Find the length of the segment ab if points a and b are the intersection points of the parabolas with equations y=−x^2+9 and y=2x^2−3 .

The length of the segment AB is √48

Step-by-step explanation:

Given the two equations, the idea is to find the solution to the system

y = x² + 9

y = 2x² - 3

you can use the equality method to find the "x" and "y" of the solution.

x² + 9 = 2x² - 3 ⇒ x² - 2x² = -3 - 9 ⇒ -x² = -12 ⇒ x² = 12 ⇒ x = ±√12.

With this value we return to the original equations and replace it to find "y" values.

y = (±√12)² + 9 ⇒ y = 21

The solutions to the system are (-√12, 21) and (√12, 21). Now you need to find the distance between this points.

d= √[(x2-x1)² + (y2-y1)²] ⇒ d = √48.

The length of the segment AB is √48.

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right

i was unable to find the answer. good