If measure of angle p=(10x-2),measure of angle o=(3x+9) , and measure of angle q=(3x-3) , list the lengths of the sides of triangle opq from longest to shortest.

OQ > PQ > OP

Step-by-step explanation:

In this question measure of all angles in a triangle has been given.

m∠ p = (10x - 2)

m∠ q = (3x - 3)

m∠ o = (3x + 9)

Since total of all angles is 180°, so we will equate the total of all angles to 180°

∠p + ∠q + ∠o = 180°

(10x - 2) + (3x - 3) + (3x + 9) = 180°

(10x + 3x + 3x) -2 - 3 + 9 = 180

16x - (2 + 3 - 9) = 180°

16x + 4 = 180

16x = 180 - 4

16x = 176

x =

Now we will find the measure of each angle.

∠p = (10x - 2) = 10×11 - 2 = (110 - 2) = 108°

∠q = (3x - 3) = 3×11 - 3 = (33 - 3) = 30°

∠o = (3x + 9) = 3×11 + 9 = (33 + 9) = 42°

As we know in a triangle, angle opposite to the largest side is largest and angle opposite side is the smallest.

Since ∠p > ∠o > ∠q

Therefore, in Δ OPQ opposite sides to these angles will be in the same ratio.

OQ > PQ > OP

$12. that is my answer.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1