The volume of a rectangular prism is the product of its length, width, and height. The length of a rectangle prism is 3 feet more than five times its height. The width is 5 feet less than six times its height. Express the length and width in terms of the height h. The length is The width is (Be sure to Write down the expanded form of the expression for the volume: expand the volume expression) (Express the interval in which the In what range must the height fall? He height must be)

Answers

Answer 1

The length and width in terms of the height h is  5h+3 feet and 6h-5 feet respectively, the volume will be  [tex]30h^3 - 7h^2 -15h[/tex] units and the height must be in the interval of [tex][0,\infty)[/tex].

According to the question,

The height of the rectangular prism is h.

The length of the rectangular prism  is  5h+3 feet

The width of the rectangular prism  is  6h-5 feet

The volume of the rectangular prism can be calculated as:

[tex]Length \times width \times height = Volume[/tex]

Substitute the value of height, length  and width in the formula:

[tex]V = (5h+3) \times (6h-5) \times h[/tex]

V = [tex](30 h^2 -7h-15)h[/tex]

[tex]V = 30h^3 - 7h^2 -15h[/tex]

The height is always positive. So, the interval in which the In what range must the height fall is [tex][0,\infty)[/tex].

The length and width in terms of the height h is  5h+3 feet and 6h-5 feet respectively and the volume will be  [tex]30h^3 - 7h^2 -15h[/tex] units

The height must be in the interval of [tex][0,\infty)[/tex].

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Related Questions

HELPPPP MEE PLEASEEE!!

Answers

Answer:

6 , 1

5 , 2

4 , 3

Step-by-step explanation:

Just swap the numbers.

Answer:

x (input) y (output)

     6             1

     5             2

     4             3

     3             4                

Step-by-step explanation:

Because it is the inverse of the red table, the blue table would be the opposite: (Answers are shown above)

I hope this helps :)

Which histogram represents the data?

4, 6, 8, 12, 14, 16, 18, 24, 28, 30, 34, 36, 38, 40, 46, 50, 54

Answers

Answer:

The first graph is correct

Step-by-step explanation:

There are 3 numbers in the 0-9 range

There are 4 numbers in the 10-19 range

There are 2 numbers in the 20-29 range

There are 4 numbers in the 30-39 range

There are 2 numbers in the 40-49 range

There are 2 numbers in the 50-59 range

The only graph that has the correct information is the first graph

I hope that this helps :)

Amy sold 10 t-shirts and 2 sweatshirts for $56.
Adam sold 5 t-shirts and 3 sweatshirts for $48.
Write a system of equations to represent this
situation. Let x=cost of a t-shirt and y=cost of a
sweatshirt.
Determine the price of one t-shirt and the price
of one sweatshirt.

Answers

Answer:

$3.6 = cost of a t-shirt

$10 = cost of a  sweatshirt

Step-by-step explanation:

Given:

10 t-shirts and 2 sweatshirts = $56.

5 t-shirts and 3 sweatshirts = $48.

x = cost of a t-shirt

y = cost of a  sweatshirt

Find:

Price

Computation:

10x + 2y = 56.......eq1

5x + 3y = 48........eq2

From 2 x eq2

10x + 6y = 96.........eq3

From eq3 - eq1

4y = 40

y = 10

from eq1

10x + 2(10) = 56

10x + 20 = 56

10x = 36

x = 3.6

$3.6 = cost of a t-shirt

$10 = cost of a  sweatshirt

If PQ = 8 units, where should the midpoint lie to divide
PQ into two congruent segments?

Answers

Answer:

midpoint of PQ will be at 4 units

Scientists from different fields are trying to understand how the global climate is reacting to the changes caused in nature, and by human activities. They have come up with conflicting interpretations. Which of these is the most likely outcome of differences in interpretations made by scientists on the issue of global climate? All old ideas would be discarded. Scientific evidence would be weakened. Scientists would look for new evidence. The limitations of science would be evident.

Answers

Answer:

Scientists would look for new evidence.

Step-by-step explanation:

Anytime scientists have different interpretations, they carry out more experments to look for new evidence. But this is after they must have tested their own hypothesis. If non of these are possible, they set out to get fresh evidences. Having different opinions would make them come up with new ideas with hope that their theories are valid. And it would also make them carry out more experiments for confirmation or for denial.

hat is the speed of a wave if the wavelength is 18 m and the frequency is 35 Hz? (Quick Hurry, need answer)

Answers

The speed is 630mp/s I think. Because you have to multiply Wavelength by Frequency to get true speed

Brainliest if you get right

Answers

Answer:

14y + -3

Step-by-step explanation:

9y + 5y = 14y

-3 = -3

14y + -3

Find the area of the rectangular field in hectares whose length and breadth are 400 m and 125 m.

Answers

Answer:

50,000 m²

Step-by-step explanation:

Alexandria High School scored 37 points in a football game. Six points are awarded for each touchdown. After each
touchdown, the team can earn one point for the extra kick or two points for a 2-point conversion. The team scored one
fewer 2-point conversions than extra kicks. The team scored 10 times during the game. How many touchdowns were
made during the game? Write and solve a system of equations to get your answer.

Answers

Answer:

Five touchdowns were made in the game

Step-by-step explanation:

Here, we want to know the number of touchdowns made during the game.

We proceed as follows;

Let the number of touch downs be x

So the total points earned through touchdowns is 6 * x = 6x

The number of scores is 10 times

Let the number of extra kick be y which means that the number of conversions will be (y-1)

So the total number of score times will be ;

x + y + y-1 = 10

x + 2y = 11 •••••••••(i)

Now let’s work with points

Touch down points = 6 * x = 6x

Points from extra kick = 1 * y = y

Points from 2-point conversions = 2(y-1) = 2y - 2

So;

6x + y + 2y -2 = 37

6x + 3y = 37 + 2

6x + 3y = 39

divide through by 3

2x + y = 13 •••••••(ii)

So now solve simultaneously

From ii, y = 13 - 2x

Put this into i

x + 2(13-2x) = 11

x + 26 - 4x = 11

x -4x = 11-26

-3x = -15

x = -15/-3

x = 5

There are five touchdowns in the game

There are Five touchdowns were made during the game.

Here,

Alexandria High School scored 37 points in a football game. Six points are awarded for each touchdown.

After each touchdown, the team can earn one point for the extra kick or two points for a 2-point conversion.

The team scored one fewer 2-point conversions than extra kicks. The team scored 10 times during the game.

We want to know the number of touchdowns made during the game.

What is system of equations?

A system of equations is a collection of two or more equations with a same set of unknowns.

Now,

Let the number of touch downs be x

So, the total points earned through touchdowns is;

6 * x = 6x

The number of scores is 10 times

Let the number of extra kick be y which means that the number of conversions will be (y-1)

So, the total number of score times will be ;

x + y + y - 1 = 10

x + 2y = 11 •••••••••(i)

Now let’s work with points

Touch down points = 6 * x = 6x

Points from extra kick = 1 * y = y

Points from 2-point conversions = 2(y-1) = 2y - 2

Hence;

6x + y + 2y -2 = 37

6x + 3y = 37 + 2

6x + 3y = 39

divide through by 3

2x + y = 13 •••••••(ii)

So, now solve this;

From ( ii ), y = 13 - 2x

Put this into ( i )

x + 2(13-2x) = 11

x + 26 - 4x = 11

x -4x = 11-26

-3x = -15

x = -15/-3

x = 5

Hence, There are Five touchdowns were made during the game.

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Figure A is a scale image of Figure B.
2
Figure A
18
Figure B
27
45
What is the value of 2?

Answers

9514 1404 393

Answer:

  30

Step-by-step explanation:

The ratios of corresponding sides in similar figures are proportional.

  x/18 = 45/27

  x = 18(45/27)

  x = 30

HELPPP ASAP PLSSS!!!

Answers

Answer:

a.) yes

b.) no

c.) yes

d.) yes

1. Yes
2. No
3. Yes
4.yes

Could someone help me with these please? I’m stuck.

Answers

Answer:

1. 23

2. 5.83 (5.8 rounded)

3. 1.18 (or 1.2 rounded)

4. unsure how to solve, sorry

Step-by-step explanation:

your formula: a^2+b^2=c^2

1. 20^2+13^2=c^2

400+169=569

(take the square root of 569)

c=23

2. 15^2+b^2=17^2

225+b^2=289

(subtract 225 from both sides)

b^2= 34

(take the square root of 34)

b=5.83 (or 5.8 rounded)

3.  0.2^2+b^2=1.2^2

0.04+b^2=1.44

(subtract 0.04 from bot sides)

b^2=1.4

(take the square root of 1.4)

b=1.18 (or 1.2 rounded)

4. unsure how to solve, sorry

Abdul receives $10 per week for his allowance. His parents have asked him to put $4 in his savings account and the rest of his allowance is spending money.​

Answers

Answer:

2.5

Step-by-step explanation:

just trust me it 2.5

The data set SMOKE.dta contains information on smoking behavior and other variables for a random sample of single adults from the United States. The variable cigs is the (average) number of cigarettes smoked per day. Do you think cigs has a normal distribution in the U.S. adult population? Explain.

Answers

Answer and explanation:

First more than half of the population of the United States do not smoke so the data for smokers in the United States cannot be normally distributed.

Cigs variable does not have a normal distribution in the United States because it is skewed while a Gaussian/normally distributed data is symmetric about it's mean meaning that more values close to the mean occur more frequently. A normally distributed data has more data in the center and is bell shaped while a non normal distribution like the smokers data for US has data skewed to the left or right

Janice is babysitting this summer. She already has $35 in her account before
she begins babysitting. If she makes $25 each week, how much does she have after 3 weeks?

Answers

Answer:

110

Step-by-step explanation:

well if she has 35 in her account already and she babysits for 3 weeks and makes $25 each week that would be 25 times 3 or 25+25+25=75 then you would add 75 to 35 witch is 110

Math question! Need help! :D

Answers

Answer:

3

Step-by-step explanation:

-21/-7 = 3

negative times negative or negative divided by negative is always positive

Clark made four of his truck payments late and was fined four late fees the total change to his saving from late fees was -52 how much was one late fee

Answers

I am not sure but I think it's seven I actually don't know but I tried my best to figure it out I couldn't sorry

there are 15 cats. ten are striped and 7 are striped with green eyes. the rest of the cats have green but are not striped how many cats have green eyes but are not striped

Answers

Answer:

5

Step-by-step explanation:

10 are striped so that only leaves 5 left that are not striped

Find two numbers if their ratio is 9:11 and their difference is 6.
The numbers can be 27, 33 or __, __

Plz help I'm so dumb -_-

Answers

This is impossible, you’ve already found the only possible answer. If you go any higher in the ratio (54;66) you will never be able to get 6 as the difference, same result if u try to go down (18;22).

What is the slope of the line on the graph below?

Answers

Answer:I can’t answer there is no graph.

Step-by-step explanation:

I need a graph, In order to answer your question

What is the answer?!!

Answers

Answer:

12.

Step-by-step explanation:

10
Which one of the following equations is equivalent to 3.3 – 12 = -9?
A x- 5 = -6
B 7x- 3=4
D2x = 4
D x+3 = x- 1

Answers

Answer:

666666600000

Step-by-step explanation:

The 8th graders are having a bake sale to raise money for their field trip to a water park.
If they sell c cupcakes and b brownies at the prices shown below, then the amount of
money raised is given by the expression 0.4C+0.45b. How much money will be raised if
the 8th graders sell 68 cupcakes and 76 brownies?
Bake Sale Prices
Brownies 450
Eupcakes
40¢

Answers

Answer:

27 dollrs for c

76dollra for b

Step-by-step explanation: because you just multiply the 68 and 76 by how much they were for

what is the answer for-4(2x+y)​

Answers

Answer:

-8x-4y

Step-by-step explanation:

distrubutive property

The unit rate/price is the rate/price per 1 item is this true or false

Answers

True unit is 1 item therefore it is the same

help asap for brainliest!

Write an equation. Is the given value a solution?
. A truck driver drove 468 miles on Tuesday. That was 132 miles farther than she drove on Monday. Let d represent the distance she drove on Monday. Did she drive 600 miles on Monday?​

Answers

Answer:No she did not she drove 336 miles

Step-by-step explanation:

Answer:368

Step-by-step explanation:

Please help! Will give 10 points and brainliest to first...only need 2,4,6,8

Answers

Answer:

Step-by-step explanation:

2:     1:4 scale factor

4: 4/5 = x/15. 5x=60. x is 12

6: it's a 2:7 ratio. so x would be 8 and y would be 35

8... it's a 4:7 ratio, as both 52 and 91 are divisible by 13 so there's the scale factor

4/7=x+3/2x-1. 7x+21=8x-4

Like terms on both sides

x=25

–3х + бу = 12
What is the x and y intercept

Answers

Answer:

x = -4. y= 2 is the answer

Step-by-step explanation:

-3x + 6(0) = 12

-3x=12

divide 12 by -3

-4

-3(0) + 6y = 12

6y= 12

12 divided by 6

2

Answer: y=1/2x+2

Step-by-step explanation:

IF YOU GET THIS RIGHT (First )YOU GET BRAINLIEST AND FIVE STAR RATING AND THANKS

A cowboy rides to the town on Friday. Three days later, he leaves on Friday. How is this possible?

Answers

Answer:

The name of the horse is Friday.

Step-by-step explanation:

Cowboy and his Horse !

need these asap, will give brainiest and points

Answers

1)

2 12 Yes its Proportional
3 18 M=6
4 24 y=6x
5 30



2)

2 6 Yes proprional
3 9 m=3
4 12 y=3x
5 15


3)

3 2.25 Yes proportional
4 3.00 m=.75
5 3.75 y=.75x
6 4.50


4)


2 10 —
3 15 m=5
4 20 y=5x
6 30
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