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3 years ago

What are two angles whose sides form two pairs of opposite rays?

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

3 0

Answer:

vertical angles

Step-by-step explanation:

<em>Vertical angles</em> are found where lines cross, so meet the requirements of this description. They share a vertex, but not a side. The sides of one of a pair of vertical angles are rays opposite the rays that make up the sides of the other vertical angle in the pair.

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In the diagram below, ST is parallel to PQ. If ST is 4 more than PS,SR = 12, and PQ = 15, find the length of PS. Figures are not

Tpy6a [65]

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,

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

Furthermore,

$PS=PR-RS$

Finding PR and RS,

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

Then,

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

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.

Hence, the answer is PS=6

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A bag contains 80 marbles: 40 are red, 20 are blue, and 20 are black. what is the probability of selecting a red or blue marble

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denis-greek [22]

Answer:

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Step-by-step explanation:

did the assignment on Edge 2020

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