A box in the shape of a rectangular prism has a volume of 72 cubic feet. The box has a length of x feet, a width of (x − 1) feet, and a height of (x + 9) feet. Find the dimensions of the box.

Answers

Answer 1

72 = l . w . h

72 = x . (x - 1) . (x + 9)

72 = (x² - x) . (x + 9)

72 = x³ + 9x² - x² - 9x

72 = x³ + 8x² - 9x

0 = x³ + 8x² - 9x - 72

0 = x² (x + 8) - 9 (x + 8)

0 = (x² - 9)(x + 8)

0 = (x - 3)(x + 3)(x + 8)

x = 3 or x = -3 or x = -8

so, x = 3

length = x = 3

width = x - 1 = 2

height = x + 9 = 12

Answer 2

Final answer:

To find the dimensions of the rectangular prism, set up an equation using the volume formula and solve for x. The dimensions of the box are 3 feet, 2 feet, and 12 feet.

Explanation:

To find the dimensions of the box, we need to set up an equation using the volume formula for a rectangular prism. The volume of a rectangular prism is given by V = length x width x height.

So, we have the equation x(x - 1)(x + 9) = 72.

Simplifying this equation, we get x³ + 8x² - 9x - 72 = 0.

Using factoring or synthetic division, we find that x = 3 is a solution to the equation. Therefore, the length of the box is 3 feet, the width is 2 feet, and the height is 12 feet.


Related Questions

WHICH SENTENCE IDENTIFIES THE Y INTERCEPT AND ORDERED PAIR OF THE POINT ON THE GRAPH

Answers

C

The line intercepts the y axis at 2, so that is the y intercept.

The ordered pair is (1,3) because ordered pairs go (x,y)

The family size bottle of sunscreen holds 12 fluid ounces of sun screen .The regular bottle holds 75%

Answers

I’m pretty sure the answer is supposed to be 9

Answer:

3!!!!!!!!!!

Step-by-step explanation:

Please just believe me

ƒ(x) = -2x + 3?

(-1, ___)

Answers

Answer:

(-1, 5)

Step-by-step explanation:

When f(x) = f(-1)

f(-1) = -2(-1) + 3

f(-1) = 2 + 3

f(-1) = 5

-1 is x

5 is y

(-1, 5)

Answer:  (-1, 5)

Answer:

(-1,5)

Step-by-step explanation:

x=-1 then

f(-1)=-2*(-1)+3=2+3=5

Write the number 3.636408 to the nearest ten-thousandth

Answers

Your answer will be 3.6364
Because 4 is in the ten-thousandth place and if the number next to the 4 is not greater than 1 your number will stay the same and all the numbers after will disappear☕︎

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The number 3.636408 to the nearest ten-thousandth will be 3.636.

What is a number line?

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

The given decimal number 3.636408 can be written to the nearest ten-thousandth with the help of a number line. The two of the closest number to 3.636408 are 3.636 and 3.637.

Now, as it can be observed that the distance between 3.636408 and 3.636 is less than 3.636408 and 3.637.

Therefore, the number 3.636408 to the nearest ten-thousandth will be 3.636.

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There are 27 girls and 36 boys who want to participate in a math competition. If each team must have the same ratio of girls and boys what’s the greatest number of teams that can enter?

Answers

Since the ratio of girls and boys must be the same in each team, and all the competitors must be involved, it means that each team's ratio of boys : girls must be equal to the total ratio of Boys : Girls = 36 :27= 4 / 3.

Now 4 / 3, the most simplified version of 36 / 27, happens by dividing the numerator & demoninator by 9 (the greatest number it can divide by). So the greatest number will be 9 teams, each of  4 Boys & 3 Girls

Answer:

4 Boys & 3 Girls

Step-by-step explanation:

what’s the relationship? linear, exponential, or neither?

Answers

Answer:

This relationship is linear

Step-by-step explanation:

As x goes up by 5, y goes up 3. Since this is a constant rate, this relationship is, therefore, linear

9.0758 to 2 significant figures.

Answers

Answer w/ explanation:

The answer is 9.1

To round to 2 significant figures, we have to find the first significant figure. We find the first sig fig by looking for the first nonzero digit in the number (it can be before or after the decimal point), which is "9"

The next digit is "0". This will also be a significant figure in our answer.

It may seem we are done now since we found the two significant figures. However, let's look at the digit after "0" to see if we need to round up or down.

The digit after "0" is "7". Since 7 is greater than 5, we round up the "0" to a "1" in our final answer, making the answer 9.1

Side note:

The definition and concept of significant figures can be very confusing overall, so please continue to ask questions if you are still struggling with them.

Let me know if you need any clarifications, thanks!

~ Padoru

A number 9.0758 to 2 significant figures is, 9.1

We have to give that,

A number is,

⇒ 9.0758

Since There are 5 significant numbers.

Hence, A number 9.0758 to 2 significant figures is,

⇒ 9.0758

Since 7 is greater than 5.

Hence,

9.0758 ≈ 9.1

So, The solution is, 9.1

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slope:
y-intercept:
equation:

Answers

Slope= m
y intercept= b
Equation: y=mx+b

We can conclude -

m = -A/B   → unit rate of change of [y] with respect to [x].c = - C/A   → the point where the graph cuts the [y] axis.Equation  → y = mx + c

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

Given is a straight line.

The equation of a straight line is written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Now, from this we get -

m = -A/B     {Slope}

c = - C/A     {y - intercept}

So, the equation will be -

y = mx + c

We can also calculate slope by -

m = (y₂ - y₁)/(x₂ - x₁)

Therefore, we can write -

m = -A/B   → unit rate of change of [y] with respect to [x].

c = - C/A   → the point where the graph cuts the [y] axis.

Equation  → y = mx + c

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Can diagonal of a parallelogram be congruent to one of its sides?

Answers

Answer: Opposite sides of a parallelogram are parallel (by definition) and so will never intersect. The area of a parallelogram is twice the area of a triangle created by one of its diagonals. The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides.

Answer:

is that a yes

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Which best describes the graphs of the line that passes through (−12, 15) and (4, −5), and the line that passes through (−8, −9) and (16, 21)?


A)
They are parallel lines.


B)
They are vertical lines.


C)
They are perpendicular lines.


D)
They are intersecting lines.

Answers

Answer:

C) They are perpendicular lines.

Step-by-step explanation:

We first need to find the slope of the graph of the lines passing through these points using:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

The slope of the line that passes through (−12, 15) and (4, −5) is

[tex] m_{1} = \frac{ - 5 - 15}{4 - - 12} [/tex]

[tex]m_{1} = \frac{ - 20}{16} = - \frac{5}{4} [/tex]

The slope of the line going through (−8, −9) and (16, 21) is

[tex] m_{2} = \frac{21 - - 9}{16 - - 8} [/tex]

[tex] m_{2} = \frac{21 + 9}{16 + 8} [/tex]

[tex]m_{2} = \frac{30}{24} = \frac{5}{4} [/tex]

The product of the two slopes is

[tex]m_{1} \times m_{2} = - \frac{4}{5} \times \frac{5}{4} = - 1[/tex]

Since

[tex]m_{1} \times m_{2} = - 1[/tex]

the two lines are perpendicular.

Answer:D) They are intersecting lines.

Step-by-step explanation: that other answer was wrong .

how to solve
Y+2=4
Y-2=8

Answers

Answer:

First question -> y = 2

Second question -> y = 10

Step-by-step explanation:

Step 1:  Solve y + 2 = 4

Subtract 2 from both sides

y + 2 - 2 = 4 - 2

y = 2

Step 2:  Solve y - 2 = 8

Add 2 to both sides

y - 2 + 2 = 8 + 2

y = 10

Answer:  First question -> y = 2

               Second question -> y = 10

What is the angle of a triangle if one angle is 68 and the other is 52

Answers

Answer:

The last angle is 60 degrees

Step-by-step explanation:

All triangles add up to 180 degrees

Step 1:  Make an equation

What is the angle of a triangle if one angle is 68 and the other is 52.

68 + 52 + x = 180

Step 2:  Combine like terms

68 + 52 + x = 180

120 + x = 180

Step 3:  Subtract 120 from both sides

120 + x - 120 = 180 - 120

x = 60

Answer:  The last angle is 60 degrees

The sum of the angles in a triangle will be equal to 180°.

68 + 52 = 120°

180 - 120 = 60° (This is the 3rd angle)

Best of Luck!

Look at the image used by the author of "Heads Up on
Sports Safety
Look at the image used by the author of "Heads Up on
Sports Safety
The author most likely included this image from an outside
resource to show how

stadiums have changed.

photographic technology has changed.

football uniforms have changed.

football strategies have changed.

Answers

The author most likely included this image to show how football uniforms have changed.

Why the image is added?

The thesis of "Heads Up on Sports Safety" is, as the name implies, sports safety.

The image shows some kids, all of them with their correspondent football equipment (protective equipment).

So, what is being presented in the image, is in some way how the "football uniforms have changed." In a way in which the safety of the players is a priority.

So that is the correct option.

If you want to learn more about sports, you can read:

https://brainly.com/question/11352260

How do I find side length x and would I use sin cos or tan

Answers

Check the picture below.

Make sure your calculator is in Degree mode.

a pair of running shoes costs $37 less than twice the cost of a pair of basketball sneakers. The sneakers cost $48.50. How much do the running shoes cost?

Answers

Answer:

11.5

Step-by-step explanation:

Sneakers = 48.50

Expression for cost of running shoes = 2(sneakers) - 37

Plug in value of sneakers and solve:

2(48.50) - 37

97 - 37

$60

The running shoes cost $60.

Hope this helps!! :)

Sales tax in Pennsylvania is 6%. Carlos bought a mountain bike that costs $125.50 before tax. What was the cost of the new bike including sales tax?

Answers

I’m pretty sure the answer is 113.03

Answer:

$878.50

Step-by-step explanation:

it's asking about new bike  cost including sales tax.

You are riding your bicycle. It takes you 9min to go 2.5 mi. If you continue traveling at the same rate, how long will it take you to go 7 mi?

Answers

Answer:

Step-by-step explanation:

To find out how many miles you are going per minute you would find the unit rate. The unit rate is 3.6

You are going at 3.6 minutes per mile.

So you would multiply 3.6 by 7 to get 25.2 minutes.

If I have 30 vegetables and 2 of the vegetables are beans. What percentage of vegetables are beans​

Answers

Answer:

6%

Step-by-step explanation:

.02 times 30

.6=6%

I believe it would be 6%

Since there are 2 beans, you divide by 100, so you get 0.02

Then, to find the percentage, you take the 0.02 and multiply it with 30.

And your answer should be 0.06, which is 6%, found by doing 0.02 • 30.

I hope this helps :)

What is 40% of 35 I NEEEED TO NOOOO

Answers

Answer:

14

Step-by-step explanation:

%40 * 35 is same as 0.4 * 35

14

Answer:  14

Answer:

14

Step-by-step explanation:

between the time Iko woke up and lunchtime, the temperature rose by 11°. Then by the time he went to bed, the temperature dropped by 14 °. Write an addition expression for the temperature relative to when Iko woke up.

Answers

Answer:

x + (11) + (-14)  [x being temperature when Iko woke up]

Step-by-step explanation:

Let the temperature be "x" when Iko woke up

Then,

Temperature ROSE 11° in lunch

The temp in lunch was:  x + 11

Then the temperature DROPPED 14° when he went to bed, relative to lunch temperature, so we can say:

(x + 11) - 14

So, the final temperature that end of day was:

x + 11 - 14

As addition expression, it will be:

x + (11) + (-14)

The answer to the question

Answers

Answer:

Step-by-step explanation:

NIPO

1. Find the x-intercept of the line: 5x - y = 10

2. Find the y-intercept of the line: 9x + 3y = -18

3. What are the x- and y- intercepts of the graph of 6x - 4y = -12

Answers

Final answer:

The x-intercept of the line 5x - y = 10 is (2, 0), the y-intercept of the line 9x + 3y = -18 is (0, -6), and the equation 6x - 4y = -12 has an x-intercept at (-2, 0) and a y-intercept at (0, 3).

Explanation:

To find the x-intercept of a line, we set the value of y to zero and solve for x. For the equation 5x - y = 10, we set y to 0:

5x - (0) = 10

5x = 10

x = 2

The x-intercept is therefore the point (2, 0).

To find the y-intercept of a line, we set the value of x to zero and solve for y. For the equation 9x + 3y = -18, we set x to 0:

(0) + 3y = -18

3y = -18

y = -6

The y-intercept is therefore the point (0, -6).

For the equation 6x - 4y = -12, the x-intercept and y-intercept can be found similarly. Let's start with the x-intercept. Set y to 0:

6x - (0) = -12

6x = -12

x = -2

The x-intercept is the point (-2, 0). Now, for the y-intercept, we set x to 0:

(0) - 4y = -12

-4y = -12

y = 3

The y-intercept is the point (0, 3). Thus, for 6x - 4y = -12, the intercepts are x = -2 and y = 3.

Find the distance from the point (3,2) to the line 2y + 3x = 5. Round your answer to the nearest tenth.

Answers

Answer:

  (8/13)√13 ≈ 2.2

Step-by-step explanation:

The distance from point (x, y) to line ax+by=c can be found using the formula ...

  d = |ax +by -c|/√(a²+b²)

Filling in the given values, we find the distance to be

  d = |3·3 +2·2 -5|/√(3² +2²) = 8/√13

  d = (8√13)/13 ≈ 2.2 . . . . . after rationalizing the denominator

Which statement show equivalent expressions? PLEASE HELP ME ASAP
A 5(x−2)=5x−3
B 3(x+6)+x=4x+9
C 8(2x+3)=16x+24
D 4(5x+2)−6=20x+14

Answers

Answer:

c.

Step-by-step explanation:

8(2x+3) = 16x + 24

8(2x) + 8(3) = 16x + 24

Answer:

C)

Step-by-step explanation:

C) 8(2x+3)=8*2x+8*3=16x+24 true

Which is true about the degree of the sum and difference of the polynomials 3xy - 2xy4 - 7xy and -8xy + 2x°y4 + xy?
O Both the sum and difference have a degree of 6.
O Both the sum and difference have a degree of 7.
The sum has a degree of 6, but the difference has a degree of 7.
The sum has a degree of 7, but the difference has a degree of 6.

Answers

Answer:

It's C I just did it

Step-by-step explanation:

The degree of the sum and difference of the polynomials are 6 and 7 respectively.

The degree of the sum and difference of the polynomials.

3x⁵y - 2x³y⁴ - 7xy³ and -8x⁵y + 2x³y⁴ + xy³

The degree of sum = monomial with the highest power = 5 + 1 = 6

The degree of difference = monomial with the highest power = 3 + 4 = 7

Therefore, the degree of the sum and difference of the polynomials are 6 and 7 respectively.

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Which expressions are equivalent to
2 In a + 2 In b - In a?
Check all that apply.

Answers

Answer:

ln ab^2

ln a + 2 ln b

ln a^2 + ln b^2 - ln a.

Step-by-step explanation:

2 ln a + 2 ln b - ln a

= ln a^2 + ln b^2 - ln a

= ln (a^2/a) + ln b^2

= ln a + 2 ln b

= ln a + ln b^2

= ln ab^2.

Yo sup??

2lna+2lnb-lna

=lna²+lnb²-lna

=lna²b²/a

=lnab²

correct answer is option E

Hope this helps

The circumference of a circular frisbee is 20 centimeters. If
we multiply the radius of the frisbee by 5, what will be the
circumference of the new frisbee?
OA) 981 cm
OB) 100 cm
OC) 1451 cm
OD 2007 cm

Answers

Answer:

100cm

Step-by-step explanation:

since the circumference is 20cm and formula for finding a circumference of a circle is c=2(pi)r, where r is radius and pi is constant value which is equivalent to 22/7. so the radius of 20cm circumference is 3.1847 by using this eqn c/2(pi)=r. now the calculated radius will b multiply by 5 to get 15.92cm which is put in cirumference formula i.e. c=2(pi)r we get 100cm circumference.

Determine the area of the composite figure to the nearest whole number.
A) 563 in2
B) 680 in2
C) 776 in2
D) 1,030 in2
And I want an explanation

Answers

The answer is c which is correct

Answer:

B

Step-by-step explanation:

Let’s review our area formulas first:

Area of rectangle: l*w

Area of quarter circle:(pi*r^2)/4

Area of triangle:(b*h)/2

What we need to do is find the areas of these individual figures and add them up to find the area of the total figure WHEn CALCUlATING AReA Be SURE TO OnLY LOOK AT THE OnE figure and ignore all other shapes!

So

Rectangle=11.1(length)*21.1(width)

Rectangle=234.21

Quarter circle=(pi*(21.1)^2)/4

Quarter circle= 349.667116326

Triangle:(9.1*21.1)/2

Triangle=96.005

So

96.005+234.21+ 349.667116326=679.8821(round up to 680)

Hope this helps!

Use rounding to estimate the product.

8.24 × 5.88

40
45
48
85

Answers

The answer would be 48. I hope that helped

Answer:

Its 48.4512 and rounded it is 48 :)

[]: what is 20056x345

Answers

Answer:

6,919,320

Step-by-step explanation:

20056 * 345

6919320

Answer:  6,919,320

Answer:

6,919,320.00

Step-by-step explanation:

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Your computer system loses power while you are working on a project for a very important client. When the computer restarts, you hear continuous beeps coming from your computer, and the monitor is showing no signal. All of the following are factors likely to affect energy expenditure during exercise EXCEPT: A. fitness level of individual B. duration of the exercise period C. consumption of multi-vitamin supplements D. muscle mass used while exercising If a bacterial cell culture contains 2 cells at time zero, 8 cells one hour later, 32 cells after 2 hours, and 128 cells after 4 hours, then which of the following describes the growth of this culture?A) g = 0.5 h, v = 5 h^-1B) g = 0.5 h, v = 2 h^-1C) g = 2 h, v = 0.5 h^-1D) g = 1 h, v = 1^-1 According to the passage, why were people arrested The odds against an event are 4:7. Find the probability that that event will occur Easy question! Please help! And please tell me which line to use! (open circle or closed circle) Which of the following statement is true? a. the MAC address cannot be spoofed b. the IP address can be spoofed, so if you want to read response from the deceived party, you can use c. IP spoofing to hide yourself IP spoofing can be used for denial of service attack d. IP spoofing can be prevented or detected by switches Which of the following are ordered pairs for the equation y = 1/8x + 11?(0,11) (8,12) (16,13)(0,11) (7,13) (8,15)(0,11) (5,12) (7,13)(0,11) (6,12) (8,13) Between 1994 and 2006, Fort Myers home prices have increased Faster than the rate of inflation. Using your knowledge of markets, in 25 words or more explain why. How many miles separated pompeii and Rome Sophie is a US citizen. She married Ivan, an acquaintance whose tourist visa has expired, but who wants to remain in the United States. Which of these is true?A)Ivan becomes a US citizen immediately.B)Ivan becomes a lawful permanent resident immediately.C)Ivan becomes a US citizen if they stay married for a year.D)Ivan is eligible to apply to be a lawful permanent resident. Which BEST analyzes the use and effect of the word choices in section three? A)Multiple words have positive connotations that create a sense of adoration and reverence. B)Multiple words have negative connotations that show the extreme neediness of of Aunt Zeze. C)Multiple words have positive connotations that emphasize the absolute necessity for religious devotion. D)The word choices include positive, negative, and neutral connotations to reveal the author's disdain for Monjardin. The Copy Center can purchase a new copier for $15,000. It would last for 3 years and have a salvage value of $3,000. Depreciation cost would be $4,000 per year and cash operating costs would equal $1,000 per year. The same copier could be leased for $6,500 per year. Using a discount rate of 7%, and the tables in Supplement 11A, it is best to (buy/lease) the copier because the difference in cost is___________ $ . show all work to multiply (6+-64)(3--16) Unexpected expense. In a random sample 765 adults in the United States, 322 say they could not cover a $400 unexpected expense without borrowing money or going into debt.(a) What population is under consideration in the data set?(b) What parameter is being estimated?(c) What is the point estimate for the parameter?(d) What is the name of the statistic can we use to measure the uncertainty of the point estimate?(e) Compute the value from part (d) for this context.(f) A cable news pundit thinks the value is actually 50%. Should she be surprised by the data?(g) Suppose the true population value was found to be 40%. If we use this proportion to recompute the value in part (e) using p = 0:4 instead of ^p, does the resulting value change much? what would happen if our lungs where made up of only one big alveoli? Find the area of this figure28 cm23.7 cm8 cm5.7 cm What is the diffrence between a star and a planet In a hypothetical situation, a certain species of flea feeds only on pronghorn antelopes. In rangelands of the western United States, pronghorns and cattle often associate with one another. If some of these fleas develop a strong preference for cattle blood and mate only with other fleas that prefer cattle blood, then over time which of these should occur, if the host mammal can be considered as the fleas' habitat There are two buses. Bus A can travel 125 miles in 3 hours,and Bus B can travel 85 more miles than bus A within thesame time. What is the speed of Bus B?mph.