Answer:
3.471 + 7.2516 x
Step-by-step explanation:
Given the data:
(1,3) (2,0) (5,-8) (9, -25) .
X:
1
2
5
9
Y:
3
0
-8
-25
The line of best fit for the data given can be obtained using an online regression calculator :
The equation of best fit for the data is thus;
Best fit equation; y = -3.471 + 7.2516x
Intercept = - 3.471 ;
Slope = 7.2516
Distance formula : d = sqrt (x2 - x1)^2 + (y2 - y1)^2
(-5,-9)...x1 = -5, and y1 = -9
(-5,13)...x2 = -5 and y2 = 13
now we sub and solve
d = sqrt (-5 - (-5)^2 + (13 - (-9)^2
d = sqrt (-5 + 5)^2 + (13 + 9)^2
d = sqrt (0^2 + 22^2)
d = sqrt (484)
d = 22 <==
Let the number of coats Michael has = x
As given, Minnie gathers 3 times as many coats as Michael
So, Minnie has = 3x
Total number of coats = 52
Equation becomes,



Hence, Michael contributed 13 coats.
Starting off with the polynomial in standard form would be extremely difficult, but we can construct one fairly easily with the zeroes we've been given.
We know from the given zeroes that our function has the value 0 when x = 1, x = -2, and x = 2. Manipulating each equation, we can rewrite them as x - 1 = 0, x + 2 = 0, and x - 2 = 0. To construct our polynomial, we simply use all three of the expressions on the left side of the equation as factors and multiply them together, obtaining:

Notice that we can easily obtain each our three zeroes by dividing both sides by the two other factors. From here, we just need to expand the left-hand side of the equation. I'll show the work required here:
=0\\ (x^2-x+2x-2)(x-2)=0\\ (x^2+x-2)(x-2)=0\\ (x^2+x-2)x-(x^2+x-2)2=0\\ x^3+x^2-2x-(2x^2+2x-4)=0\\ x^3+x^2-2x-2x^2-2x+4=0\\ x^3+(x^2-2x^2)+(-2x-2x)+4=0\\ x^3-x^2-4x+4=0\\](https://tex.z-dn.net/?f=%28x-1%29%28x%2B2%29%28x-2%29%3D0%5C%5C%0A%5Cbig%5B%28x-1%29x%2B%28x-1%292%5Cbig%5D%28x-2%29%3D0%5C%5C%0A%28x%5E2-x%2B2x-2%29%28x-2%29%3D0%5C%5C%0A%28x%5E2%2Bx-2%29%28x-2%29%3D0%5C%5C%0A%28x%5E2%2Bx-2%29x-%28x%5E2%2Bx-2%292%3D0%5C%5C%0Ax%5E3%2Bx%5E2-2x-%282x%5E2%2B2x-4%29%3D0%5C%5C%0Ax%5E3%2Bx%5E2-2x-2x%5E2-2x%2B4%3D0%5C%5C%0Ax%5E3%2B%28x%5E2-2x%5E2%29%2B%28-2x-2x%29%2B4%3D0%5C%5C%0Ax%5E3-x%5E2-4x%2B4%3D0%5C%5C)
So, in standard form, our cubic polynomial would be
Q1 shows the position of the first 25% of the data set. Since Q1 = 110, 25% of the electricians had a score of 110 or less.