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2 years ago

Any suggestions or answers

Mathematics

1 answer:

tatiyna2 years ago

6 0

Answer:

The correct answer is A) $7.00

Step-by-step explanation:

In order to determine that, you can use any two points and the slope formula. For the purpose of this, we'll use (1, 39) and (3, 53)

m(slope) = (y2 - y1)/(x2 - x1)

m = (53 - 39)/(3 - 1)

m = 14/2

m = 7

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Part 2) The focus is the point (-82.75,-9)

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Step-by-step explanation:

step 1

Find the vertex

we know that

The equation of a horizontal parabola in the standard form is equal to

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

where

p≠ 0.

(h,k) is the vertex

(h + p, k) is the focus

x=h-p is the directrix

In this problem we have

$x=y^{2} +18y-2$

Convert to standard form

$x+2=y^{2} +18y$

$x+2+81=y^{2} +18y+81$

$x+83=(y+9)^{2}$

This is a horizontal parabola open to the right

(h,k) is the point (-83,-9)

The vertex is the point (-83,-9)

step 2

we have

$x+83=(y+9)^{2}$

Find the value of p

$4p=1$

$p=1/4$

Find the focus

(h + p, k) is the focus

substitute

(-83+1/4,-9)

The focus is the point (-82.75,-9)

step 3

Find the directrix

The directrix of a horizontal parabola is

$x=h-p$

substitute

$x=-83-1/4$

$x=-83.25$

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