5. Simplify: -15y^2+3[-y^2-2(5-y^2)]

-6 (2 y^2 + 5)

Step-by-step explanation:

Simplify the following:

3 (-y^2 - 2 (5 - y^2)) - 15 y^2

Hint: | Distribute -2 over 5 - y^2.

-2 (5 - y^2) = 2 y^2 - 10:

3 (2 y^2 - 10 - y^2) - 15 y^2

Hint: | Group like terms in 2 y^2 - y^2 - 10.

Grouping like terms, 2 y^2 - y^2 - 10 = (2 y^2 - y^2) - 10:

3 (2 y^2 - y^2) - 10 - 15 y^2

Hint: | Combine like terms in 2 y^2 - y^2.

2 y^2 - y^2 = y^2:

3 (y^2 - 10) - 15 y^2

Hint: | Distribute 3 over y^2 - 10.

3 (y^2 - 10) = 3 y^2 - 30:

3 y^2 - 30 - 15 y^2

Hint: | Group like terms in 3 y^2 - 15 y^2 - 30.

Grouping like terms, 3 y^2 - 15 y^2 - 30 = (3 y^2 - 15 y^2) - 30:

(3 y^2 - 15 y^2) - 30

Hint: | Combine like terms in 3 y^2 - 15 y^2.

3 y^2 - 15 y^2 = -12 y^2:

-12 y^2 - 30

Hint: | Factor out the greatest common divisor of the coefficients of -12 y^2 - 30.

Factor -6 out of -12 y^2 - 30:

-6 (2 y^2 + 5)

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.