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3 years ago

-4,11)(-9,6) Find x and y intercepts!! show work plzzz

Mathematics

1 answer:

iren [92.7K]3 years ago

5 0

Answer:

(-15, 0) --> x intercept

(0, 15) --> y intercept

Step-by-step explanation:

First, you need to find the equation of the line:

gradient equals 1 --> (6 - 11)/(-9 - (-4))

y = x + c

sub point (-9, 6)

6 = -9 + c

c = 6 + 9

c = 15

Equation of line: y = x + 15

x-intercept is when y = 0

0 = x + 15

x = -15 (that's the x-intercept)

(-15, 0)

y-intercept is when x = 0

y = 0 + 15

y = 15 (this is the y-intercept). The y-intercept is also the contant 'c'

(0, 15)

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Given the function f(x) = 3|x – 2| + 6, for what values of x is f(x) = 18?

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Answer:

x = - 2, x = 6

Step-by-step explanation:

Given f(x) = 18 we require to solve

3 | x - 2 | + 6 = 18 ( subtract 6 from both sides )

3 | x - 2 | = 12 ( divide both sides by 3 )

| x - 2 | = 4

The absolute value function always returns a positive value, however, the expression inside can be positive or negative, thus

x - 2 = 4 ( add 2 to both sides )

x = 6

- (x - 2) = 4

- x + 2 = 4 ( subtract 2 from both sides )

- x = 2 ( multiply both sides by - 1 )

x = - 2

As a check substitute these values into the left side of the equation and if equal to the right side then they are the solutions

x = 6 → 3|6 - 2| + 6 = 3|4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True

x = - 2 → 3|- 2 - 2| + 6 = 3|-4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True

Hence solutions are x = - 2, x = 6

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3 years ago

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Kathy wants to buy a camera with an original price of $389. The camera is on sale with a 33% discount. What is the amount of dis

Verizon [17]

Answer:

$128.37

Step-by-step explanation:

Find 33% of 389:

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The amount of the discount is $128.37

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3 years ago

The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute. At the instant when the volume of

Inessa05 [86]

Using implicit differentiation, it is found that the rate of change of the surface area of the sphere -2201.293 square centimeters per second.

<h3>What is the volume of a sphere?</h3>

The volume of a sphere, of radius r, is given by:

$V = \frac{4\pi r^3}{3}$

<h3>What is the surface area of a sphere?</h3>

The surface area of a sphere, of radius r, is given by:

$S = 4\pi r^2$

<h3>What is the rate of change?</h3>

Applying <em>implicit differentiation</em>, the rate of change of both the volume and the surface area can be found, as follows:

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

$\frac{dS}{dt} = 8\pi r\frac{dr}{dt}$

Volume of 3131 cubic centimeters, hence:

$V = \frac{4\pi r^3}{3}$

$\frac{4\pi r^3}{3} = 3131$

$4\pi r^3 = 3(3131)$

$r = \sqrt[3]{\frac{3(3131)}{4\pi}}$

$r = 9.0754$

The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute, hence:

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

$-9988 = 4\pi (9.0754)^2\frac{dr}{dt}$

$\frac{dr}{dt} = -\frac{9988}{4\pi (9.0754)^2}$

$\frac{dr}{dt} = -9.651$

Then, the <u>rate of change of the surface area</u> of the sphere is given by:

$\frac{dS}{dt} = 8\pi (9.0754)(-9.651) = -2201.293$

The rate of change of the surface area of the sphere -2201.293 square centimeters per second.

To learn more about implicit differentiation, you can take a look at brainly.com/question/25608353

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3 years ago

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Answer:

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df = 20 - 1 = 19

99% confidence interval

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