Mathematics, 04.09.2020 04:01 Paigex3

Write the equation of the line in slope intercept form that passes through the given point and satisfies the given condition. (-3,-5); parallel to y=-4x+1

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Answer from: ccory0626

y=-4x-17

Step-by-step explanation:

So we want a line that passes through (-3,-5) and is parallel to y=-4x+1.

Recall that parallel lines have the same slope. This means that our new line must also have a slope of -4.

And with that, we can write our equation by using the point-slope form. The point-slope form is:

y-y_1=m(x-x_1)

Let m be -4 and let's let (-3,-5) be x₁ and y₁. Thus:

y-(-5)=-4(x-(-3))

Simplify:

y+5=-4(x+3)

Distribute the right:

y+5=-4x-12

Subtract 5 from both sides:

y=-4x-17

And we're done!

Answer from: imello51

y = -4x-17

Step-by-step explanation:

y=-4x+1

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is -4

Parallel lines have the same slope

Using the slope intercept form

y = -4x+b

Substituting the point into the equation

-5 = -4(-3) +b

-5 = 12+b

Subtract 12 from each side

-5-12 = b

-17 =b

y = -4x-17

Answer from: Quest

b. the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

so the change in y-value for function f is (6 )) = 9.

the table tells us

g(-2) = 1g(1) = 31

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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