Answer:
Step-by-step explanation:
Midpoint Theorem: The line joining the midpoints of two sides of the triangle is half of the length of the third side and parallel to it.
From the given figure we can see that BE is the line segment joining midpoints of two sides of the triangle. This means that
[ By midpoint theorem]
Substituting values of the lengths of BE and CD
Simplifying and solving for x.
Subtracting both sides by 2
∴
Your numbers are all over the place, I will assume that you are saying that the slope is 13.
Looking at the formula for calculating slope/gradient, it is Rise/Run.
Rise/Run = y2 - y1 divided by x2 - x1. The reason for this is because if you minus one y value from the other y value you get the difference in values which is the rise, and if you minus one x value from the other x value you get the difference in value which is the run.
So by using this formula, you get:
(7 - 6) / (v - 9) = 13
Therefore 1/(v - 9) = 13
If you multiply both sides by (v-9), you get 1= 13v - 117
you rearrange it to 13v = 118
If you divide by 13, you get your answer = 9.0769
You can check your answer by putting this value back into the gradient formula.
(7-6)/(9.0769-9)
=13.004
<h2>
Answer with explanation:</h2>
As per given , we have
Sample size : n= 5
Degree pf freedom = : df= 5-1=4
Significance level for 90% confidence = 
Using t-value table , t-critical value for 90% confidence:
Margin of error of 
: 
Interpretation : The repair cost will be within $12.39 of the real population mean value 90% of the time.
Answer:
Step-by-step explanation:
Represent the length of one side of the base be s and the height by h. Then the volume of the box is V = s^2*h; this is to be maximized.
The constraints are as follows: 2s + h = 114 in. Solving for h, we get 114 - 2s = h.
Substituting 114 - 2s for h in the volume formula, we obtain:
V = s^2*(114 - 2s), or V = 114s^2 - 2s^3, or V = 2*(s^2)(57 - s)
This is to be maximized. To accomplish this, find the first derivative of this formula for V, set the result equal to 0 and solve for s:
dV
----- = 2[(s^2)(-1) + (57 - s)(2s)] = 0 = 2s^2(-1) + 114s - 2s^2
ds
Simplifying this, we get dV/ds = -4s^2 + 114s = 0. Then either s = 28.5 or s = 0.
Then the area of the base is 28.5^2 in^2 and the height is 114 - 2(28.5) = 57 in
and the volume is V = s^2(h) = 46,298.25 in^3
