Clare wants to make an open-top box by cutting out corners of a 30 inch by 25 inch piece of poster board and then folding up the sides. The volume, `V\left(x\right),` in cubic inches of the open-top box is a function of the side length, `x,`in inches, of the square cutouts.

Answers

Answer 1

Answer:

V(x) = 4x³ - 110x² + 750x

Step-by-step explanation:

For each side of the base of the open-top box, since x inches is cut out from each side, we have 2x inches removed from each sides dimension.

Since the dimensions of the poster are 30 inches by 25 inches, the area of the base of the open-top box is thus

A(x) = (30 - 2x)(25 - 2x) since we remove 2x inches from each dimension.

Now, the height of the open-top box is x. So, its volume is V(x) = Ax

V(x) = (30 - 2x)(25 - 2x)x

V(x) = (750 - 60x - 50x + 4x²)x

V(x) = (750 - 110x + 4x²)x

Expanding the bracket, we have

V(x) = 750x - 110x² + 4x³

Re-arranging, we have

V(x) = 4x³ - 110x² + 750x


Related Questions

You are adding to rational numbers with different signs. How can you tell if the sum will be positive, negative, or zero? #24​

Answers

Answer:

it would be positive

Step-by-step explanation:

Answer:

Step-by-step explanation:

A positive plus a negative equals a negative:

4 + (-3) = 1

A positive plus a positive equals a positive:

4 + 4 = 8

A negative plus a negative equals a negative:

(-2 )+ (-2) = -4

If two number have the same absolute value, they will equal zero:

-3 + 3 = 0

- 2 + 2 = 0

The length of a cell phone is 1.8 1.8 inches and the width is 4.4 4.4 inches. The company making the cell phone wants to make a new version whose length will be 1.17 1.17 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone

Answers

Answer: Width=2.86 in.


Explanation: Since we have a proportion, we can use the equation 1.8/4.4=1.17/x.

Cross multiplying gives us 1.17*4.4=1.8x and solving for x gives us 2.86 in.

What is -4 1/2 - (-1.07)

Answers

Answer:

The answer is -3.43

Step-by-step explanation:

The difference between two numbers is 3.50. The lesser number is 1.65.
What is the other number?

Answers

Answer:

5.15

Step-by-step explanation:

you add 3.50 and 1.65 to get the other number

Write a system of equations with the solution (4,-3). Show your work.

Answers

Answer:

4x4 then dived by 8you will get 4x4=16 dived by 8=8

can you help me again UwU

Answers

Answer:

Upper Left

Bigger slopes means steeper lines.

Good luck!

4x + 6y - z=-18
3x +2y - 4z = -24
- 5x + 3y + 2z = 15
find x y and z

Answers

Answer:

x = -2, y = -1, z = 4

Step-by-step explanation:

4x + 6y - z=-18

z  = 18  + 4 x  +  6 y

3x +2y - 4z = -24

z  = 6  + (3x)/ 4  +  y /2

- 5x + 3y + 2z = 15

z = 15/2 + (5x)/2 - (3y)/2

18  + 4 x  +  6 y = 6  + (3x)/ 4  +  y /2  = 15/2 + (5x)/2 - (3y)/2

x = -22y/13 - 48/13

4(-22y/13 - 48/13) + 6y - (15/2 + (5(-22y/13 - 48/13))/2 - (3y)/2) = -18

Compute the output value of the variables x and y with respect to the input values of x, y, and z coefficients.

What is the equation of the line through the points (3, 2), (8, 5), (13, 8) and (18, 11)? HELP ASAP I WILL MAKR BRAINLIEST PLSSSSSSS

Answers

Is it multiple choice?

Answer:(it might be)

y=5/3x+1/3

Step-by-step explanation:

Is -4pi a rational number

Answers

Answer:

no

Step-by-step explanation:

Pi is irrational

Answer:

No it is a irrational number

Step-by-step explanation:

-4pi is not a whole number, integer number, or a rational number. It is only a irrational number.

7x-5=8(x*3) what value of x makes this equation true

Answers

The given equation is:

[tex]\displaystyle 7x-5=8(x+3)[/tex]

The first step you need to do is open the parentheses and distribute the 8 to x+3. It will be 8 times x and 3 times x.

[tex]8(x+3)=8 \times x+ 8 \times 3\\\\8 \times x=8x\\8 \times 3=24[/tex]

[tex]8(x+3) \rightarrow 8x+24[/tex]

Rewrite the equation:

[tex]7x-5=8x+24[/tex]

Now you need to move one of the variables to the other side.

If you move 7x to the other side, then:

You can move the variable by doing the opposite of it. Since 7x is positive, you can move it by subtracting 7x, which is negative. Subtract 7x on both sides:

[tex]7x-5-7x=8x+24-7x\\-5=x+24[/tex]

Now you need to leave x alone. x is being added to 24, so remove it by subtracting both sides by 24. Remember that when you're subtracting from a negative number, you're actually adding while keeping the negative sign.

[tex]-5-24=x+24-24[/tex]

Subtract:

[tex]\bf-29=x[/tex]

If you move 8x to the other side, then:

8x is positive, so you can move it by subtracting 8x, which is negative. Subtract 8x on both sides:

[tex]7x-5-8x=8x+24-8x\\-x-5=24[/tex]

You need to leave the variable alone, so move -5 to the other side. You can do this by adding 5 to both sides.

[tex]-x-5+5=24+5\\-x=29[/tex]

Lastly, x is negative, but you're looking for the value of positive x. Divide both sides by -1 to remove the negative sign.

[tex]\displaystyle \frac{-x}{-1} =\frac{29}{-1}[/tex]

Remember that a positive number divided by a negative number is negative. Divide:

[tex]\bf x=-29[/tex]

The answer to your question is x = -29.

Step-by-step explanation:

Question:-

Solve for x

[tex]\\ \tt{:}\leadsto 7x-5=8(x+3)[/tex]

SOLUTION:-

[tex]\\ \tt{:}\leadsto 7x-5=8(x+3)[/tex]

[tex]\\ \tt{:}\leadsto 7x-5=8x+24[/tex]

[tex]\\ \tt{:}\leadsto 7x-8x=24+5[/tex]

[tex]\\ \tt{:}\leadsto -x=29[/tex]

[tex]\\ \tt{:}\leadsto x=29[/tex]

Which point is the y-intercept of the line represented by the equation y-3=13(x+6)?







(0,9)
(0,5)
(5,0)
(0,2)

Answers

Answer:

The equation for a zero slope line is one where the X value may vary but the Y value will always be constant. An equation for a zero slope line will be y = b, where the line's slope is 0 (m = 0).

The y-intercept of the equation will be at (0, 81). Then the correct option is A.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y - 3 = 13(x + 6)

Convert the linear equation into slope-intercept form. Then the equation is written as,

y - 3 = 13x + 78

y = 13x + 78 + 3

y = 13x + 81

The y-intercept of the equation will be at (0, 81). Then the correct option is A.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

The options are wrong. Then the correct options are given below.

A. (0, 81)

B. (0, -81)

C. (-81, 0)

D. (81, 0)

What is an equation of the line that passes through the point
(6,7) and is parallel to the line
2x−3y=9?

Answers

Answer:

The equation of line parallel to given line passing through (6,7) is: [tex]y = \frac{2}{3}x+3[/tex]

Step-by-step explanation:

Given equation of line is:

[tex]2x-3y = 9[/tex]

We have to convert the equation in slope-intercept form. The slope-intercept form is given by:

[tex]y= mx+b[/tex]

Adding 3y on both sides and subtracting 9 from both sides

[tex]2x-3y+3y-9 = 9+3y-9\\2x-9 = 3y\\3y = 2x-9[/tex]

Dividing whole equation by 3

[tex]\frac{3y}{3} = \frac{2x-9}{3}\\y = \frac{2}{3}x - \frac{9}{3}\\y = \frac{2}{3}x-3[/tex]

Let m be the slope of given line then

m = 2/3

Let m1 be the slope of line parallel to given line. Slopes of two parallel lines is equal that means:

m = m1 = 2/3

The equation of line will be:

[tex]y = m_1x +b\\y = \frac{2}{3}x+b[/tex]

Putting the point (6,7) in equation

[tex]7 = \frac{2}{3}(6) +b\\7 = 2(2) +b\\7 = 4+b\\b = 7-4\\b = 3[/tex]

Putting the value of b

[tex]y = \frac{2}{3}x+3[/tex]

Hence,

The equation of line parallel to given line passing through (6,7) is: [tex]y = \frac{2}{3}x+3[/tex]

y=+/-√bx+c+d Use the inverse of the function y= x2 -18x to find the unknown values.

Answers

Answer:

a=1

b=81

c=9

Step-by-step explanation:

here you go, have a great day!

Tracy is borrowing $10,700 on a six-year, %, add-on interest loan. What will Tracy's monthly payments be?

Answers

Answer:

Step-by-step explanation:

Use the formula I=prt. (Interest = principle x rate x time)

So, I = 10700 x 0.07 (7% as a decimal) x 6

So, I = 749(6)

I = 4494

Now, divide 4494 by 6(12)

4494/71

This = 63.3 dollars.

Therefore, she is paying 63 dollars per month.

Tracy's monthly payments is $62.41.

What is Simple Interest?

The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.

Amount (A) = Principal (P) + Interest (I)

and, Simple Interest = PRT/100

Given:

P= 10700

Time= 6 year

Interest = 7%

Now, using simple interest

SI = P x R x T/100

SI = (10700 x 0.07 x 6)

SI = $4494

So, Tracy's yearly payments

= 4494/6

= 749

and, Tracy's monthly payments

= 749 / 12

= 62.41

Hence, Tracy's monthly payments is $62.41.

Learn more about Simple interest here:

https://brainly.com/question/25845758

#SPJ2


What is the area of the above trapezoid? Please help
I will cash app if you help out

Answers

Answer:

b should be correct

Step-by-step explanation:

no need to cash app me its been a while since ive done math so i dont even know if this is right

When given a table, what operations do you use to determine the slope of the graph?
Group of answer choices

Subtraction

Division

Both A & B

None of the Above

Answers

Answer:

division

Step-by-step explanation:

2(x+3)=x-4
help!
45 points!

Answers

2(x+3) = x-4
2x +6 = x-4
x + 6 = -4
x= -10 :)

The graph shows how much money Priya has in her savings account weeks after she started saving on a regular basis. How much money does Priya have in the account after 10 weeks? How long did it take her to save $200? How much money did Priya have in her savings account when she started to save regularly? Write an equation to represent the dollar amount in her savings account and the number of weeks of saving. Be sure to specify what each variable represents.

Answers

Answer:

How much money does priya have after 10 weeks? 320

How long did it take her to save 200? 5

How much did priya have in her savings account when she started to save regularly? 80

Buying three tires at $80 each and getting a fourth tire free

Answers

Answer

3 x 80=240

240 / 4=$60 effective unit rate for each tire.

Step-by-step explanation:

mark me as brainliest!

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

Pick two points on the line, then use the slope formula.
The slope is

Answers

The slope is 1/2. Hope this helps!!

Answer:

the slope is 1/2

Step-by-step explanation:

ill give the right answer brainliest!

Answers

Answer:

C=84, D=80,b=99 and a=81

Step-by-step explanation:

In a quadrilateral, it's opposite measurements has to be equal to 180 degrees. So, for example if one side is 100 then the opposite side has to be equal to 80 so that if you add them there sum would be 180 degree.

Sorry, but I am not sure about a but you can try 81 degrees if you want. Hope this helps you!

1. Estimate twenty-nine percent of forty-eight. Please again no decimal form!
2. Estimate sixty-two percent of one hundred twenty-four. no decimal form please!
3. WORK Karl made $365 last month doing odd jobs after school. If 75% of the money he made was from doing yardwork, about how much did Karl make doing yardwork?

Answers

Number 1...

[tex]\boxed{29\;percent\;of\;48=(?)}[/tex]

What is the equation of a line parallel to y=7x-8 that passes through (5, 22)?

Answers

Answer:

y = 7x - 13

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 7x - 8 ← is in slope- intercept form

with slope m = 7

Parallel lines have equal slopes, thus

y = 7x + c ← is the partial equation

To find c substitute (5, 22) into the partial equation

22 = 35 + c ⇒ c = 22 - 35 = - 13

y = 7x - 13 ← equation of parallel line

answer this strenuous question

Answers

Yes very tru jnhibjhgyufhgcghcguv

the awnser is 15 i did it by steep like there is 16 ones then you multiply and thye awnser i got was 15.

there you go :D

Answers

Answer:

What is the question

Step-by-step explanation:

Upload a picture

TRUE OR FALSE: Determine whether the figure is a parallelogram for the given values of the variables

Answers

Answer:

True

Step-by-step explanation:

jrhudoakueieeisp

Answer:

A: True

B: False

Step-by-step explanation:

8a: x=5 and y=11

A= 84°

B= 96°

C= 96°

D= 84°

8b: x=4 and y=2

A= 66°

B= 6°

C= 15°

D= 64°

Tell me if this is correct?
How many parts is the
whole divided into?

Solve this too?
Divided into ____ Equal Parts

Answers

Answer:

Divided into five equal parts

A factory makes 300 sheets of construction paper per hour. How many sheets of construction paper will the factory make in 2 hours?

Answers

Answer: 600 sheets

Step-by-step explanation:

300/1 -> 300 sheets per 1 hour

To find the number in two hours, multiply the numerator and the denominator by 2.

300 x 2 = 600

1 x 2 = 2

Thus, the factor makes 600 sheets in 2 hours.

Write an equation for the graph in the form Y=KX

Answers

Answer:

Step-by-step explanation:

y=8x

You are packing a canoe for a
river trip. The canoe weighs 45 pounds and each supply pack weighs 12 pounds. How many supply packs can you put in the canoe if your total weight must be under 117 pounds?

Answers

Answer:

12x + 45 < 117

If you want an exact number, it is 6 packs. That will make the weight of the canoe exactly 117 pounds
Other Questions
What were the 3 Acts the made up the "Intolerable Acts"? Write the square of (2x+1/x) Green tea Oreos in China, chocolate and peanut butter Oreos in Indonesia, and banana dulce de leche Oreos in Argentina are examples of Kraft using ________ strategy.a. an internationalb. amultidomesticc. a single countryd. a transnational The perimeter of a rectangle is 152 meters. The width is 22 meters less than 3/4 of its length. Find the length and width. Division and sub division of arteries finally end into ......... I am begging THIS IS FOR PPL THAT HAVE READ The Highwayman PLZ HELP! Question IS IN image BELLOW ignore THE GREEN square This table can be used to organize Gigis credit card balances and payments over 6 months. The annual percentage rate on the credit card is 14%. Gigis Credit Card Payments Month Balance Payment Interest Rate Interest Charged 1 $650 $300 0.01167 $4.08 2 $354.08 $50 0.01167 3 $307.63 $50 0.01167 4 $260.64 $50 0.01167 5 $213.10 $50 0.01167 6 $165 $50 0.01167 What is the amount of interest charged for the first 6 months? $ Question #1Multiple SelectWhich collections can contain duplicate items?dequeO datasetO listtupleorganizer I am making mashed potatoes with 1.25 pounds of mashed potatoes, .14 pounds of olive oil, and .33 pounds of almond milk. How much will the final dish weigh? please help if you can. what is the protagonists main motivation in the story condensed milk Explain how the members of the legislature are chosen. maikling reaksyon tungkol sa kasaysayan ng wikang pambansa Simplify.(6x5+4x^2)+(2x2) HELP ASAP!right answer Ill give you a crown x^2 - x -12 < 0 a) {-3} b) (-infinity, -3) u (3, infinity)c) (-3, 4)d) [-3, 4] Alonzo raises sheep and goats. Alonzo sells each sheep for $125 and each goat for $75. Alonzo raised 14 sheep and goats this year and sold them all for a total of $1,500. How many sheep and how many goats did Alonzo sell? Read this passage about Christopher Reeve.Christopher Reeve was born on September 25, 1952, in New York City. His mother was a journalist, and his father was a professor. As a kid he played sports, did well in school, and liked acting. His passion for acting goes back to playing with his brother when they were little. Reeve acted in his first play at the age of nine. After attending college, taking acting classes, and acting in many plays and movies, Reeve landed his biggest role. In 1978, he played the title role in Superman. He received very positive reviews for his performance and starred as Superman in all the sequels. Reeve was soon acting as the lead role in dozens of movies after Superman. Once well-known, Reeve used his celebrity status for good causes, such as visiting very sick children through the Make-A-Wish foundation. He was also a track and field coach at the Special Olympics.Besides acting, Reeve was also a licensed pilot and liked horseback riding. He learned to ride horses for a movie role, and he continued riding in his free time. Unfortunately, while riding one day in 1995, Reeve fell from his horse and became paralyzed from the neck down. Being confined to a wheelchair did not hold back Reeve from being socially active, and after many surgeries and rehabilitation, he decided to dedicate his life to helping people with spinal-cord injuries. He created the Christopher Reeve Foundation, which supports the improvement of the lives of people with disabilities and helps fund research to find a cure for paralysis. He was also politically active, working with senators to make sure that people with disabilities were treated fairly in the workplace. Reeve received many awards for his dedication to public service. He also wrote two books about his experiences, and a documentary was made about his life. Reeve passed away in 2004, but his legacy lives on today. He touched the lives of many people and showed us what it means to overcome extreme odds by never giving up.Which fact about Reeve best displays the qualities that make him a good candidate for a "Most Devoted" honor in a yearbook?A) Reeve fell from his horse and became paralyzed from the neck down.B) Reeve passed away in 2004, but his legacy lives on today.C) He decided to dedicate his life to helping people with spinal-cord injuries.D) Christopher Reeve was born on September 25, 1952, in New York City. im really badat this stuff anyone knows the answer I dont know where to use akk. Or dat.