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o-na [289]
3 years ago
14

HELP ASAP: Factor By Grouping: 12a^3 - 9a^2 + 4a - 3

Mathematics
1 answer:
MAVERICK [17]3 years ago
7 0

We have been given an expression 12a^3 - 9a^2 + 4a - 3. We are asked to factor the given expression by grouping.

First of all, we will make two groups of our expression as:

(12a^3-9a^2)+( 4a - 3)

Now we will factor of greatest common factor from each group.

(3a^2\cdot 4a-3a^2\cdot 3)+( 4a - 3)

3a^2(4a-3)+1( 4a-3)

Now we will factor out common terms (4a-3) as:

(4a-3)( 3a^2+1)

Therefore, the factorized form of our given expression would be (4a-3)( 3a^2+1).

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ABCD – FECG<br> what does (x) =
Helen [10]

9514 1404 393

Answer:

  x = 12

Step-by-step explanation:

Sides of similar figures are proportional, so ...

  AB/FE = BC/EC

  x/6 = 10/5

  x = 6·(10/5) . . . multiply by 6

  x = 12

5 0
3 years ago
This rational expression is nonequivalent. 5x / 25x^4 ; x^3 / 5x^15<br> True or false?????
FromTheMoon [43]

It is nonequivalent. Figure it out this way. Think about what number has to be multiplied by both the numerator and the denominator of \frac{5x}{25x^4} to get to \frac{x^3}{5x^15}. It has to be the samee number for the one expression to be equivalent to the other. To get from 5x to x^3, we have to multiply by 1/5x^2. When we do that we get x^3. Good. Now we have to multiply the denominator by the same thing, 1/5x^2. 25x^4(\frac{1}{5}x^2)=5x^6. As you can see, they are not equivalent.

8 0
3 years ago
Read 2 more answers
I need help please
Dima020 [189]

It's either A or D.

6 0
3 years ago
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Mrs.Stone is three times older than her younger daughter, Joyce, but only two times older than her older daughter, Alex. How old
olchik [2.2K]

Answer:

54 years

Step-by-step explanation:

Joyce age = x

Alex age = y

3x = 2y - - - (1)

y - 9 = 2(x - 9)

y - 9 = 2x - 18

-9 + 18 = 2x - y

9 = 2x - y

y = 2x - 9 - - (2)

3x = 2y

3x = 2(2x - 9)

3x = 4x - 18

18 = 4x - 3x

18 = x

Hence,

Mrs stone is 3 * 18 = 54 years

5 0
2 years ago
Could someone help me rnnn?
GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola:  y=3x^2-4

Step-by-step explanation:

Given:

  • y-intercept of parabola: -4
  • parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola:  y=a(x-h)^2+k

(where (h, k) is the vertex and a is some constant)

Substitute point (0, -4) into the equation:

\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}

Substitute point (-2, 8) and ah^2+k=-4 into the equation:

\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}

Substitute point (1, -1) and ah^2+k=-4 into the equation:

\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}

Equate to find h:

\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}

Substitute found value of h into one of the equations to find a:

\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}

Substitute found values of h and a to find k:

\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}

Therefore, the equation of the parabola in vertex form is:

\implies y=3(x-0)^2-4=3x^2-4

So the vertex of the parabola is (0, -4)

5 0
2 years ago
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