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,
Furthermore,
Finding PR and RS,
Then,
Solving for PS,
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}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5CRightarrow%20PS%5E2%2B16PS-132%3D0%20%5C%5C%20%5CRightarrow%20PS%3D%5Cfrac%7B-16%5Cpm%5Csqrt%5B%5D%7B16%5E2-4%28-132%29%7D%7D%7B2%7D%3D%5Cfrac%7B-16%5Cpm28%7D%7B2%7D%20%5C%5C%20%5CRightarrow%20PS%3D-22%2C6%20%5Cend%7Bgathered%7D)
And PS is a segment; therefore, it has to be positive.
Hence, the answer is PS=6
The change is the remaining money that is needed to take from the seller so a change of Umberto will be $6.62.
<h3>What is subtraction?</h3>
To subtract in mathematics is to take something away from a group or a number of objects.
The group's total number of items decreases or becomes lower when we subtract from it.
Given that,
Umberto buys a game for $7.89 and some batteries for $5.49.
Total money of buying = 7.89 + 5.49 = $13.38
Now he gives a $20 bill.
Remaining (change) = 20 - 13.38
⇒ $6.62
Hence "The change of Umberto will be $6.62".
For more about subtraction,
brainly.com/question/1927340
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Answer: x = 3/80
Step-by-step explanation:
153 x 7.14 = 1092.42
so every year she gets $1092.42
so times that by 6 and the answer is $6554.52
