I Really Need help with these math problems?

Question

These math problems are driving me crazy and no ppl at school will help and teachers dont have time to help at all.....please help

1) A Cardboard box has a length of x-2, a width of x+1, and a height of 2x. *(This question will have a following 2 part question that includes letters a & b)

a) Write an expression, in terms of x, to represent the volume of the box.

b) If x=8 centimeters, what is the number of cubic centimeters in the volume of the box

2) Solve x: 15-3(3x+4)=6

3) A fish tank with a rectangular base has a volume of 3,360 cubic inches. The length and width if the tank are 14 inches and 12 inches, respectively. Find the height, in inches, of the tank.

Answer 1

1)
a) Recall that the volume of a box is given by the following formula.

V = (length) times (width) times (height)

Since it is given that the length is (x - 2), the width is (x + 1), and the height is (2x), all we have to do is plug those into the formula for the volume. Remember that brackets are ABSOLUTELY important.

V = (x - 2)(x + 1)(2x)

b) If x = 8 centimeters, all you have to do is plug x = 8 into the formula for volume that we just solved above.

V = (8 - 2) (8 + 1) (2(8))
V = (6)(9)(16) = 864 centimeters cubed.

2)

15 - 3(3x + 4) = 6

Your first step is to distribute the -3 over the brackets. This means you multiply -3 by each term within the brackets. Doing that, you should get

15 - 3(3x) - 3(4) = 6. Now, multiply it out.

15 - 9x - 12 = 6. Move everything without an x to the right hand side. Keep in mind that whenever you move something to the other side of the equal sign, the sign changes. The 15 would become a -15. The -12 would become a +12.

-9x = 6 - 15 + 12

Simplifying, we get

-9x = 3

Dividing both sides by -9, we get

x = -3/9 = -1/3

3) Since we have a fish tank with a rectangular base, our volume of the tank would be

V = (length) times (width) times (height)

It is given that the volume V = 3360. It is also given that the length is 14 and the width is 12. We're NOT given the height, but we will call it h. Therefore, if we plug in ALL of these values in that formula I just typed out, we would get

3360 = (14)(12)(h)

Multiply 14 and 12 out on the right hand side, to get

3360 = 168h

Now, divide both sides by 168 to isolate the h, to get

20 = h

Therefore, h = 20, which means the height of our tank is 20 inches.

Answer 2

1) A Cardboard box has a length of x-2, a width of x+1, and a height of 2x. *(This question will have a following 2 part question that includes letters a & b)

a) Write an expression, in terms of x, to represent the volume of the box.
Volume = length times width times height=
(x-2)(x+1)(2x) = (x^2-x-2)(2x) = 2x^3-2x^2-2x

b) If x=8 centimeters, what is the number of cubic centimeters in the volume of the box

V = 2(8)^3 - 2(8)^2 -2(8)
= 2*512 - 2(64) - 16 =1024 - 128 -16 = 880 cm^3



2) Solve x: 15-3(3x+4)=6
15 -9x -12 =6
-9x =6+12-15
-9x=3
x=-3/9 = -1/3


3) A fish tank with a rectangular base has a volume of 3,360 cubic inches. The length and width if the tank are 14 inches and 12 inches, respectively. Find the height, in inches, of the tank.

V= l*w*h
3360 = 14*12*h
h = 3360/(14*12) = 20 inches

Answer 3

1. volume = l * b * h (lenght * breath * height)
l = (x-2)
b = (x + 1)
h = (2x)
a. v = l * b * h
=>v = (x - 2) * (x+1) * (2x) [ans.]
b). if x = 8 then
l = 8-2 = 6 cm (centimeter)
b = 8 + 1 = 9 cm
h = 2(8) = 16 cm
v = l * b * h
v = 6 * 9 * 16 = 864 cubic centimeter [volume].

2) 15-3(3x+4)=6

3)v = l*b*h
= 3360 = 14 * 12 * h
= 3360 = 168h
=> h = 3360/169
=> h = 20 inches [of the tank]

Answer 4

1
a) Volume = length * width * height

Volume = (x-2)(x+1)2x = (x^2-x-2)*2x = 2x^3 - 2x^2 - 4x

b) It is easier tio use unexpanded formula above so

Volume = 6*9*16 = 864

2

15 - 3*(3x+4) = 6
=>
15 - 9x-12 = 6
=>
3 - 9x = 6
-9x = 3
x = -3/9 = -1/3

3) V = Length* Width * Height = 14*12*H

V = 3360 = 14*12H

280 = 14H

H = 20

Answer 5

I'll do 1a). Someone else do 1b). Let's split the work up!

1a) Volume = length x width x volume

Sooo:

Vol = (x-2)(x+1)(2x) ........we multiply these together to get volume.
Do the first two brackets first:
(x-2)(x+1) = x^2 + x - 2x -2

Simplified, that gives us (x^2 - x - 2)

(in words: x squared, minus x, minus 2).

Now multiply it all by the 2x above (4th line of my answer):
(x^2 - x - 2)(2x) = 2x^3 - 2x^2 - 4x

Now simplify:

volume = (2x)(x^2 - x - 2)

can also be written:

volume = (2x)(x -2)(x+1 )

Answer 6

1. (x-2)(x+1)(2x)
(8-2)(8+1)(2x8) = 864

2. x= 12(3x+4)=6
x =(3x+4)= .5
3x=4.5
x= -1.5

3. 14x12x H= 3360
H= 3360/14(12)
H= 3360/168

You will have to solve this last part as I do not have a calculator handy.

Answer 7

1)2x^3(-2)=Volume

b)864 cm^3

2)-3/2

3)20 Inches Tall

ohh yea and ^ means to the power of.

I hope this helps!!

Answer 8

Shouldn't you be trying to do your own homework?

Answer 9

my head hurts from reading those questions