All categories

3 years ago

What is the expression in factored form? 9x^2 - 12x + 4

Mathematics

2 answers:

spayn [35]3 years ago

8 0

Answer:

C. (3x - 2)²

Step-by-step explanation:

The square of a binomial can be written as (a + b)². If you expand this formula, you get

(a + b)(a + b). Use F.O.I.L. to multiply this out..

F - stands for 'Firsts' (the first values in each set of parenthesis)

O - stands for 'Outsides' ( the first value in the first set of parenthesis, and the

second value in the second set of parenthesis)

I - stands for 'Insides' ( the second value in the first set of parenthesis, and

the first value in the second set of parenthesis)

L - stands for 'Lasts' ( the second value in each set of parenthesis)

This is the order you multiply them in...so we get

F - a² (a times a)

O - ab

I - ba (which we rewrite as ab, since order doesn't matter when multiplying)

L - b²

We add them together to get a² + ab + ab + b²

which simplifies to a² + 2ab + b²

Read this as, the square of the first term in the parenthesis (a²), plus twice the product of the terms (2ab is twice the product of a and b), plus the square of the last term in the parenthesis)

So to solve this we need to factor 9x² - 12x + 4

Look at the bold paragraph above and work backwards.

Take the square root of the term 9x², which is 3x. That goes in the first value of the parenthesis, so we have

(3x + b)²

We know that -12x is twice the product of the two terms, so we divide by 2 to see the product of the two terms.

-12x/2 = -6x,

We know one term, so divide -6x by the first term, 3x, to find the second term.

-6x/3x = -2

So the last term in our set of parenthesis is -2, so we have

(3x - 2)²

Aleonysh [2.5K]3 years ago

5 0

The answer is (3x-2)^2

You might be interested in

How can you convert 0.23 into a fraction?

madreJ [45]

Answer:

First take 0.23 as 0.23/1

Then Multiply the numerator and denominator by any number, Let us say 100

So it becomes,

0.23 x 100/100

=> 23/100

4 0

3 years ago

Arthur tells you that he is thinking of an irrational number between 4 and 5, and he wants you to guess what it is. One possibil

Naddika [18.5K]

Answer:

$\sqrt{20}$

Step-by-step explanation:

Square root of 9 is 3

20 is 4.472135955

27 is 5.19615242271

4.5 is intantly wrong because it is rational.

3 0

2 years ago

The Volunteer Club raked leaves at several senior citizens’ homes in the neighborhood. If each group of three students could rem

ozzi

12 students would create 4 groups, if they get 8 cubic meters per hour and they have 5 hours, the equasion would look like: (8*5)*4)=160. They would clear 160 cubic meters in 5 hours.

7 0

3 years ago

A population has the following characteristics. (a) A total of 75% of the population survives the first year. Of that 75%, 25% s

Artemon [7]

Answer:

$= \left[\begin{array}{ccc}1344\\84\\28\end{array}\right] \left \begin{array}{ccc}{0 \ \leq age \leq 1 }\\{ 1 \ \leq age \leq 2 }\\{2 \ \leq age \leq 3}\end{array}\right$

i.e after the first year ;

there 1344 members in the first age class

84 members for the second age class; and

28 members for the third age class

Step-by-step explanation:

We can deduce that the age distribution vector x represents the number of population members for each age class; Given that in each class of age there are 112 members present.

The current age distribution vector is as follows:

$x = \left[\begin{array}{ccc}1&1&2\\1&1&2\\1&1&2\end{array}\right] \left[\begin{array}{ccc}{0 \ \leq age \leq 1 }\\{ 0 \ \leq age \leq 2 }\\{0 \ \leq age \leq 3}\end{array}\right]$

Also , the age transition matrix is as follows:

$L = \left[\begin{array}{ccc}3&6&3\\0.75&0&0 \\0&0.25&0\end{array}\right]$

After 1 year ; the age distribution vector will be :

$x_2 =Lx_1 = \left[\begin{array}{ccc}3&6&3\\0.75&0&0 \\0&0.25&0\end{array}\right] \left[\begin{array}{ccc}1&1&2\\1&1&2\\1&1&2\end{array}\right]$

$= \left[\begin{array}{ccc}1344\\84\\28\end{array}\right] \left \begin{array}{ccc}{0 \ \leq age \leq 1 }\\{ 1 \ \leq age \leq 2 }\\{2 \ \leq age \leq 3}\end{array}\right$

6 0

2 years ago

PLEASE I NEED HELP!!!!!!!!

Yanka [14]

Answer:

1) x= 3i, x= - 3i

2) x= +i $\sqrt{7}$ , x = - i

Step-by-step explanation:

1) x^2+9=0

(x+3i)(x-3i)=0

x= 3i, x=-3i

2) x^2-4=-11

x^2=-7

x= ±i $\sqrt{7}$

x= +i $\sqrt{7}$ , x = - i

hope this helps!! :))

7 0

2 years ago