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Dmitry_Shevchenko [17]
3 years ago
14

A rectangular box has the dimensions shown in the diagram. The volume of the box is given by the function V(x) = x3 – 4x, where

x is the height in inches.
What is the height of the box if the volume is 15 in.3?


There is a rectangular box with length x+2 in. , width x-2 in. , and height x in.


height = in.

Mathematics
1 answer:
marta [7]3 years ago
3 0

Answer:

Height =3

Step-by-step explanation:

Given

Length = x + 2

Width = x - 2

Height = x

Volume = 15

Required

Find the height

The volume is calculated as thus:

Volume = Length * Width * Height

This gives

15 = (x + 2) * (x - 2) * x

Apply difference of two squares

15 =(x^2 - 4 ) * x

15 = x^3 - 4x

Subtract 15 from both sides

x^3 - 4x - 15 = 0

Using a calculator to factorize, we have:

(x-3)(x^2+3x+5) = 0

Split

x - 3 = 0 or x^2 + 3x + 5 = 0

x = 3 or  x^2 + 3x + 5 = 0

x has complex roots for x^2 + 3x + 5 = 0

Hence:

x = 3

Recall that:

Height = x

Height =3

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Solve linear equation 1/4 x + 18 = X
Anton [14]

Answer:

24

Step-by-step explanation:

1 / 4 x + 18 = x

x / 4 + 18 = x

x = x / 4 + 18

x - x / 4 = 18

( 4x / 4 ) - ( x/4 ) = 18

( 4x - x ) / 4 = 18

3x / 4 = 18

3x = 18 * 4

x = ( 18 * 4 ) / 3

  = 6 * 4

x = 24

3 0
3 years ago
19) At a local river, there were 48 alligators lying on the riverbank. If of the alligators wereasleep, how many were not asleep
sergey [27]
19) 48 alligators; 7/8 of the alligators were asleep. How many were not asleep?

8/8 - 7/8 = 1/8
48 * 1/8 = 48/8 = 6 alligators were not asleep.

20) 2/3 of the student population participated. 1,500 is the student population of the school. HOw many attended the bike rally?

1500 * 2/3 = 1500*2 / 3= 3000 / 3 = 1000 students attended.

21) 18 times at bat:
Kayla 5/6 of the time = 18 * 5/6 = 18*5 / 6 = 90/6 = 15 hits
Tia 8/9 of the time = 18 * 8/9 = 18*8 / 9 = 144/9 = 16 hits

Tia got more hits.
3 0
3 years ago
Mm
Novay_Z [31]

Answer:

x + 2(2x-4) = 10

Step-by-step explanation:

Here in this question, we want to select which is the correct answer if we substitute for the value of y in the second equation, using the first.

In the first, we have;

y = 2x -4

Now, let’s input this value of y into the second equation.

By direct substitution, what we have is the following;

x + 2y = 10

—-> x + 2(2x -4) = 10

8 0
3 years ago
What is the value of a in the polynomial
Alexandra [31]

Answer: a= 16

Step-by-step explanation:

We have the following expression:

(y-4)(y^2 +4y +16)

To find the value of the coefficient "a" you must use the distributive property to multiply the expression:

(y-4)(y^2 +4y +16)

until you transform it to the form:

y^3 +4y^2 +ay -4y^2 -ay-64

Then we have

(y-4)(y^2 +4y +16)\\\\(y^3 +4y^2 +16y -4y^2 -16y-64)\\\\

Therefore the value of a in the polynomial is 16

5 0
3 years ago
4-3x2 + x2 + 5x – 7)
kompoz [17]

Answer:

7x - 9

Step-by-step explanation:

1: Multiply the numbers

4 - 3 x 2 + 2x + 5x - 7

4 - 6 + 2x + 5x - 7

2: Add the numbers

4 - 6 + 2x + 5x - 7

-9 + 2x + 5x

3: Combine like terms

-9 + 2x + 5x

-9 + 7x

4: Rearange terms

-9 + 7x

7x - 9

Solution

7x - 9

Can i be brainliest

4 0
3 years ago
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