Step-by-step explanation:
P varies directly as the cubic root of Q means that:
![p = x \times \sqrt[3]{q}](https://tex.z-dn.net/?f=p%20%3D%20x%20%5Ctimes%20%20%5Csqrt%5B3%5D%7Bq%7D%20)
, where x is a real constant number.
Which means that:
![x = \frac{p}{ \sqrt[3]{q} }](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7Bp%7D%7B%20%5Csqrt%5B3%5D%7Bq%7D%20%7D%20)
for q ≠0.
So we get that for q=8,p=4 which means:
![x = \frac{4}{ \sqrt[3]{8} } = \frac{4}{2} = 2](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B4%7D%7B%20%5Csqrt%5B3%5D%7B8%7D%20%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7B2%7D%20%20%3D%202)
As a result we get that for Q=64:
![p = 2 \times \sqrt[3]{64} = 2 \times 4 = 8 \\ since \: {4}^{3} = 4 \times 4 \times 4 = \\ 16 \times 4 = 64](https://tex.z-dn.net/?f=p%20%3D%202%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B64%7D%20%20%3D%202%20%5Ctimes%204%20%3D%208%20%5C%5C%20since%20%5C%3A%20%20%7B4%7D%5E%7B3%7D%20%20%3D%204%20%5Ctimes%204%20%5Ctimes%204%20%20%3D%20%20%5C%5C%20%2016%20%5Ctimes%204%20%3D%2064)
So for q=64,p=8.
120x + 80
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The values of the variables x and y in the triangle are 1.25 and 1.75
<h3>How to determine the values of the variables x and y?</h3>
The tringle represents the given parameter
On the triangle, we have the following equivalent ratio
5 : 8 = 5 + x : 10
7 : 8 = 7 + y : 10
These are true because the horizontal lines of the triangles are parallel
So, we have
5 : 8 = 5 + x : 10
Express as fraction
5/8 = 5 + x/10
This gives
5 + x = 6.25
Solve for x
x = 1.25
Similarly, we have
7 : 8 = 7 + y : 10
So, we have
7/8 = 7 + y/10
This gives
7 + y = 10*7/8
Evaluate
7 + y = 8.75
So, we have
y = 1.75
Hence, the values of x and y are 1.25 and 1.75
Read more about triangles at
brainly.com/question/14285697
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Answer: y - 19 = 2(x - 5)
Step-by-step explanation:
The point slope form is expressed as
y - y1 = m(x - x1)
Where
m represents slope
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
The given points are (5,19) and (-5,-1)
y2 = - 1
y1 = 19
x2 = - 5
x1 = 5
Slope,m = (- 1 - 19)/(- 5 - 5) = - 20/- 10 = 2
To determine the equation, we would substitute x1 = 5, y1 = 19 and m= 2 into the point slope form equation. It becomes
y - 19 = 2(x - 5)
Its not right. because the angles are congruent to on another <span />
