If you could take a better picture that would be great.
<u>Given</u>:
Given that the triangle PQR is similar to SQT.
The length of PS is (x + 5)
The length of SQ is 8.
The length of ST is (x - 9)
The length of PR is 21.
We need to determine the value of x.
<u>Value of x:</u>
Using the similar triangles property, we shall determine the value of x.
Hence, we have;
![\frac{PQ}{SQ}=\frac{PR}{ST}](https://tex.z-dn.net/?f=%5Cfrac%7BPQ%7D%7BSQ%7D%3D%5Cfrac%7BPR%7D%7BST%7D)
Substituting the values, we get;
![\frac{x+5+8}{8}=\frac{21}{x-9}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B5%2B8%7D%7B8%7D%3D%5Cfrac%7B21%7D%7Bx-9%7D)
![\frac{x+13}{8}=\frac{21}{x-9}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B13%7D%7B8%7D%3D%5Cfrac%7B21%7D%7Bx-9%7D)
Cross multiplying, we get;
![(x+13)(x-9)=(21)(8)](https://tex.z-dn.net/?f=%28x%2B13%29%28x-9%29%3D%2821%29%288%29)
![x^2+13x-9x-117=168](https://tex.z-dn.net/?f=x%5E2%2B13x-9x-117%3D168)
![x^2+4x-285=0](https://tex.z-dn.net/?f=x%5E2%2B4x-285%3D0)
The value of x can be determined using the quadratic formula.
Thus, we have;
![x=\frac{-4 \pm \sqrt{16+1140}}{2}}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4%20%5Cpm%20%5Csqrt%7B16%2B1140%7D%7D%7B2%7D%7D)
![x=\frac{-4 \pm \sqrt{1156}}{2}}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4%20%5Cpm%20%5Csqrt%7B1156%7D%7D%7B2%7D%7D)
![x=\frac{-4 \pm 36}{2}}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4%20%5Cpm%2036%7D%7B2%7D%7D)
![x=\frac{-4+36}{2}} \ or \ x=\frac{-4-36}{2}}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4%2B36%7D%7B2%7D%7D%20%5C%20or%20%5C%20x%3D%5Cfrac%7B-4-36%7D%7B2%7D%7D)
![x=\frac{32}{2}} \ or \ x=\frac{-40}{2}}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B32%7D%7B2%7D%7D%20%5C%20or%20%5C%20x%3D%5Cfrac%7B-40%7D%7B2%7D%7D)
![x=16 \ or \ x=-20](https://tex.z-dn.net/?f=x%3D16%20%5C%20or%20%5C%20x%3D-20)
Since, x cannot take negative values, then x = 16.
Hence, the value of x is 16.
The expression that is equivalent to
is
.
Given trigonometric expression is:
![Cos(\frac{\pi }{2}+r )](https://tex.z-dn.net/?f=Cos%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%2Br%20%29)
<h3>What is the
value of
![Cos(\frac{\pi }{2}+\theta )](https://tex.z-dn.net/?f=Cos%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%2B%5Ctheta%20%29)
?</h3>
The value of
is
because
lies in the second quadrant and the cosine function is negative in the second quadrant.
So, ![Cos(\frac{\pi }{2}+r )= -Sin r](https://tex.z-dn.net/?f=Cos%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%2Br%20%29%3D%20-Sin%20r)
The range of sine and cosine functions is the same i.e. [-1,1].
Both the functions are periodic functions with periods 2π.
Hence, the expression that is equivalent to
is
.
To get more about trigonometric functions visit:
brainly.com/question/2193113
Answer:
15 hours
Step-by-step explanation:
9 lawns is 3 times as much as 3 lawns
it will take 3 times as long
3 * 5 hours = 15 hours
Answer:
xy=10
Step-by-step explanation:
Vary inversely means x and y have a constant product. The graph is not a straight line. We find the product from the given set of values a=2, b=5 to get ab=10. Therefore xy=10 is the equation.