71 and 72 please help.

Mathematics

1 answer:

Hitman42 [59]3 years ago

5 0

71) The triangle is isos. so the base angles are congruent

2a+b=5b-3a
5a=4b

The angles of a triangle all add up to 180

180=5a -2b + 2a +b + 5b -3a
180=4a+4b

Substitute 4b with 5a

180=4a+5a
180=9a
a=20

And substitute a into the equation: 5a=4b to solve for b and solve for the measurements of the angles

72) Angles that are supplementary add up to 180

8(y-x)+124=180
9x-2y+124=180

8x-8y=56
(9x-2y=56)4

Use elimination to solve for the variables

8x-8y=56
-(36x-8y=224)
-28x=-168
x=48

Substitute x into the other equation to solve for y and find the measurements of the angles

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The focus of a parabola is located at (4,0), and the directrix is located at x =-4. Which equation represents the parabola?

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Answer:

Step-by-step explanation:

One of the important things to remember about parabolas is that the vertex is directly in between the focus and the directrix. Our focus is at (4, 0) and the directrix is at (-4, 0), so that means that the vertex (h, k) is at the origin (0, 0). Another important thing to remember is that the distance between either the vertex and the focus or the vertex and the directrix is the p value, the value that tells us how stretched or compressed the parabola is. Another thing to remember is that a parabola will always wrap itself around the focus away from the directrix. So here's what we know then:

Our parabola opens to the right, the equation for that is

$(y-k)^2=4p(x-h)$ ,