The volume of a rectangular solid is given by the polynomial 3x^4-3x^3-33x^2+54x. If the length of the solid is 3x and the width of the solid is x-2 Find the height?

The Volume Of A Rectangular Solid Is Given By The Polynomial 3x^4-3x^3-33x^2+54x. If The Length Of The

Answers

Answer 1

Answer:

[tex]\mathsf{height}=x^2+x-9[/tex]

Step-by-step explanation:

Volume of a cuboid = L x w x h

(where L is the length, w is the width and h is the height)

[tex]\implies \mathsf{height=\frac{volume}{width \times length} }[/tex]

Given:

[tex]\mathsf{volume}=3x^4-3x^3-33x^2+54x[/tex]

[tex]\mathsf{width}=x-2[/tex]

[tex]\mathsf{length}=3x[/tex]

[tex]\implies \mathsf{height}=\frac{3x^4-3x^3-33x^2+54x}{3x(x-2)}[/tex]

Factor expression for volume

Factor out common term [tex]3x[/tex]:  [tex]3x(x^3-x^2-11x+18)[/tex]

Factor [tex]x^3-x^2-11x+18[/tex]:  [tex]3x(x-2)(x^2+x-9)[/tex]

[tex]\implies \mathsf{height}=\frac{3x(x-2)(x^2+x-9)}{3x(x-2)}[/tex]

Cancel the common factors [tex]3x(x-2)[/tex]:  

[tex]\implies \mathsf{height}=x^2+x-9[/tex]


Related Questions

PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS!!
WHAT IS THE VALUE OF X?

Answers

Answer:

x = 20

Step-by-step explanation:

180 - 45 = 5x + 35

180 - 45 = 135

5x + 35 = 135

5x + 35 - 35 = 135 - 35

5x = 100

5x/5 = 100/5

x = 20

Answer:

x=20

Step-by-step explantion:

180-45=135

we have,

135=5x+35

135-35=5x

100=5x

100/5=x

20=x

Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x))

Answers

Answer:

Step-by-step explanation:

Function f(g(x)) is the amount of money Raul earns per ticket sold.

here are the steps to find f(g(x)):

Define the functions f(x) and g(x).

f(x) = amount of money Raul earns per ticket

g(x) = number of tickets Raul sells per hour

Substitute g(x) for x in the function f(x).

f(g(x)) = amount of money Raul earns per ticket * number of tickets Raul sells per hour

Simplify the expression.

f(g(x)) = amount of money Raul earns per ticket * number of tickets Raul sells per hour

= amount of money Raul earns per ticket sold

Therefore, f(g(x)) is the amount of money Raul earns per ticket sold.

Here is an example:

Let's say f(x) = $10 and g(x) = 2 tickets/hour. If Raul works for 1 hour, he will sell 2 tickets and earn $20.

f(g(x)) = f(2) = $10 * 2 = $20

To learn more about Function here:

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Draw a line to match each word with its definition

Thx ! ♡☆​

Answers

Answer:

1. C

2. E

3. D

4. B

5. A

Hope This Helps!!!

Answer:

4 -2,3 -4,2 -5,5 -1,1 -3

I hope this helps you

Find the volume of a right rectangular prism that has a base area of 54 square centimeters and a height of 413 centimeters.

Answers

Answer:multiply base times height

Step-by-step explanation:

V=lwh

V=bh

lw=V

find the value of the power.
0.9^2 =

Answers

Hello!

0,9^2

0,9²

0,9 × 0,9

0,81

The value of the power 0,9^2 is 0,81

_____________________________

Maura wants to buy fencing to install around a square garden in her yard. the perimeter of the garden can be represented by the equation p = 4√a where a is the area of the garden.
Examine the graph that represents this situation.



Examine the graph that represents this situation.
The graph appears to begin at (0,0).
Is (0,0) a valid point in terms of the context of the situation? Why or why not?

Select the option that correctly answers both questions.

A) The point is valid in terms of the context because when Maura buys 0 feet of fence, the perimeter of the garden is 0 feet.

B) The point is not valid in terms of the context because the garden can't have an area of 0 square feet.

C) The point is valid in terms of the context because it represents the smallest garden Maura can have as well as the amount of fence she must buy.

D) The point is valid in terms of the context because it shows that the area and perimeter start at 0.

Answers

The correct option regarding the point (0,0) is the context of this function is given by:

D) The point is valid in terms of the context because it shows that the area and perimeter start at 0.

What is the function?

The perimeter of a garden of area a is given by:

[tex]p = 4\sqrt{a}[/tex]

If there is no garden, that is, the area is 0, the perimeter is also 0, hence point (0,0) is valid, which means that option D is correct.

More can be learned about functions at https://brainly.com/question/25537936

solve: 2x + 5y = -1
3x + 2y = 4

Answers

Answer:

x = 2, y = -1

(x,y) = > (2,-1)

Step-by-step explanation:

2x + 5y = -1

3x + 2y = 4

-3(2x + 5y = -1) = > -6x - 15y = 3

2(3x + 2y = 4) = > 6x + 4y = 8

-6x - 15y = 3

6x + 4y = 8

-11y = 11

/-11  /-11

y = -1

2x + 5y = -1

2x + 5(-1) = -1

2x -5 = -1

   +5   +5

2x = 4

/2   /2

x = 2

(x,y) = > (2,-1)

Hope this helps!

Use the sketch below and determine how many squares will be in Step 4.

Answers

From step 1 to step 2 they added 3 squares.

From step 2 to step 3 they added 5 squares.

Each step they add the next odd number in sequence: 3,5,7,9,etc.

So for step 4 they would add 7 more squares. Add 7 to the number of squares in step 3 for total squares:

7 + 9 = 16


step 4 will have 16 squares.

Please help me out!! Show your work:()

Answers

Answer:

23.6

Step-by-step explanation:

A=1/2abSinC

A=1/2*6*8*Sin80

= 24 * Sin 80

=23.635

Not sure if this is 100% correct Sowwie

Solve B) simultaneously please

Answers

Answer: .....

Ok done. Thank to me :>

Please answer quickly ( 70 points)

Answers

Answer:

maybe 4 hours

____________

Answer: 4 hours

Step-by-step explanation: 10 for the first hour then 12 x 4=58

Based on the Pythagorean Theorem, which of
the following is NOT true?
F b2 + a2 = c2
G b2 + c2 = a 2
H C2 - a2 = 62
J c2-b2 = a2

Answers

Answer:

G is not TRUE.

Step-by-step explanation:

using the law A+B = B+A

PYTHAGOREAN THEOREM

A²+B² =C² is equal to B² +A² = C²

So for A²,

B² - c² = A. remember if a positive number move from the left to the right over an equal sign it becomes negative and vice versa

C² - A²= B²

Is the expression a polynomial? If so, is it a monomial, binomial or
trinomial? 8x - 2y

Answers

Answer:

8x2y is a monomial.

Step-by-step explanation:

Solve system of equations:

-9x - 8y = 14
10x + 4y = 4

Answers

Point form: (2, -4)
Equation form: x = 2, y = -4

―6 + (4 + 4)2 ÷ 2
This is my problem I need help with

Answers

Answer:

2

Step-by-step explanation:

you do the (* first so it 8 then you add it with -6 which decreases it that makes 2 and 2 divided by 2 is one so add all together and get 2

By using BIDMAS
BIDMAS stands for brackets, index , division,multiplication,additional,subtract
-6 + (8)2\2
-6+8x1
So you got -6+8 which is 2

1.35 = 7x what is x ( other than 0.19285714 )

Answers

Hey there!

7x = 1.35


DIVIDE 7 to BOTH SIDES

7x/7 = 1.35/7


CANCEL out: 7/7 because it give you 1

KEEP: 1.35/7 because it give you the x-value


NEW EQUATION: x = 1.35/7


SIMPLIFY IT!

x = 0.192857

x ≈ 192,857/1,000,000


Therefore, your answer is:

x = 0.192857 or x = 192,857/1,000,000


Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

What is 22 (Square root) rounded to the nearest whole number?

Answers

Answer:

[tex]\sqrt{22}\approx5[/tex]

Step-by-step explanation:

We know that [tex]\sqrt{16}=4[/tex] and [tex]\sqrt{25}=5[/tex], so since 22 is closest to 25, then we can say that [tex]\sqrt{22}\approx5[/tex]

In a city, 49% of the adults are male. Of the adults, 24% are male and rent action-movie DVDs and 10% are female and rent action-movie DVDs.
If an adult is randomly picked, the probability that the person rents action-movie DVDs, given that the person is female, is
.

Answers

Answer:

I getting the probability of the adult female that will rent the action movies in DVDs in by dividing the possible probability outcome which is 10% of all adults by the total number of possible outcome. So all of the population of the female is 51% and the ones who rent is only 10%. the probability is 19%

The solution is, 0.20 is the probability that the person rents action-movie DVDs, given that the person is female.

What is probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

Data:

A: the adult is a male, P(A) = 0.49

B: the adult rent action-movie DVDs

C: the adult is a female,  P(C) = 1 - P(A) = 1 - 0.49 = 0.51  

24% of the adults are male and rent action-movie DVDs, then P(A ∩ B) = 0.24

10% of the adults are female and rent action-movie DVDs, then P(C ∩ B) = 0.10

The conditional probability of B (the adult rents action-movie DVDs) given C (the adult is female) is computed as follows:

P(B|C) = P(C ∩ B)/P(C)

          = 0.1/0.51

          = 0.2

Hence, The solution is, 0.20 is the probability that the person rents action-movie DVDs, given that the person is female.

To learn more on probability click:

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Two – a third of a number is 4 more than 6 .Find the number

Answers

Answer:

-24

Step-by-step explanation:

First, at up an equation based on the problem:

2 - ⅓x = 4 + 6

Then, solve for x:

2 - ⅓x = 10

-⅓x = 8

x = -24

OR

2 = 10 + ⅓x

-8 = ⅓x

-24 = x

Can u answer this for me please step by step I'm desperate
-| -40 |

Answers

Answer:

- 40

Step-by-step explanation:

The absolute value always returns a positive value , that is

- | - 40 | = - | 40 | = - 40

PLEASE HELP



The table shows the area of circles with a radius of 1 through 3 feet.
Recall that pi has a vale of about 3. Write an equation in two variables
To represent the relation in the table.

Answers

Answer is in image hope this helps

Find the value of f(-7).
y =f(x)

Answers

Move -7 to the left of f. -7f

What are the coordinates of point S"?
2. (x, IM) o Do. 1 (x, y is applied
The composition D
y
to ARST to create the image of AR"S"T", which is not
shown.
(
( )
y
14
12
10
E
0 0
8
6
4
2+
2
(이
2
-14-12-10 -8 6 4 22
X
4 6 8 10 12
4
6
-8-
T
-10
-12
-145

Answers

Answer:

  S" = (-3/2, 9/2) = (-1.5, 4.5)

Step-by-step explanation:

The two dilation factors multiply each other, so the dilation of the final image relative to the initial figure is (3/2)(1/2) = 3/4.

  S" = 3/4S = 3/4(-2, 6)

  S" = (-3/2, 9/2) = (-1.5, 4.5)

The coordinates of point S"  are (-3/2, 9/2) = (-1.5, 4.5)

What are Coordinates?

This involves the use of one or more numbers to uniquely determine the position of the points or other geometric elements.

We have to multiply the dilation factors which will result in:

(3/2)(1/2) = 3/4.

S" = 3/4S = 3/4(-2, 6)

S" = (-3/2, 9/2) = (-1.5, 4.5)

Read more about Coordinates here https://brainly.com/question/17206319

please help me!!!!!!

Answers

Answer:

sorry i can see it its blured

In the given figure, find the value of x and y?​

Answers

Answer:

x = 6 cmy ≈ 14.5°

Step-by-step explanation:

The given diagram shows two points labeled B. Rename the one on segment CD as E.

We assume that AE is supposed to be the bisector of angle A. Since triangle ABC is isosceles, segment AE will be perpendicular to BC. In that case, triangle EBC is also isosceles, which means BE is also 6 cm.

Angle ABC is exterior to triangle BCD, so has a measure that is the sum of angles BDC and BCD. That is, angle ABC is 2y+y=3y. Angle CBE is also y, so angle ABE will be 3y+y=4y. This exterior angle to triangle BED is the sum of angles BED and BDE. We know BDE is 2y, so BED is 4y-2y=2y, which means triangle BED is isosceles and BD=BE=EC=x=6 cm.

__

Finding the measure of angle y is a bit tricky. We know that angle ABC is 3y, and angle EBC is y. If we say X is the midpoint of BC, where AE crosses BC, then we can write the trig relations ...

  BX=BA·cos(3y)

  BX=BE·cos(y)

Filling in the measures of BA and BE, we can equate expressions for BX to get ...

  8cos(3y) = 6cos(y)

Using the trig identity for cos(3y), we can write this as ...

  8(4cos(y)³ -3cos(y)) = 6cos(y)

  32cos(y)³ -30cos(y) = 0

  2cos(y)(16cos(y)² -15) = 0

This has solutions cos(y)=0 and cos(y) = ±√(15/16). We are interested in the positive solution only:

  y = arccos(√15/16) ≈ 14.478°

The value of y is about 14.5°.

slove for x. round to the nearest tenth if necessary

Answers

Answer:

65,93 cm or what is it is x

Help me with geometry please

Answers

Answer: Choice B

SAS

=========================================

Explanation:

SAS = side angle side

One pair of congruent sides is AC = CE (single tickmark). That takes care of one "S" of "SAS".

The other pair of congruent sides is BC = CD (double tickmark). This takes care of the other "S" of "SAS". The order of the "S" terms doesn't matter as long as the angles are between those sides.

The congruent pair of angles is angle ACB = angle ECD. Vertical angles are always congruent. Since we have a pair of congruent angles, this takes care of the "A" of "SAS". The angles are between the sides mentioned in the previous paragraphs.

Solve each system of equations using the elimination method

3x+4y=23
3x-2y=11

Answers

Answer: (x,y) = (5,2)

In other words, x = 5 and y = 2

====================================================

Explanation:

Subtract the equations straight down.

The x terms subtract to 3x-3x = 0x and they go away (hence the term "elimination").The y terms subtract to 4y-(-2y) = 6yThe right hand sides subtract to 23-11 = 12

We end up with 6y = 12 which solves to y = 2 after dividing both sides by 6.

Now use this y value to find x.

If we used the first equation, then we have these steps

3x+4y = 23

3x+4(2) = 23

3x+8 = 23

3x = 23-8

3x = 15

x = 15/3

x = 5

Or we could use the second equation

3x-2y = 11

3x-2(2) = 11

3x-4 = 11

3x = 11+4

3x = 15

x = 15/3

x = 5

We get the same x value either way.

The solution is (x,y) = (5,2)

To check the answer, plug those coordinates into each equation. After simplifying, you should get the same number on both sides.

------------------

Check:

3x+4y = 23

3(5)+4(2) = 23

15+8 = 23

23 = 23 .. that works

and,

3x-2y = 11

3(5)-2(2) = 11

15 - 4 = 11

11 = 11 .. that works as well

Both original equations are true for those x and y values.

The solution is fully confirmed.

find an expression equivalent to 4x – 4 – 2x + 3.

Answers

Answer:

2x-1

Step-by-step explanation:

⇒ [tex]4x-4-2x+3\\\\[/tex]

⇒ [tex]4x-2x-4+3[/tex]

⇒ [tex]2x-1[/tex]

Hence, 2x-1 is equivalent to 4x – 4 – 2x + 3.

Hope it will help you.

Answer:

2x - 1

Step-by-step explanation:

4x - 2x - 4 + 3

2x - 1

hope this helps

A gardener needs to plant 60 plants.In 2 hours, he planted 25% of the plants. How many plants does he still have left to plant?

Answers

Answer:

45

Step-by-step explanation:

Because 15 plants is 25% of 60 plants

Hope it helps :)

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