles run based on how many hours he runs for. What is the total number of miles he ran if he runs for 17 hours?
Mathematics
1 answer:
DanielleElmas [232]2 years ago
4 0

Answer:

y = 2.5x + 33.4, y = 75.9 miles

Step-by-step explanation:

Equation is y = 2.5x + 33.4

17 = 2.5 x + 33.4

y = 2.5 (17) + 33.4

y = 42.5 + 33.4

y = 75.9 miles

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Which statement describes the inverse of m(x) = x^2 – 17x?
DochEvi [55]

Given:

The function is

m(x)=x^2-17x

To find:

The inverse of the given function.

Solution:

We have,

m(x)=x^2-17x

Substitute m(x)=y.

y=x^2-17x

Interchange x and y.

x=y^2-17y

Add square of half of coefficient of y , i.e., \left(\dfrac{-17}{2}\right)^2 on both sides,

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x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2

x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2        [\because (a-b)^2=a^2-2ab+b^2]

Taking square root on both sides.

\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}

Add \dfrac{17}{2} on both sides.

\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y

Substitute y=m^{-1}(x).

m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}

We know that, negative term inside the root is not real number. So,

x+\left(\dfrac{17}{2}\right)^2\geq 0

x\geq -\left(\dfrac{17}{2}\right)^2

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3 years ago
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<u><em>Explanation:</em></u>
To solve for g, we will need to isolate the g on one side of the equation.
<u>This can be done as follows:</u>
</span>\frac{4g}{14} -  \frac{3}{7} -  \frac{g}{14} =  \frac{3}{14}<span>

<u>1- multiply all terms by 14 to get rid of the fraction:</u>
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<u>2- Combine like terms:</u>
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<u>3- Isolate the g:</u>
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