John is six year older than Bill. If their combined

Question 1,2, and 3 how do i factor those? Can you show the work and explain how?

DiKsa [7]

1: $3n^{2}+9n+6$

notice that each part is divisible by 3

$3n^{2}$ ÷ 3 = $n^{2}$

9n ÷ 3 = 3n

6 ÷ 3 = 2

so it becomes $3(n^{2} +3n+2)$

3n can be rewritten as 2n+n

-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)

which would get you

$3(n^{2} +2n+n+2)$

Now that it's rewritten, you can factor out n + 2 from the equation.

the answer is

3(n+2)(n+1)

And you can check that by multiplying (n+2)(n+1) which is $n^{2} +2n+n+2$ and then each of those by 3, which is $3n^{2} +6n+3n+6$ or $3n^{2}+9n+6$ , our origional equation

2: $28+x^{2} -11x$

So I rewrote this as $x^{2} -11x+28$ (it's the same thing, just reordered using the commutative property)

now -11x can be rewritten as -4x-7x

(remember, the two numbers should multiply to equal 28, which is our constant.)

$x^{2} -4x-7x+28$

now we can factor out x from the first expression and -7 from the second

$x(x-4)-7(x-4)$

and lastly you factor out x-4,

which would give you

(x-4)(x-7)

Make sure to check your work and make sure it multiplies to $x^{2} -11x+28$

3: $9x^{2} -12x+4$

The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12

So if you rewrite 9 as $3^{2}$ and 4 as $2^{2}$ , the equation becomes

$3^{2} x^{2} -12x+2^{2}$

now that $3^{2} x^{2}$ is ugly so it can be turned into $(3x)^{2}$

and -12x can be rewritten as $-2*3x*2$

so our equation now looks like $(3x)^2-2*3x*2+2^{2}$

There's a rule that says $a^{2} -2ab+b^{2} = (a-b)^{2}$

In our case, a=3x and b=2

so the final answer is

$(3x-2)^2$

5 0

3 years ago

It took 7 hours to mow 4 lawns. How many lawns can I mow in 35 hours? Confused.. Please Check!!!

blondinia [14]

7 35 4x35/7= 20 lawns
4 x

6 0

4 years ago

Compare the graph of f (x) with the graph of k (x) = 2 (x-8)2

Bingel [31]

Answer:

one is not linear

Step-by-step explanation:

7 0

3 years ago

Given a right triangle with sides a = 3 , b = 4, and c = 5. Find the missing side c of another right triangle with a = 6 and b =

horsena [70]

c = 10

Step-by-step explanation:

We can find out the missing side of a right triangle by using the Pythagorean theorem.

The Pythagorean theorem is...

$a^2+b^2=c^2$

We can even double check the first problem by plugging in everything into the theorem and solving, everything will come out correct. We can plug in the numbers from the second problem into the theorem and find c, also please note that the hypotenuse of a triangle will always be c. It doesn't matter which you put in for a or b, but since the problem gives us which one is a and which one is b, I'll just be plugging it in like that.

$6^2+8^2=c^2$

$36+64=c^2$

$100=c^2$

A lot of people will stop here and think that the answer is 100, but you need to find the square root of 100, since c is squared. The square root of 100 is 10, so...

c = 10

7 0

3 years ago

Https://www.hmhco.com/one/assessment/#/formativeLive Assessment/

GuDViN [60]

A. equation: y = -3x - 2

B. y-intercept: -2

Solution:

Given that,

Write the equation 12x = - 4y - 8 in slope-intercept form

The slope intercept form is given as:

$y = mx + c$

Where,

m is the slope and "c" is the y intercept

From given

$12x = -4y - 8\\\\Rewrite\\\\-4y-8 = 12x\\\\Move\ the\ constant\ to\ right\ side\\\\-4y = 12x + 8\\\\y = \frac{12x}{-4} + \frac{8}{-4}\\\\y = -3x -2$

Thus the slope intercept form is found

Comparing with y = mx + c ,

c = -2

Thus the y intercept is -2

3 0

3 years ago