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kvasek [131]
3 years ago
14

19. Which of the following is a correct

Mathematics
1 answer:
svp [43]3 years ago
8 0

Answer:

b.

Step-by-step explanation:

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Stuck on this it's Algebra 2 12x^{3} -3x^{2} =0
olchik [2.2K]

Answer:

Exact Form:

x = 0, 1/4

Decimal Form:

x = 0, 0.25

Step-by-step explanation:

<u>Step 1: Factor 3x^2 out of 12x^3 - 3x^2 </u>

Factor 3x^2 out of 12x^3:

<em> 3x^2 (4x) - 3x^2 = 0</em>

Factor 3x^2 out of -3x^2:

<em> 3x^2 (4x) + 3x^2 (-1)  = 0</em>

Factor 3x^2 out of -3x^2 <em>(4x) + 3x^2 (-1) </em>:

<em> 3x^2 (4x-1) = 0</em>

<em />

<u>Step 2: Divide each term by 3 and simpify</u>

<u></u>

divide each term in 3x^2 (4x-1) = 0 by 3.

3x^2 (4x-1) / 3 = 0 / 3

<em>simplify 3x^2 (4x-1) / 3.</em>

<em />

<em>Cancel the common factors.</em>

<u><em>3</em></u><em> </em>x^2 (4x -1) / <em><u>3</u></em> = 0 / 3

divide x^2 (4x-1) by 1.

x^2 (4x-1) / 3 = 0 / 3

Apply the Distributive Property

Reorder.

Rewrite using the commutative property of multiplication.

4x^2 x + x^2 · -1 = 0 / 3

Move -1  to the left of  x^2

4x^2 x -1 · x^2  = 0 / 3

Simplify each term

multiply x^2 by x^2 by adding the exponents.

Move x

4 (x · x^2) -1 · x^2= 0 / 3

Multiply x by x^2

Rase x to the power of 1.

4 (x^1 · x^2) -1 · x^2= 0 / 3

Use the power rule a^m a^n = a^m+n to combine exponents

4x^1+2 -1 · x^2= 0 / 3

Add 1 and 2.

4x^3 -1 · x^2= 0 / 3

Rewrite -1x^2  as -x^2.

4x^3 -x^2= 0 / 3

Divide 0 by 3

4x^3 -x^2= 0

<u>Step 3: Factor x^2 out of 4x^3 -x^2.</u>

Factor x^2 out of 4x^3

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

Factor x^2 out of -x^2

x^2 (4x) x^2 · -1 = 0

Factor x^2 out of x^2 (4x) x^2 · -1

x^2 (4x -1) = 0

If any individual factor on the left side of the equation is equal to 0,  the entire expression will be equal to  0

x^2 = 0

4x -1 = 0

Set x^2 equal to 0 and solve for x

x = 0

Set 4x -1 equal to 0 and solve for x

x = 1/4

The final solution is all the values that make x^2 (4x-1) = 0 true

x= (0, 1/4)

6 0
3 years ago
I cannot figure out the work for this problem.
Vedmedyk [2.9K]
Your answer should be -2
Use PEMDAS if confused!
Parentheses
Exponent
Multiplication
Division
Addition
Subtraction.
You would first calculate the number in between your parentheses which would give you -1. Then do -1 to the power of 4(-1^4) which still gives you -1 and then multiply it by 2 which should give you your answer -2. :)
Hope this helps.
8 0
3 years ago
Please help me solve this I’m really struggling
NikAS [45]

Answer:

y =x^2 +8x +15

factories form

y =( x+5 )( x+3 )

x intercept where the graph meet the x axis

y = x^2 +8x +15

let y =0

0 = x^2 +8x +15

0 = ( x + 5) (x+3)

o = x+5 or 0 = x+3

-5 = x or x = - 3

x intercept

(-5;0)

(-3 ;0)

axis of symmetry : where you will cut the graph into two half

x = - b/2a

x = - 8/2(1)

x = - 8/2

x = - 4

Domain

XER

Range

y > -1

5 0
3 years ago
Help please.
gavmur [86]
I think the answer is 16.21 degrees
5 0
3 years ago
The number N of bacteria present in a culture at time t (in hours) obeys the equation N = 1000e^0.01t After how many hours will
jasenka [17]

Answer: N(t) = (2^t)*1500

Step-by-step explanation:

Let's define the hour "zero" as the initial population.

So if N(t)  is the number of bacteria after t hours, then:

N(0) = 1500.

Now, we know that the population doubles every hour, so we will have that after one hour, at t = 1

N(1) = 2*1500 = 3000

after two hours, at t = 2.

N(2) = 2*(2*1500) = (2^2)*1500

After three hours, at t = 3

N(3) = 2*(2^2)*1500 = (2^3)*1500

So we already can see the pattern, the number of bacteria after t hours will be:

N(t) = (2^t)*1500

5 0
3 years ago
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