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otez555 [7]
3 years ago
15

A bike path is 3 miles long. there are distance markers every path one fourth mile to the end of the path. which number line cor

rectly models this situation and the total number of distance markers?
Mathematics
1 answer:
Fynjy0 [20]3 years ago
5 0

Given :

A bike path is 3 miles long. there are distance markers every path one fourth mile to the end of the path.

To Find :

Which number line correctly models this situation and the total number of distance markers.

Solution :

It is given that their are markers every 1/4 part of mile.

So, their are 4 markers per mile.

Numbers of markers in 3 miles long path is :

n = 3\times 4\\\\n = 12

Therefore, the total number of distance markers in 3 mile path is 12.

Hence, this is the required solution.

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Detmermine the best method to solve the following equation, then solve the equation. (3x-5)^2=-125
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(3x-5)^2=-125

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Let us begin by expanding the parenthesis;

\begin{gathered} (3x-5)^2\Rightarrow(3x-5)(3x-5) \\ (3x-5)(3x-5)=9x^2-15x-15x+25 \\ (3x-5)^2=9x^2-30x+25 \end{gathered}

Now that we have expanded the left side of the equation, we would have;

\begin{gathered} 9x^2-30x+25=-125 \\ \text{Add 125 to both sides and we'll have;} \\ 9x^2-30x+25+125=-125+125 \\ 9x^2-30x+150=0 \end{gathered}

We shall now solve the resulting quadratic equation using the quadratic formula as follows;

\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where;} \\ a=9,b=-30,c=150 \\ x=\frac{-(-30)\pm\sqrt[]{(-30)^2-4(9)(150)}}{2(9)} \\ x=\frac{30\pm\sqrt[]{900-5400}}{18} \\ x=\frac{30\pm\sqrt[]{-4500}}{18} \\ x=\frac{30\pm\sqrt[]{-900\times5}}{18} \\ x=\frac{30\pm\sqrt[]{-900}\times\sqrt[]{5}}{18} \\ x=\frac{30\pm30i\sqrt[]{5}}{18} \\ \text{Therefore;} \\ x=\frac{30+30i\sqrt[]{5}}{18},x=\frac{30-30i\sqrt[]{5}}{18} \\ \text{Divide all through by 6, and we'll have;} \\ x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3} \end{gathered}

ANSWER:

x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3}

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8 months ago
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Answer:

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given the following functions f(x) and g(x), solve (f g)(3) and select the correct answer below: f(x) = 6x 3 g(x) = x − 7 4 17 2
NeTakaya
Hello,
+++++++++++++++++++++++++++++++++++++++++
Thanks for the incorrect formula!
+++++++++++++++++++++++++++++++++++++++++
I have tested (fog)(x) ,(f*g)(x) and finally (f+g)(x)

f(x)=6x++++++++++++++++++++++++3
g(x)=x-7
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(f+g)(3)=7*3-4=17

Answer B
++++++++++++++++++++++++++++++++++++

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