3 years ago

Which equation is equivalent to 8x + 3(x + 5) - 5(x - 4) = 2?

Mathematics

1 answer:

12345 [234]3 years ago

3 0

Answer:

x = -11/2

Step-by-step explanation:

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Given: <SPT = <RQT, ST = RT Prove: PR = QS

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Answer:

See explanation

Step-by-step explanation:

Consider triangles PTS and QTR. In these triangles,

$ST=RT$ - given;
$\angle SPT=\angle RQT$ - given;
$\angle STP=\angle RTQ$ - as vertical angles when lines PR and SQ intersect.

Thus, $\triangle PTS\cong \triangle QTR$ by AAS postulate.

Congruent triangles have congruent corresponding sides, so

$PT=QT$

Consider segments PR and QS:

$PR=PT+TR\ [\text{Segment addition postulate}]\\ \\QS=QT+TS\ [\text{Segment addition postulate}]\\ \\PT=QT\ [\text{Proven}]\\ \\ST=RT\ [\text{Given}]$

So,

$PR=SQ\ [\text{Substitution property}]$

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