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dedylja [7]
3 years ago
14

What are 2 equationsthat have infinetely many solutions

Mathematics
1 answer:
svetlana [45]3 years ago
3 0

the equation 8x = 8x has infinitely  many solutions. You can substitute any real number for x and the equation will always be true no matter what. Another example are quadratic equations, such as (x +1)(x-2)= 0. The solutions to the equations are x=1 and x=2 substitute anither number its still true




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In the diagram below, we have $ST = 2TR$ and $PQ = SR = 20$. Find the length $UV$.
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Answer:

12

Step-by-step explanation:

1. ST=2TR and SR=20, then by segment addition postulate

ST+TR=SR\\ \\2TR+TR=SR\\ \\3TR=20\\ \\TR=\dfrac{20}{3}\\ \\ST=2\cdot \dfrac{20}{3}=\dfrac{40}{3}

2. Consider triangles PQU and TSU. These triangles are similar by AA similarity theorem (triangles have congruent vertical angles PUQ and TUS and congruent alternate interior angles PQU and TSU). Similar triangles have proportional corresponding sides, so

\dfrac{QU}{US}=\dfrac{PQ}{ST}=\dfrac{20}{\frac{40}{3}}=\dfrac{60}{40}=1.5

QU=1.5US

3. Consider triangles QUV and QSR. These triangles are similar by AA similarity theorem. Similar triangles have proportional corresponding sides, so

\dfrac{QU}{QS}=\dfrac{UV}{SR}\\ \\\dfrac{QU}{QU+US}=\dfrac{1.5US}{1.5US+US}=\dfrac{1.5}{2.5}=0.6

so

\dfrac{UV}{SR}=0.6\Rightarrow UV=0.6SR=0.6\cdot 20=12

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