﻿ Thomas buys a cardboard sheet that is 12 by 8 inches. Create an equation for this situation, find the zeros, and sketch the function. What is the size of the cutout he needs to make so that he can fit the maximum amount of food in the box? If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be? What would be the dimensions of this box? Using complete sentences, explain the connection between the cutout and the volume of the box. Design an equation that would work for any cardboard sheet length, q, and width, p. - AssignmentGrade.com

# Thomas buys a cardboard sheet that is 12 by 8 inches. Create an equation for this situation, find the zeros, and sketch the function. What is the size of the cutout he needs to make so that he can fit the maximum amount of food in the box? If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be? What would be the dimensions of this box? Using complete sentences, explain the connection between the cutout and the volume of the box. Design an equation that would work for any cardboard sheet length, q, and width, p.

QUESTION POSTED AT 19/02/2020 - 01:10 PM

For the answer to the question above,

1. If we let x as the side of the square cut-out, the formula for the capacity (volume) of the food dish is:
V = (12 - 2x)(8 - 2x)(x)
V = 96x - 40x^2 + 4x^3
To find the zeros, we equate the equation to 0, so, the values of x that would result to zero would be:
x = 0, 6, 4

2. To get the value of x to obtain the maximum capacity, we differentiate the equation, equate it to zero, and solve for x.
dV/dx = 96 - 80x + 12x^2 = 0
x = 5.10, 1.57
The value of x that would give the maximum capacity is x = 1.57

3. If the volume of the box is 12, then the value of x can be solved using:
12 = 96x - 40x^2 + 4x^3
x = 0.13, 6.22, 3.65
The permissible value of x is 0.13 and 3.65

4. Increasing the cutout of the box increases the volume until its dimension reaches 1.57. After that, the value of the volume decreases it reaches 4.

5. V = (q -2x) (p - 2x) (x)

## Related questions

### PLEASE HELP ME VERY FASTTTTTTT!!!!!! I WILL GIVE BRAINLIEST TO WHO HELPS ME!!! PLZ:0 ILL MAKE IT WORTH 17 POINTS FOR YOU During a sale, a baseball team allows people to buy either a classic ticket (C), or an autograph event ticket (A). Suppose two customers buy one ticket each. What is the sample space for this action? Drag and drop the choices into the box to correctly complete the table. If an item is not in the sample space, do not drag it to the table the choices to be dragged in the sample space are ..... AAA CCC CAC CC AC CA CAA C AAC ACA A CCA ACC AA

AC

CC

CA

AA

hope it helps

can I get the brainliest please???

ANSWERED AT 28/03/2020 - 01:00 PM

QUESTION POSTED AT 28/03/2020 - 01:00 PM

### Which graph represents the function y=1/2x+4 1/2-3

No graphs are shown......

ANSWERED AT 28/03/2020 - 12:59 PM

QUESTION POSTED AT 28/03/2020 - 12:59 PM

### Need help on number 4. Complete Sentences Please! Thank you, ✨

No, because the eagles acid in its stomach is stronger and when the pellet is found most of the bones will be dissolved or disintegrated

ANSWERED AT 28/03/2020 - 12:59 PM

QUESTION POSTED AT 28/03/2020 - 12:59 PM

### Compute and compare the side lengths of the two figures. Does this support an argument claiming that they are congruent? What else must be true to say two polygons are congruent?

The side lengths of the two figures can be calculated with the distance formula:

√ (x1 - x2)² + (y1 - y2)²

AB = √13

BC = √13

CD = √13

DA = √13

A'B' = √13

B'C' = √13

C'D' = √13

D'A' = √13

They are all the same lengths. This supports an argument claiming that they are congruent because if the sides are congruent, then the two polygons are congruent.

Something else that must be true to say that two polygons are congruent is that the angles have equal measures.

Hope this helps! :)

ANSWERED AT 28/03/2020 - 12:59 PM

QUESTION POSTED AT 28/03/2020 - 12:59 PM

### Which number is the most convenient to multiply by when solving this linear system of equations by elimination? 3x - 2t = 4 2x -5 = -t A) -3 B) -1 C) 1 D) 2

I got D) 2 on USATestprep

ANSWERED AT 28/03/2020 - 12:58 PM

QUESTION POSTED AT 28/03/2020 - 12:58 PM

### Write the equation for this table and if you can explain(not required)

I need help with the same stuff

ANSWERED AT 28/03/2020 - 12:57 PM

QUESTION POSTED AT 28/03/2020 - 12:57 PM

### On monday elijah opened a box of cereal and ate 1/8 of its contents.on tuesday he ate 1/6 of what was left.how much did he eat on Tuesday plz help

He basically ate a a third of it  aka 1/3

ANSWERED AT 28/03/2020 - 12:56 PM

QUESTION POSTED AT 28/03/2020 - 12:56 PM

### #7 Casey said that 40 people were surveyed. Is his answer reasonable? Explain

NO because he didn't explain or say what the people were being surveyed about.

ANSWERED AT 28/03/2020 - 12:56 PM

QUESTION POSTED AT 28/03/2020 - 12:56 PM

### Given points A(4,5) and B(-4,11). Find the distance AB to the nearest tenth.

If A(x', y') & B(x",y") the the distance AB is given by the following formula:

AB =√[(x"-x')² + (y"-y')²]

Plug into the above with A(4,5) and B(-4,11).

AB =√[(-4-4)²+(11-5)²] =√(-8)²+(6)² = √(64) + (36) =√100 = 10

ANSWERED AT 28/03/2020 - 12:55 PM

QUESTION POSTED AT 28/03/2020 - 12:55 PM

### Writing to Explain How could you show the inverse operation of Exercise 5 above? Exercise 5 --- E 5 7 9 11 _ _ 42 54 66 {_= unknown you need to solve}

To figure this out, you can do 66/11, which is 6. 54/9 is 6, and 42/7 is also 6. I hope this helps, I can explain more if you need me too.

ANSWERED AT 28/03/2020 - 12:55 PM

QUESTION POSTED AT 28/03/2020 - 12:55 PM

### One of the angles of a parallelogram is equal to 40°. Find the rest of the angles.

Is there some type of image for this?

ANSWERED AT 28/03/2020 - 12:55 PM

QUESTION POSTED AT 28/03/2020 - 12:55 PM

### How can you use a scatter plot to find a trend line

It helps you determine the characteristics of the plot/graph. I am not sure so it is your choose.

ANSWERED AT 28/03/2020 - 12:54 PM

QUESTION POSTED AT 28/03/2020 - 12:54 PM

### What is the approximate probability that the next flower (flower 11) will be at least 60 inches

ANSWERED AT 28/03/2020 - 12:53 PM

QUESTION POSTED AT 28/03/2020 - 12:53 PM

### A: 6x − 3y = -4 B: -4x − y = 5 To solve this system of equations by elimination, what could you multiply each equation by to cancel out the y-variable? A) Multiply A by 2 and B by 3 B) Multiply A by 1 and B by -3 C) Multiply A Multiply A by 1 and B by 3

The answer to this is letter A)

ANSWERED AT 28/03/2020 - 12:53 PM

QUESTION POSTED AT 28/03/2020 - 12:53 PM

### # 7 Casey said that 40 people were surveyed , is his answer reasonable? Explain.

Can't see #7 would help if I could see

ANSWERED AT 28/03/2020 - 12:52 PM

QUESTION POSTED AT 28/03/2020 - 12:52 PM

### Maria has $28 to spend on bottles of water Each bottle of water costs$1.29. There is a $1.50 recycling fee for buying bottled water. 28.150=26.5 is the amount you can spend on water. so 26.5/1.29= 20.54 so you can buy 20 bottles of water ANSWERED AT 28/03/2020 - 12:52 PM QUESTION POSTED AT 28/03/2020 - 12:52 PM ### What is the effect on the graph of the function f(x) = 2x when f(x) is changed to f(3x)? A) vertical stretching B) vertical compression C) horizontal compression D) horizontal stretching Answer: C) Horizontal compression Step-by-step explanation: Since, if y = f(x) is a function, Then y = a f(x) gives a vertical stretch if a > 1 and gives a vertical compression if 0 < a < 1. Also, y = f(bx) gives a horizontal stretch when 0 < b < 1 and gives a horizontal compression if b > 1. Here, The given parent function is, f(x) = 2x And, 3 > 1 Thus, by the above statements, f(3x) will give a horizontal compression. Hence, Option C is correct. ANSWERED AT 28/03/2020 - 12:51 PM QUESTION POSTED AT 28/03/2020 - 12:51 PM ### On monday morning elijah opened a box of cereal and ate 1/8 of it and on tuesday he ate 1/6 how mutch is left How much cereal was in the box??? ANSWERED AT 28/03/2020 - 12:51 PM QUESTION POSTED AT 28/03/2020 - 12:51 PM ### 1) Which answer is a solution of the equation? 2x-y=5 A) (3,-1) B) (1,2) C) 7 D) (2,-1) 2) What is the slope of the line that passes through the points (1,3) and (5,-2)? A) -4/5 B) 4/5 C) 5/4 D) -5/4 For the first one it's D. and the second one is D. as well ANSWERED AT 28/03/2020 - 12:50 PM QUESTION POSTED AT 28/03/2020 - 12:50 PM ### A student solved this problem and said the answer is quarts Jason mixed three kinds of juice to make punch. He mixed quarts of apple juice, quarts of grape juice, and quarts of cranberry juice. What was the total amount of juice in the punch? Is the student's answer reasonable? A. Yes, the answer is reasonable. B. No, the answer is not reasonable. It should be about 3 quarts. C. No, the answer is not reasonable. It should be a bit less than 5 quarts. D. No, the answer is not reasonable. It should be a bit less than 6 quarts. B. no the answer isn't reasonable, it should be about 3 quarts. ANSWERED AT 28/03/2020 - 12:49 PM QUESTION POSTED AT 28/03/2020 - 12:49 PM ### How do you graph the quadratic function 8(x-6)^2 8 translation: narrow or compress graph by a scale factor of 8 -6 translation: shift graph 6 points right ANSWERED AT 28/03/2020 - 12:49 PM QUESTION POSTED AT 28/03/2020 - 12:49 PM ### Joseph received a$20 gift card for downloading music. Each downloaded song costs $1.29. Explain how to write and solve an inequality that can be used to determine the number of songs that he can purchase. Interpret the solution. Let x be the number of songs downloaded. Each song is$1.29; the total cost would be found by multiplying the cost by the number of songs, or 1.29x.
This cannot be more than 20, so we set this less than or equal to 20:
1.29x ≤ 20.

To solve this, we divide both sides by 1.29:
≤ ;
x ≤15.5.

We cannot download half of a song, so we round this down to 15 (although the number rounds up mathematically, he would not have enough money to download 16 songs). This means he can download at most 15 songs.

ANSWERED AT 28/03/2020 - 12:48 PM

QUESTION POSTED AT 28/03/2020 - 12:48 PM

### The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle. 1. 14 m, 5 m, 4 m 2. 3 in., 4 in., 5 in. Are these right triangles?

In a right triangle, the hypotenuse is always the longest side.  Plus, the hypotenuse squared has to equal the sum of the squares of the other 2 sides.  For the first "triangle" above: does ?  Let's check.  196 = 25 + 16 so does 196 = 41?  Obviously not.  So that is not a right triangle.  Let's check the second one the same way.  Does ?  25 = 9 + 16.  Does 25 = 25?  Of course it does!  So 1 is not a right triangle, but 2 is!

ANSWERED AT 28/03/2020 - 12:48 PM

QUESTION POSTED AT 28/03/2020 - 12:48 PM

### An ice cream store owner randomly samples 50 customers each day on three separate days to give their opinion about which flavor should be the flavor of the month. Vanilla - Day 1 = 13 Chocolaté - Day 1 = 12 Rocky Road - Day 1 = 11 Cheesecake- Day 1 = 14 Total = 50 Vanilla - Day 2 = 12 Chocolate - Day 2 = 15 Rocky Road - Day 2 = 11 Cheesecake- Day 2 = 12 Total = 50 Vanilla - Day 3 = 15 Chocolate - Day 3 = 7 Rocky Road - Day 3 = 8 Cheesecake - Day 3 = 20 Total = 50 Select from the drop- down menu to complete the statement using the information in the table. Based on the results of the survey, if the ice cream store owner asks 2300 people, ( choose ) 40 150 460 613 will most likely pick vanilla to be the flavor of the month. Please help 10 points will be given and marked brainliest if answers asap and correct:)

correct option is:

613

Step-by-step explanation:

Out of 150 people(50 people day 1, 50 people day 2 and 50 people day 3)

40 people prefer vanilla (13 of day 1,12 of day 2 and 15 of day 3)

That means,   out of 150  : 40 prefer vanilla

out of 2300 :   prefer vanilla

≈  613

Hence, the correct option is:

613

ANSWERED AT 28/03/2020 - 12:47 PM

QUESTION POSTED AT 28/03/2020 - 12:47 PM

### A web designer charges a $200 fee plus$50 an hour to build a website. Which equation represents the total cost, y, to a consumer based on the number of hours, x, it takes to build the website

Y=200+50x...........

ANSWERED AT 28/03/2020 - 12:47 PM

QUESTION POSTED AT 28/03/2020 - 12:47 PM

### What are the intercepts of 6x + 8y = 24? a.(4, 0) and (0, 1) b.(12, 0) and (0, 1) c.(3, 0) and (0, 4) d.(4, 0) and (0, 3)

6x + 8y = 24

x intercept is the value when y =0 & y intercept is the value when x=0

for y=0 ==> 6x+0 =24 ==> x=4 for x=0==> 0+8y =24 ==> y=3

ANSWERED AT 28/03/2020 - 12:46 PM

QUESTION POSTED AT 28/03/2020 - 12:46 PM

### Ιғ a cιrcle нaѕ a radιυѕ oғ 12 cм and a ѕecтor deғιned вy a 120 degree arc, wнaт ιѕ тнe area oғ тнe ѕecтor

120
times 12 - 360
it should give you the right answer if you solve the problem like that

ANSWERED AT 28/03/2020 - 12:46 PM

QUESTION POSTED AT 28/03/2020 - 12:46 PM

### Jorge needs to ship a thin metal rod to a metalworking shop. The only boxes available for shipping are 7-inch cubes. To the nearest inch, what is the length of the longest metal rod that can be sent? 11 inches 12 inches 13 inches 14 inches

The length of the longest metal rod that can be sent is 12 inches.

## Step-by-step explanation:

As given, the only boxes available for shipping are 7-inch cubes. As Jorge needs to ship a thin metal rod to a metalworking shop, he will put the rods diagonally or space diagonally in the box.

The space diagonal of a cube can be found by the formula :

=

Here, x is 7 inches.

So, Diagonal is =

= inches.

Rounding this to nearest whole number we get 12.

So, the length of the longest metal rod that can be sent is 12 inches.

ANSWERED AT 28/03/2020 - 12:44 PM

QUESTION POSTED AT 28/03/2020 - 12:44 PM

### Joe has two empty boxes, one box is 15 inches wide, 20 inches long and 10 inches high. The second box has the same length and width but is 4 inches taller. How much additional spaces is in the box

Space in the box = volume
volume = length x width x height
box 1 volume = 15 x 20 x 10 = 3000
box 2 volume = 15 x 20 x 14 = 4200
how much space is left = box 2 - box 1 = 1200 inches

ANSWERED AT 28/03/2020 - 12:44 PM

QUESTION POSTED AT 28/03/2020 - 12:44 PM

### PLZZZ HELP A student solved this problem by making a table. Jules bought a scarf and a patch for each of the 8 summer campers in his group. The scarves cost $5.75 each and the patches cost$2.50 each. How much money did Jules spend? Number of campers 1 2 3 4 5 6 7 8 Total cost $8.25$16.50 $24.75$33 $41.25$49.50 $57.75$66 Jules spent a total of $66. Solve this problem using a similar strategy. Donna charges$25.75 for a haircut and $40.50 for a color treatment. Donna did 5 haircuts and 3 color treatment each day for 6 days. How much money did Donna earn altogether?$

Jules spent \$64 if u multiply each cost times 8 and add it u get that

ANSWERED AT 28/03/2020 - 12:44 PM

QUESTION POSTED AT 28/03/2020 - 12:44 PM