Acandle burned at a steady rate. after 38 minutes, the candle was 11.2 inches tall. eighteen minutes later, it was 10.75 inches tall. use an equation in point-slope form to determine the height of the candle after 4 hours. round the answer to the tenth place if necessary.

Let us take time by x variable and height of the candle by y variable.

We can setup two coordinates form the given statements:

After 38 minutes, the candle was 11.2 inches tall : (38, 11.2)

Eighteen minutes later, it was 10.75 inches tall : (56,10.75).

We need to write slope -intercept form of the equation first.

Slope-intercept form is :

y-y1 = m(x-x1).

In order to find slope-intercept form we need to find the slope of the given equation.

Slope between (38, 11.2) and (56, 10.75) points :

Let us apply slope-intercept form y-y1 = m(x-x1).

Now, we need to find the height of the candle after 4 hours.

We took time in minutes.

Therefore, 4 hours = 4× 60 = 240 minutes.

In order to find the height of the candle after 4 hours, we need to plug x=240 in above slope-intercept form.

y- 11.2 = -0.025 (240-38)

y-11.2 = -0.025 ( 202)

y-11.2 = -5.05

Adding 11.2 on both sides, we get

y-11.2+11.2 = -5.05+11.2

y = 6.15

We need to round it to the tenth place.

Therefore, y = 6.15.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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step-by-step explanation:

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