Use matrices to determine the coordinates of the vertices of the rotated figure. then graph the pre-image and the image of the same coordinate grid. (pictureprovided)

The coordinates of the vertices of the rotated figure are :

U' (1 , -6), V' (-8 , -4), W' (-5 , 7) ⇒ the right answer is figure (d)

Step-by-step explanation:

* Lets study the matrices of the Rotation by 180°  

- When we rotate a point around the origin by 180° clockwise

 or anti-clockwise, we change the sign of the x-coordinate and

 the y-coordinate of the point

- Then matrix of the rotation 180° is

* Now lets solve the problem

- We will multiply the matrix of the rotation  by each point to

 find the image of each point

- The dimension of the matrix of the rotation  is 2×2 and the

 dimension of the matrix of each point is 2×1,  then the

 dimension of the matrix of each image is 2×1

∵ Point U is (-1 , 6)

∴

∴ U' = (1 , -6)

∵ Point V is (8 , 4)

∴

∴ V' = (-8 , -4)

∵ Point W is (5 , -7)

∴

∴ W' = (-5 , 7)

* Now look to the figures to find the right answer

∵ The images of the points are U' (1 , -6), V' (-8 , -4), W' (-5 , 7)

∴ The right answer is figure (d)

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0

the homeowners insurance cost for a 115,000 wood frame house is 80,500.

step-by-step explanation:

it is given that the coverage rate for wood frame house is 0.7.

the value of wood frame house is 115,000.

.

homeowners insurance cost for a 115,000 wood frame house is

therefore the homeowners insurance cost for a 115,000 wood frame house is 80,500.