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kramer
3 years ago
14

Simplify (x+4)(x^2-6x

Mathematics
1 answer:
lesya [120]3 years ago
4 0

Answer:

The answer is x^3 - 2x^2 - 24x

Step-by-step explanation:

(x+4)(x^2-6x)

= (x+4)(x^2 + -6x)

= (x)(x^2) + (x)(-6x) + (4)(x^2) + (4)(-6x)

=x^3 - 6x^2 + 4x^2 - 24x

=x^3 - 2x^2 - 24x

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Carlos is draining an aquarium. The graph shows the amount of water ( in liters) in the aquarium versus time ( in minutes
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Using a linear function, we have that:

a) The amount of water in the aquarium at 0 minutes is of 300 liters.

b) As time increases, the amount of water decreases at a rate of 60 liters per minute.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = ax + b

In which:

  • a is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, we have that the y-intercept is of 300, hence the amount of water in the aquarium at 0 minutes is of 300 liters.

The amount <u>decreases 60 liters in a minute,</u> hence:

As time increases, the amount of water decreases at a rate of 60 liters per minute.

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1 year ago
A bookmark has a perimeter of 46 centimeters and an area of 102 square centimeters. What are the dimensions of the bookmark?
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Answer:

  6 cm by 17 cm

Step-by-step explanation:

The area is the product of the dimensions; the perimeter is double the sum of the dimensions.

So, we want to find two numbers whose product is 102 and whose sum is 23.

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3 years ago
For all values of x
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Answer:

A.) gf(x) = 3x^2 + 12x + 9

B.) g'(x) = 2

Step-by-step explanation:

A.) The two given functions are:

f(x) = (x + 2)^2 and g(x) = 3(x - 1)

Open the bracket of the two functions

f(x) = (x + 2)^2

f(x) = x^2 + 2x + 2x + 4

f(x) = x^2 + 4x + 4

and

g(x) = 3(x - 1)

g(x) = 3x - 3

To find gf(x), substitute f(x) for x in g(x)

gf(x) = 3( x^2 + 4x + 4 ) - 3

gf(x) = 3x^2 + 12x + 12 - 3

gf(x) = 3x^2 + 12x + 9

Where

a = 3, b = 12, c = 9

B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)

To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula

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X = 3y + 3

Make y the subject of formula

3y = x - 3

Y = x/3 - 3/3

Y = x/3 - 1

Therefore, g'(x) = x/3 - 1

For g'(12), substitute 12 for x in g' (x)

g'(x) = 12/4 - 1

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g'(x) = 2.

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