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2 years ago

20 POINTS!!!

1 answer:

4 0

3 drops : 4 pints = x drops : 16 pints

3drops/4pints = x/16pints

(3drops/4pints)*16pints = x
*cancel pints unit*
(3drops/4)*16 = x
(16*3)drops/4 = x
48 drops / 4 = x
12 drops = x (ANSWER)

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Tpy6a [65]

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$\frac{SR}{PR}=\frac{RT}{RQ}=\frac{TS}{QP}$

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$\begin{gathered} ST=4+PS \\ SR=12 \\ PQ=15 \end{gathered}$

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

Solving for PS,

$\begin{gathered} 12\cdot15=(PS+12)(PS+4) \\ \Rightarrow180=PS^2+16PS+48 \end{gathered}$

Solve the quadratic equation in terms of PS, as shown below

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

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

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9 months ago