D 66 cats
Hope this helps!
Common difference is +6 and I think nth term is 5 (pretty sure it's always the first term) and the second one im not so sure about I'm sorry.
All you have to do is follow PEMDAS (if you don't know what that is, search it up).
-2-5(4n-6)=-132
Distribute the 5 to everything in the parentheses.
-2-20n+30= -132
Combine like terms.
-20n+28 = -132
Subtract 28 from both sides.
-20n = -160
Divide by -20 on both sides.
n = 8
To find the value of q, we need to find d(-8). Put another way, we need to find the value of d(x) when x = -8
![d(x) = -\sqrt{\frac{1}{2}x+4}](https://tex.z-dn.net/?f=d%28x%29%20%3D%20-%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7Dx%2B4%7D)
![d(-8) = -\sqrt{\frac{1}{2}(-8)+4}](https://tex.z-dn.net/?f=d%28-8%29%20%3D%20-%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%28-8%29%2B4%7D)
![d(-8) = -\sqrt{-4+4}](https://tex.z-dn.net/?f=d%28-8%29%20%3D%20-%5Csqrt%7B-4%2B4%7D)
![d(-8) = -\sqrt{0}](https://tex.z-dn.net/?f=d%28-8%29%20%3D%20-%5Csqrt%7B0%7D)
![d(-8) = 0](https://tex.z-dn.net/?f=d%28-8%29%20%3D%200)
So this means q = 0. Note that -0 is just 0.
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The value of r will be a similar, but now we use f(x) this time.
Plug in x = 0
![f(x) = \sqrt{\frac{1}{2}x+4}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7Dx%2B4%7D)
![f(0) = \sqrt{\frac{1}{2}*0+4}](https://tex.z-dn.net/?f=f%280%29%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%2A0%2B4%7D)
![f(0) = \sqrt{0+4}](https://tex.z-dn.net/?f=f%280%29%20%3D%20%5Csqrt%7B0%2B4%7D)
![f(0) = \sqrt{4}](https://tex.z-dn.net/?f=f%280%29%20%3D%20%5Csqrt%7B4%7D)
![f(0) = 2](https://tex.z-dn.net/?f=f%280%29%20%3D%202)
Therefore, r = 2.
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For s, we plug x = 10 into f(x)
![f(x) = \sqrt{\frac{1}{2}x+4}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7Dx%2B4%7D)
![f(10) = \sqrt{\frac{1}{2}*10+4}](https://tex.z-dn.net/?f=f%2810%29%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%2A10%2B4%7D)
![f(10) = \sqrt{5+4}](https://tex.z-dn.net/?f=f%2810%29%20%3D%20%5Csqrt%7B5%2B4%7D)
![f(10) = \sqrt{9}](https://tex.z-dn.net/?f=f%2810%29%20%3D%20%5Csqrt%7B9%7D)
![f(10) = 3](https://tex.z-dn.net/?f=f%2810%29%20%3D%203)
So s = 3.
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Finally, plug x = 10 into d(x) to find the value of t
![d(x) = -\sqrt{\frac{1}{2}x+4}](https://tex.z-dn.net/?f=d%28x%29%20%3D%20-%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7Dx%2B4%7D)
![d(10) = -\sqrt{\frac{1}{2}(10)+4}](https://tex.z-dn.net/?f=d%2810%29%20%3D%20-%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%2810%29%2B4%7D)
![d(10) = -\sqrt{5+4}](https://tex.z-dn.net/?f=d%2810%29%20%3D%20-%5Csqrt%7B5%2B4%7D)
![d(10) = -\sqrt{9}](https://tex.z-dn.net/?f=d%2810%29%20%3D%20-%5Csqrt%7B9%7D)
![d(10) = -3](https://tex.z-dn.net/?f=d%2810%29%20%3D%20-3)
A shortcut you could have taken is to note how d(x) = -f(x), so this means
d(10) = -f(10) = -9 since f(10) = 9 was found in the previous section above.
Whichever method you use, you should find that t = -3.
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<h3>In summary:</h3><h3>q = 0</h3><h3>r = 2</h3><h3>s = 3</h3><h3>t = -3</h3>
Answer:
4
Step-by-step explanation:
(3 - 5)^2
-2^2 = 4