Answer:
In rectangle PQRS, the value of PQ = 24, if the value of SP = 7 and the value of PR = 25.
Step-by-step explanation:
Answer:
![f(t) = 4(t-1)^2 +4](https://tex.z-dn.net/?f=%20f%28t%29%20%3D%204%28t-1%29%5E2%20%2B4)
So then we see that the required values are:
![a = 4, h =1, k =4](https://tex.z-dn.net/?f=%20a%20%3D%204%2C%20h%20%3D1%2C%20k%20%3D4)
And the vertex for this case would be:
![V_x = -\frac{-8}{2*4} = 1](https://tex.z-dn.net/?f=%20V_x%20%3D%20-%5Cfrac%7B-8%7D%7B2%2A4%7D%20%3D%201)
![V_y = 4](https://tex.z-dn.net/?f=%20V_y%20%3D%204)
![V(1,4)](https://tex.z-dn.net/?f=%20V%281%2C4%29)
Step-by-step explanation:
For this case we have the following function given:
![f(t) = 4t^2 -8t +8](https://tex.z-dn.net/?f=%20f%28t%29%20%3D%204t%5E2%20-8t%20%2B8)
And we want to wrote this equation in the form a(x − h)2 + k
We can divide both sides of the equation and we got:
![\frac{f(t)}{4} = t^2 -2t +2](https://tex.z-dn.net/?f=%20%5Cfrac%7Bf%28t%29%7D%7B4%7D%20%3D%20t%5E2%20-2t%20%2B2)
Now we can comple the square in the rigth part with this:
![\frac{f(t)}{4} = t^2 -2t +1 +(2-1)](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28t%29%7D%7B4%7D%20%3D%20t%5E2%20-2t%20%2B1%20%2B%282-1%29)
![\frac{f(t)}{4} = (t^2 -2t +1) +(2-1)= (t-1)^2 +1](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28t%29%7D%7B4%7D%20%3D%20%28t%5E2%20-2t%20%2B1%29%20%2B%282-1%29%3D%20%28t-1%29%5E2%20%2B1)
And now we can multiply both sides by 4 and we got:
![f(t) = 4(t-1)^2 +4](https://tex.z-dn.net/?f=%20f%28t%29%20%3D%204%28t-1%29%5E2%20%2B4)
So then we see that the required values are:
![a = 4, h =1, k =4](https://tex.z-dn.net/?f=%20a%20%3D%204%2C%20h%20%3D1%2C%20k%20%3D4)
And the vertex for this case would be:
![V_x = -\frac{-8}{2*4} = 1](https://tex.z-dn.net/?f=%20V_x%20%3D%20-%5Cfrac%7B-8%7D%7B2%2A4%7D%20%3D%201)
![V_y = 4](https://tex.z-dn.net/?f=%20V_y%20%3D%204)
![V(1,4)](https://tex.z-dn.net/?f=%20V%281%2C4%29)
L = W + 12
P = 7W = 2L + 2W
7W = 2W + 24 + 2W
3W = 24
W = 8
L = 20
Answer:
d) 5/3 x
Step-by-step explanation:
You substitute a for 2c and b for 5d, so your equation will look like this:
c/d - 2c/5d = x
Then you just simplify into x by making c/d into 5c/5d so you have a common denominator.
5c/5d - 2c/5d = x
3c/5d = x
5/3 is your answer
The range of years would be 493 to 745.
According to the empirical rule, 99.7% of data will fall within 3 standard deviations from the mean. Using this information, we have
619+3(42) and 619-3(42)
619+126 and 619-126
745 and 493