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lina2011 [118]
3 years ago
15

How to solve polynomial by factoring and using the zero product principle for x^3+3x^2=4x+12

Mathematics
1 answer:
Lady_Fox [76]3 years ago
3 0

Answer:

The solutions to the equation are -3,-2,2

Step-by-step explanation:

x^3+3x^2=4x+12

Subtract 4x +12 from each side

x^3+3x^2-4x-12=4x+12-4x-12

x^3+3x^2-4x-12=0

I will use factoring by grouping

x^3+3x^2     -4x-12=0

I will factor out x^2 from the first group and -4 from the second group

x^2 (x+3) -4(x+3) =0

Now we can factor out (x+3)

(x+3) (x^2-4) =0

We can use the zero product principle since the right hand side is equal to 0

x+3 =0            x^2-4 =0

x+3-3=0-3        x^2 -4+4=0+4

x=-3                    x^2=4

                           Take the square root of each side

                            sqrt(x^2) = sqrt(4)

                                      x=±2

The solutions to the equation are -3,-2,2

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A rocket carrying fireworks is launched from a hill 60 feet above a lake. The rocket will fall into the lake after exploding at
castortr0y [4]

Answer:

<h3>A) 204m</h3><h3>B) 188m</h3>

Step-by-step explanation:

Given the rocket's height above the surface of the lake given by the function h(t) = -16t^2 + 96t + 60

The velocity of the rocket at its maximum height is zero

v = dh/dt = -32t + 96t

At the maximum height, v  = 0

0 = -32t + 96t

32t = 96

t = 96/32

t = 3secs

Substitute t = 3 into the modeled function to get the maximum height

h(3) = -16(3)^2 + 96(3) + 60

h(3) = -16(9)+ 288 + 60

h(3) = -144+ 288 + 60

h(3) = 144 + 60

h(3) = 204

Hence the maximum height reached by the rocket is 204m

Get the height after 2 secs

h(t) = -16t^2 + 96t + 60

when t = 2

h(2) = -16(2)^2 + 96(2) + 60

h(2) = -64+ 192+ 60

h(2) = -4 + 192

h(2) = 188m

Hence the height of the rocket after 2 secs is 188m

3 0
3 years ago
Pls answer i need answer fast
puteri [66]

Answer:

-24

Step-by-step explanation:

Given expression:

      3z (2y - 4)²

  z = -2 and y = 3

To solve this problem, simply substitute:

       3z (2y - 4)² = 3(-2){2(3) - 4}²

                           = -6(6-4)²

                           = -6 (2)²

                          = -6 x 4

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3 years ago
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I = prt
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3 years ago
Last year, Nicholas started babysitting to earn extra spending money. Over the summer, he tracked how much money he earned at ea
Ierofanga [76]

Answer:

25%

Step-by-step explanation:

The 5 values of the given box plot are;

The minimum value = 20

The first quartile, the 25th percentile point, Q₁ = 25

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The range = The maximum value - The minimum value

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We note that Nicholas earned $25 or less from the minimum value up to first quartile, Q₁, which is the 25th percentile point, where we have 25 percent of the data points

Therefore, the percent of the time Nicholas earned $25 or less is 25 percent of the time.

8 0
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Answer:

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x/7 = -8

Multiply each side by 7

x/7 *7 = -8*7

x = -56

8 0
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