Answer:
k=20
Step-by-step explanation:
The constant of proportionality, k, measures the constant value of the ratio between two proportional quantities, being y and x in this case. Essentially, y/x will always equal 20, the constant of proportionality.
Answer:
1. The slope of the graph is 3/1 or 3
2. The slope of the graph is 3/4
3. The slope of the points is 2
4. The slope of the points is Undefined
5. The slope of the graph is 1
6. The slope of the points is -1/4
Step-by-step explanation:
To find the slope of the graph you use rise over run
To find the slope of the points you use y2-y1 over x2-x1
Hope this is very helpful!!
Answer:
exact form is x=85/6
decimal form is x=14.16 repeating
mixed number is x=14 1/6
Answer: Choice B
![x^{1/8}y^{8}](https://tex.z-dn.net/?f=x%5E%7B1%2F8%7Dy%5E%7B8%7D)
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Explanation:
The two rules we use are
![(a*b)^c = a^c*b^c](https://tex.z-dn.net/?f=%28a%2Ab%29%5Ec%20%3D%20a%5Ec%2Ab%5Ec)
![(a^b)^c = a^{b*c}](https://tex.z-dn.net/?f=%28a%5Eb%29%5Ec%20%3D%20a%5E%7Bb%2Ac%7D)
When applying the first rule to the expression your teacher gave you, we can say that:
![\left(x^{1/4}y^{16}\right)^{1/2} = \left(x^{1/4}\right)^{1/2}*\left(y^{16}\right)^{1/2}](https://tex.z-dn.net/?f=%5Cleft%28x%5E%7B1%2F4%7Dy%5E%7B16%7D%5Cright%29%5E%7B1%2F2%7D%20%3D%20%5Cleft%28x%5E%7B1%2F4%7D%5Cright%29%5E%7B1%2F2%7D%2A%5Cleft%28y%5E%7B16%7D%5Cright%29%5E%7B1%2F2%7D)
Then applying the second rule lets us say
![\left(x^{1/4}\right)^{1/2}*\left(y^{16}\right)^{1/2} = x^{1/4*1/2}*y^{16*1/2} = x^{1/8}y^{8}](https://tex.z-dn.net/?f=%5Cleft%28x%5E%7B1%2F4%7D%5Cright%29%5E%7B1%2F2%7D%2A%5Cleft%28y%5E%7B16%7D%5Cright%29%5E%7B1%2F2%7D%20%3D%20x%5E%7B1%2F4%2A1%2F2%7D%2Ay%5E%7B16%2A1%2F2%7D%20%3D%20x%5E%7B1%2F8%7Dy%5E%7B8%7D)
Therefore,
![\left(x^{1/4}y^{16}\right)^{1/2} = x^{1/8}y^{8}](https://tex.z-dn.net/?f=%5Cleft%28x%5E%7B1%2F4%7Dy%5E%7B16%7D%5Cright%29%5E%7B1%2F2%7D%20%20%3D%20x%5E%7B1%2F8%7Dy%5E%7B8%7D)
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In short, we just multiplied each exponent inside by the outer exponent 1/2.
So that explains why the exponents go from {1/4,16} to {1/8,8} for x and y in that exact order.
Answer:
r = 2x + 7
Step-by-step explanation:
get r on one side
8x + 12 + 16 = 4r
divide both sides by 4 to get r by itself
8x/4 + 12/4 + 16/4 = 4r/4
2x + 3 + 4 = r
2x + 7 = r
or
r = 2x + 7