Given that the triangles are similar, find the value of x. Find the length of NR. S T 40 60 R 2x-2 8
N
M
X=
NR =
1 answer:
Answer:
NR = 12
Step-by-step explanation:
Given that both trjangles are similar, therefore, it follows that their corresponding side lengths would be proportional to each other. Thus:
Cross multiply
(addition property of equality)
Divide both sides by 10
x = 7
✔️NR = 2x - 2
Plug in the value of x
NR = 2(7) - 2 = 14 - 2
NR = 12
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Answer:
3 more students need to sign up
Step-by-step explanation:
Let the equal number of students in 9 teams be x.
Total number of signed up students = 690.
Let t be the required number of students to be signed.
Therefore, 9x = 690+t.
This means, 690+t is a multiple of 9.
The least value of t to make 690+t, a multiple of 9 is 3 and hence,
= 77
Hence, 3 more students need to sign up and each of the 9 teams consists of 77 students.
That'd be true only if the value of "s" is the exact same one for both
namely if sec(s) = cos(s)
then solving for "s"
thus
![\bf sec(s)=cos(s)\qquad but\implies sec(\theta)=\cfrac{1}{cos(\theta)} \\\\\\ thus\cfrac{1}{cos(s)}=cos(s)\implies 1=cos^2(s)\implies \pm \sqrt{1}=cos(s) \\\\\\ \pm 1=cos(s)\impliedby \textit{now taking }cos^{-1}\textit{ to both sides} \\\\\\ cos^{-1}(\pm 1)=cos^{-1}[cos(s)]\implies cos^{-1}(\pm 1)=\measuredangle s](https://tex.z-dn.net/?f=%5Cbf%20sec%28s%29%3Dcos%28s%29%5Cqquad%20but%5Cimplies%20sec%28%5Ctheta%29%3D%5Ccfrac%7B1%7D%7Bcos%28%5Ctheta%29%7D%0A%5C%5C%5C%5C%5C%5C%0Athus%5Ccfrac%7B1%7D%7Bcos%28s%29%7D%3Dcos%28s%29%5Cimplies%201%3Dcos%5E2%28s%29%5Cimplies%20%5Cpm%20%5Csqrt%7B1%7D%3Dcos%28s%29%0A%5C%5C%5C%5C%5C%5C%0A%5Cpm%201%3Dcos%28s%29%5Cimpliedby%20%5Ctextit%7Bnow%20taking%20%7Dcos%5E%7B-1%7D%5Ctextit%7B%20to%20both%20sides%7D%0A%5C%5C%5C%5C%5C%5C%0Acos%5E%7B-1%7D%28%5Cpm%201%29%3Dcos%5E%7B-1%7D%5Bcos%28s%29%5D%5Cimplies%20cos%5E%7B-1%7D%28%5Cpm%201%29%3D%5Cmeasuredangle%20s)
namely if sec(s) = cos(s)
then solving for "s"
thus