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JulijaS [17]
3 years ago
8

A hyena runs 2 kilometers for every 25 kilometer a mouse runs. Select from the drop-down menu to correctly complete the statemen

t. The hyena runs kilometers for every kilometer the mouse runs.
Mathematics
1 answer:
xxMikexx [17]3 years ago
6 0

Given that a hyena runs 2 kilometers for every 25 kilometer a mouse runs.

Now we need to select from the drop-down menu to correctly complete the statement. Where given statement is "The hyena runs kilometers for every kilometer the mouse runs."

"every kilometer" indicates we need to find number of kilometers for hyena when mouse runs 1 kilometer.

To find that we will divide number of kilometers of hyena by number of kilometers of mouse that is divide 2 by 25.

2/25=0.08

Hence final answer will be :

"The hyena runs 0.08  kilometers for every kilometer the mouse runs."

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Since segments ST and PQ are parallel, triangles SRT and PRQ are similar due to the AAA postulate. In general, the ratio between the corresponding sides of two similar triangles is constant; therefore,

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Furthermore,

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Then,

\frac{12}{PR}=\frac{TS}{15}\begin{gathered} \Rightarrow\frac{12}{PR}=\frac{4+PS}{15} \\ \Rightarrow\frac{12}{PS+12}=\frac{4+PS}{15} \end{gathered}

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\begin{gathered} \Rightarrow PS^2+16PS-132=0 \\ \Rightarrow PS=\frac{-16\pm\sqrt[]{16^2-4(-132)}}{2}=\frac{-16\pm28}{2} \\ \Rightarrow PS=-22,6 \end{gathered}

And PS is a segment; therefore, it has to be positive.

Hence, the answer is PS=6

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