Write an equation that represents the line.
Use exact numbers.

The volume of a rectangular prism is the product of the prism's dimension (i.e. length, width and height). The dimension of the rectangular prism are:

[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]

Given that:

[tex]Volume = (18x^4 + 15x^3 - 12x^2)[/tex]

First, we factor out [tex]3x^2[/tex]

[tex]Volume = 3x^2 \times (6x^2 + 5x - 4)[/tex]

Expand

[tex]Volume = 3x^2 \times (6x^2 + 8x-3x - 4)[/tex]

Factorize

[tex]Volume = 3x^2 \times (2x(3x + 4) -1(3x + 4))[/tex]

Factor out [tex]3x + 4[/tex]

[tex]Volume = 3x^2 \times ((2x -1) (3x + 4))[/tex]

Rewrite as:

[tex]Volume = 3x^2 \times (2x -1) \times (3x + 4)[/tex]

The volume of a rectangular prism is:

[tex]Volume = Length \times Width \times Height[/tex]

So; by comparison:

[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]

Read more about polynomials and volumes at:

https://brainly.com/question/2141804

Answer:

Distance = 5 units

Slope = [tex]\displaystyle\frac{4}{3}[/tex]

Step-by-step explanation:

Hi there!

1) Finding the distance of the line

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two endpoints of a line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the points (-7,2) and (-4,6):

[tex]d=\sqrt{(-4-(-7))^2+(6-2)^2}\\d=\sqrt{(-4+7)^2+(6-2)^2}\\d=\sqrt{(3)^2+(4)^2}\\d=\sqrt{9+16}\\d=\sqrt{25}\\d=5[/tex]

Therefore, the length of the line/distance of the line is 5 units.

2) Finding the slope of the line

[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the points (-7,2) and (-4,6):

[tex]m=\displaystyle\frac{6-2}{-4-(-7)}\\\\m=\displaystyle\frac{6-2}{-4+7}\\\\m=\displaystyle\frac{4}{3}[/tex]

Therefore, the slope of the line is [tex]\displaystyle\frac{4}{3}[/tex].

I hope this helps!

Answer:x_1= -1 or x_2= -6

Step-by-step explanation:

In the pictures

By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.

Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number.

These numbers are broken down into factors or divisors.

For an integer, factorization is decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number and these composing integers are called factors of that considered integers.

Given

[tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex]

Cross multiplication;

2x(x + 4) = 6(x + 2)

[tex]2x^{2} + 8x = 6x + 12\\\\2x^{2} + 8x - 6x - 12 = 0\\\\2x^{2} + 2x - 12 = 0\\\\x^{2} + x - 6 = 0[/tex]

Divide above equation by 2, we get

[tex]x^{2} + x - 6 = 0[/tex]

(x +2) (x-3)

x = -2, 3

Therefore, By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.

Find out more information about factorization here;

brainly.com/question/1863222

#SPJ2

100-15=85%=SP

[tex]\\ \sf\longmapsto 85\%\times x=20000[/tex]

[tex]\\ \sf\longmapsto \dfrac{85}{100}x=20000[/tex]

[tex]\\ \sf\longmapsto x=20000\times \dfrac{100}{85}[/tex]

[tex]\\ \sf\longmapsto x=235.2(100)[/tex]

[tex]\\ \sf\longmapsto CP=23520[/tex]

Answer:

-7

Step-by-step explanation:

-13 - (-6)

=> -13 + 6

=> -7

So Common Difference = -7

Answer: i am good,how are you?

Step-by-step explanation:

Answer:1-10 = 9 :D

Step-by-step explanation:

Answer:

It moved for 152.7 seconds

Step-by-step explanation:

Time taken/ period, T :

[tex]{ \sf{T = \frac{distance}{speed} }}[/tex]

substitute the variables:

[tex]{ \sf{T = \frac{8482}{(200 \times 1000)} }} \\ \\ { \sf{T =0.042 \: hours }}[/tex]

In seconds:

[tex]{ \sf{T = (0.042 \times 3600) \: s}} \\ { \sf{T = 152.7 \: seconds}}[/tex]

Answer: 68.25 hrs.

Step-by-step explanation:

200 Km. to miles = 124.274 miles

8482 mi/124.274 mi =

68.25 hours

Answer:5 units

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

h= 2A/a+b

Step-by-step explanation:

you know the gig

Answer:

ans is 5.

hope it will help you.

Answer:

OPTION B

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

Step-by-step explanation:

(f o g) is the same as f(g(x))

f(x) = -6x, substitute x with g(x) = -6x+5

f(g(x)) = -6g(x) = -6(-6x+5) = 36x -30

(f o g) = 36x -30

Answer:A=2 2/7

Step-by-step explanation:

Correct me if I am wrong

Answer:

12

Step-by-step explanation:

36/12=3

48/12=4

Answer:

highest common factor of 36 and 48 is 12

Step-by-step explanation:

f(g(x))=(3x+1)^2 +2(3x+1) -4

=9x^2 +6x +1 +6x +2 -4

=9x^2 +12x +(-1)

Answer:

Distance btw (-2, -2) and (8, -6) is (10, -4)

Step-by-step explanation:

I. Give (-2, -2) is A and (8, -6) is B

                     B - A = 8 - (-2) in x

                              = -6 - (-2) in y

                    So B - A = 10, -4

II. You can prove the answer by A.value + (10, -4) = B.value

Hope that help :D

Hi ;-)

[tex]\text{A}=(-2,-2) \ \text{and} \ \text{B}=(8,-6)\\\\|AB|=\sqrt{(8-(-2))^2+(-6-(-2))^2}\\\\|AB|=\sqrt{(8+2)^2+(-6+2)^2}\\\\|AB|=\sqrt{10^2+(-4)^2}\\\\|AB|=\sqrt{100+16}\\\\|AB|=\sqrt{116}\rightarrow\boxed{|AB|=2\sqrt{29}} \ (\text{because} \ 116=4\cdot29)[/tex]

Answer:

(9,2)

Step-by-step explanation:

To find the x coordinate of the midpoint, average the x coordinates of the endpoints

(14+4)/2 = 18/2 = 9

To find the y coordinate of the midpoint, average the y coordinates of the endpoints

(-8+12)/2 = 4/2 = 2

There seems to be one character missing. But I gather that f(x) needs to satisfy

• [tex]x^3[/tex] divides [tex]f(x)[/tex]

• [tex](x-1)^3[/tex] divides [tex]f(x)^2[/tex]

I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or

[tex]f(x) = x^5 + \cdots[/tex]

Since [tex]x^3[/tex] divides [tex]f(x)[/tex], and

[tex]f(x) = x^3 p(x)[/tex]

where [tex]p(x)[/tex] is degree-2, and we can write it as

[tex]f(x)=x^3 (x^2+ax+b)[/tex]

Now, we have

[tex]f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2[/tex]

so if [tex](x - 1)^3[/tex] divides [tex]f(x)^2[/tex], then [tex]p(x)[/tex] is degree-2, so [tex]p(x)^2[/tex] is degree-4, and we can write

[tex]p(x)^2 = (x-1)^3 q(x)[/tex]

where [tex]q(x)[/tex] is degree-1.

Expanding the left side gives

[tex]p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2[/tex]

and dividing by [tex](x-1)^3[/tex] leaves no remainder. If we actually compute the quotient, we wind up with

[tex]\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}[/tex]

If the remainder is supposed to be zero, then

[tex]\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}[/tex]

Adding these equations together and grouping terms, we get

[tex](a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1[/tex]

Then [tex]b=-1-a[/tex], and you can solve for a and b by substituting this into any of the three equations above. For instance,

[tex]2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1[/tex]

So, we end up with

[tex]p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}[/tex]

Answer:

40,640,000

Step-by-step explanation:

The way I solved this equation was by dividing 320,000,000 by 1,000 (to make smaller numbers). Then, I got 320,000. From here, I was able to multiply 320,000 by 127 (the number found in this specific study group) to get 40,640,000. Or, you could just multiply 320,000,000 by 0.127 (the decimal equivalent to 127/1000) to get the same answer. Please mark Brainliest if this helped :)

Answer:

40,640,000

Step-by-step explanation:

The sample size is 1000 and 127 wear contacts so

127/1000 = x/320000000

(127 * 320000000)/1000 = x

40,640,000 = x

Step-by-step explanation:

A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.

Steps:-

First put the vertices on graph and find Triangle ABC .

Then Transact it the give amount i.e 5units and get A'B'C'

Answer:

Step-by-step explanation:

11-B

Uhhhh sorry about everything else I’ll come back when I figure it out

6-D

7-C? Maybe

Answer:

Step-by-step explanation:

The correct answer is b.

27h + 16  = 178                   Subtract 16

27h = 178 -16                      Combine

27h = 162                           Divide by 27

h = 162 / 27

h = 6

Question 6

No they are not the same. They have the same terminal point but they are going in different directions. The answer is D Direction matters.

Question 7

The vectors add if as in arithmetic if they are going in the same direction.

answer C

Answer:

0.0012*​x*​0.46

Step-by-step explanation:

Answer:

$46.20

Step-by-step explanation:

The discount of 30% brings the price down to $42, and then the sales tax would be $4.20, making the answer $46.20

Answer:

832.4 KWH of energy

Step-by-step explanation:

Find how many KWH of energy were used by dividing the total cost by 0.12:

99.89/0.12

= 832.4

So, approximately 832.4 KWH of energy were used that month.

Answer:

(a+b+c) (x+y+z)

Step-by-step explanation:

hope this helps to uh

Step-by-step explanation:

x+y+z+bx+by+bz+cx+cy+cz

Take Like terms

x+bx+cx+y+by+cy+z+bz+cz

x(b+c)+y(b+c)+z(b+c)

(x+y+z)(b+c)

hope it helps

Answer:

This is called a bisector.