East high school's student council plans to buy some stools and chairs for a new student center. They need to buy 25 more chairs than stools. The chairs cost $32 each and the stools cost $28 each. The budget is $2,620. How many chairs can they buy?

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Step-by-step explanation:

Substitutex=cos\alp,\alp∈[0:;π] \displaystyle Then\; |x+\sqrt{1-x^2}|=\sqrt{2}(2x^2-1)\Leftright |cos\alp +sin\alp |=\sqrt{2}(2cos^2\alp -1)Then∣x+ 1−x 2 ​ ∣= 2 ​ (2x 2 −1)\Leftright∣cos\alp+sin\alp∣= 2 ​ (2cos 2 \alp−1) \displaystyle |\N {\sqrt{2}}cos(\alp-\frac{\pi}{4})|=\N {\sqrt{2}}cos(2\alp )\Right \alp\in[0\: ;\: \frac{\pi}{4}]\cup [\frac{3\pi}{4}\: ;\: \pi]∣N 2 ​ cos(\alp− 4 π ​ )∣=N 2 ​ cos(2\alp)\Right\alp∈[0; 4 π ​ ]∪[ 4 3π ​ ;π] 1) \displaystyle \alp \in [0\: ;\: \frac{\pi}{4}]\alp∈[0; 4 π ​ ] \displaystyle cos(\alp -\frac{\pi}{4})=cos(2\alp )\dotscos(\alp− 4 π ​ )=cos(2\alp)… 2. \displaystyle \alp\in [\frac{3\pi}{4}\: ;\: \pi]\alp∈[ 4 3π ​ ;π] \displaystyle -cos(\alp -\frac{\pi}{4})=cos(2\alp )\dots−cos(\alp− 4 π ​ )=cos(2\alp)

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.