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2 years ago

Write an equation of the line in slope-intercept form that passes through (-3,5) and is perpendicular to y = -3x- 1

Mathematics

1 answer:

inna [77]2 years ago

6 0

9514 1404 393

Answer:

y = 1/3x +6

Step-by-step explanation:

The slope of the given line is the coefficient of x, -3. The slope of the perpendicular line will be the opposite reciprocal of that:

-1/(-3) = 1/3

The point-slope equation is then ...

y -k = m(x -h) . . . . . for line of slope m through point (h, k)

Here, we have m = 1/3, (h, k) = (-3, 5), so the point-slope equation is ...

y -5 = 1/3(x +3)

y = 1/3x + 1 + 5 . . . . eliminate parentheses, add 5

y = 1/3x +6 . . . . slope-intercept equation of the line

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xenn [34]

Answer:

Vertex form

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Standard form;

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Step-by-step explanation:

Mathematically, we have the vertex form as

y = a(x-h)^2 + k

(h,k) represents the vertex

We have h as -3 and k as 10

y = a(x+3)^2 + 10

To get a, we substitute any of the points

Let us use (-1,-6)

-6 = a(-1+3)^2 + 10

-6-10 = 4a

4a = -16

a = -16/4

a = -4

So we have the equation as;

y = -4(x+3)^2 + 10

For the standard form;

We expand the vertex form;

y = -4(x + 3)(x + 3) + 10

y = -4(x^2 + 6x + 9) + 10

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Answer:

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Step-by-step explanation:

The attachment shows the steps.

quotient: 10x +16

remainder: 28x^2 +10x +22

_____

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What is the surface area of a rectangular prism with square bases wirh measurements a= 5 cm ,b= 7cm

vazorg [7]

Answer:

190 cm^2

Step-by-step explanation:

There are 2 congruent square bases: 5 cm * 5 cm * 2 = 50 cm^2

There are 4 congruent rectangular sides: 5 cm * 7 cm * 4 = 140 cm^2

Total surface area: 50 cm^2 + 140 cm^2 = 190 cm^2

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