Answer:
Step-by-step explanation:
y = -4x^2 + 4x + 6
Factor out the leading coefficient:
y = -4(x^2 - x) + 6
Complete the square:
y = -4(x^2 - x + (½)^2) + 4(½)^2 + 6
= -4(x-½)^2 + 7
What equation describes this variation?
z = kxy
What is the constant of variation?
k = 5
When x = 1 and y = –2, z =
-10
Step by Step Explanation:
With the equation z = kxy and the values for z, x, and y, we can find k.
z = kxy
-75 = (k) (3) (-5)
-75 = (k) (-15)
5 = k
k = 5 (final answer).
To check our work, we just enter all of the values and make sure it adds up.
z = kxy
-75 = (5)(3)(-5)
-75 = 15(-5)
-75 = -75
correct!
Do the same to find the answer for the next part to get -10.
Further proof in the file attached.
Hey!
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Formula:
![=\sqrt{(x2 - x1)^2 + (y2 - y1)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%28x2%20-%20x1%29%5E2%20%2B%20%28y2%20-%20y1%29%5E2%7D)
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Solution:
![=\sqrt{(3 - 0)^2 + (2 - (-8))^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%283%20-%200%29%5E2%20%2B%20%282%20-%20%28-8%29%29%5E2%7D)
![=\sqrt{(3)^2 + (10)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%283%29%5E2%20%2B%20%2810%29%5E2%7D)
![=\sqrt{9 + 100}\\](https://tex.z-dn.net/?f=%3D%5Csqrt%7B9%20%2B%20100%7D%5C%5C)
![=\sqrt{109}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B109%7D)
≈ 10.44
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Answer:
10.44
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Hope This Helped! Good Luck!
Given:
![XR=x+8](https://tex.z-dn.net/?f=%20XR%3Dx%2B8%20)
![RY=4x-10](https://tex.z-dn.net/?f=%20RY%3D4x-10%20)
Since R is the midpoint of the line, we can set XR equal to RY and solve for x.
![RY=XR](https://tex.z-dn.net/?f=%20RY%3DXR%20)
![4x-10=x+8](https://tex.z-dn.net/?f=%204x-10%3Dx%2B8%20)
![4x=x+18](https://tex.z-dn.net/?f=%204x%3Dx%2B18%20)
![3x=18](https://tex.z-dn.net/?f=%203x%3D18%20)
![x=6](https://tex.z-dn.net/?f=%20x%3D6%20)
Now we know what x is. We can plug in x to RY and XR and then add it all together to find XY. Let's find XR:
![XR=6+8](https://tex.z-dn.net/?f=%20XR%3D6%2B8%20)
![XR=14](https://tex.z-dn.net/?f=%20XR%3D14%20)
Let's find RY now:
![RY=4(6)-10](https://tex.z-dn.net/?f=%20RY%3D4%286%29-10%20)
![RY=24-10](https://tex.z-dn.net/?f=%20RY%3D24-10%20)
![RY=14](https://tex.z-dn.net/?f=%20RY%3D14%20)
Since we know that:
![XR+RY=XY](https://tex.z-dn.net/?f=%20XR%2BRY%3DXY%20)
We can plug in our answers:
![14+14=XY](https://tex.z-dn.net/?f=%2014%2B14%3DXY%20)
Final answer:
![XY=28](https://tex.z-dn.net/?f=%20XY%3D28%20)
Hopes this helps:
Answer: x = -12
How I know I use this app called Cymath.