Answer:
The correct option is;
C. The pattern is random, indicating a good fit for a linear model
Step-by-step explanation:
A graph that has the residuals (the difference between the value observed and the value expected (regression analysis) on the vertical axis and the variable that is not affected by the other variables (independent variable) on the x or horizontal axis is known as a residual plot
A linear regression model is suited in a situation where the points are dispersed randomly on both sides of the horizontal axis
Therefore, given that the first point is below the horizontal axis and the next point is above the horizontal axis, while the third and the fourth points are below the horizontal axis, the fifth, sixth, and seventh points are above the horizontal axis and the eighth point is below the horizontal axis, the points are random around the horizontal axis, indicating the suitability of a linear regression model.
Ok, I'm going to start off saying there is probably an easier way of doing this that's right in front of my face, but I can't see it so I'm going to use Heron's formula, which is A=√[s(s-a)(s-b)(s-c)] where A is the area, s is the semiperimeter (half of the perimeter), and a, b, and c are the side lengths.
Substitute the known values into the formula:
x√10=√{[(x+x+1+2x-1)/2][({x+x+1+2x-1}/2)-x][({x+x+1+2x-1}/2)-(x+1)][({x+x+1+2x-1}/2)-(2x-1)]}
Simplify:
<span>x√10=√{[4x/2][(4x/2)-x][(4x/2)-(x+1)][(4x/2)-(2x-1)]}</span>
<span>x√10=√[2x(2x-x)(2x-x-1)(2x-2x+1)]</span>
<span>x√10=√[2x(x)(x-1)(1)]</span>
<span>x√10=√[2x²(x-1)]</span>
<span>x√10=√(2x³-2x²)</span>
<span>10x²=2x³-2x²</span>
<span>2x³-12x²=0</span>
<span>2x²(x-6)=0</span>
<span>2x²=0 or x-6=0</span>
<span>x=0 or x=6</span>
<span>Therefore, x=6 (you can't have a length of 0).</span>
If two sides of a right triangle are x and y, the hypotenuse, h is:
h^2=x^2+y^2, in this case x and y are 39 and 52 respectively so:
h^2=39^2+52^2
h^2=1521+2704
h^2=4225
h=√4225
h=65 in
So the hypotenuse is 65 inches.
