Recall the shipping box scenario from the Introduction. As an employee of a sporting goods company, you need to order shipping boxes for bike helmets. Each helmet is packaged in a box that is n inches wide, n inches long, and 8 inches tall. The shipping box you order should accommodate the boxed helmets along with some packing material that will take up an extra 2 inches of space along the width and 4 inches of space along the length. The height of the shipping box should be the same as the helmet box. The volume of the shipping box needs to be 1,144 cubic inches. The equation that models the volume of the shipping box is 8(n + 2)(n + 4) = 1,144.

Answers

Answer 1

Answer:

The dimensions of the helmet box are as follows

Width is 9 inches

Length is 9 inches

Height is 8 inches

The dimensions of the shipping box ordered are as follows;

Width is 11 inches

Length is 13 inches

Height is 8 inches

Step-by-step explanation:

8(n + 2)(n + 4) = 1144

8·n² + 48·n + 64 = 1144

8·n² + 48·n - 1080 = 0

8×(n - 9)×(n + 15) = 0

∴ n = 9 or -15 inches

The dimensions of the helmet box are as follows

Width = 9 in.

Length = 9 in.

Height = 8 in.

The dimensions of the shipping box ordered are as follows;

Width = 9 + 2 = 11 in.

Length = 9 + 4 = 13 in.

Height = 8 in.

Answer 2

Answer:

8 inches x 11 inches x 13 inches

Step-by-step explanation:

I got correct on edmentum


Related Questions

Which equation models a line that is perpendicular to y = x - 1 and goes through the point (5,4)

Answers

Answer:

y = - x + 9

Step-by-step explanation:

Because the line is perpendicular, the slope with be the opposite reciprocal. So, if the slope is 1 as in the equation y = x - 1, the opposite reciprocal is -1.

So the equation that is perpendicular will look like this so far:

y = -x + b   (b represents our y-intercept that we have not found yet)

Now we will find the y-intercept. We can find it by substituting the coordinates (5,4) as x and y into the equation right above ^^.

So,  4 = -(5) +b     or     4 = -5 + b

Add 5 to both sides to isolate b on the right side. b = 9

Therefore, the y-intercept is 9.

Now we have found everything we need for the equation, which is

y = - x + 9

Please answer correctly !!!! Will mark brainliest !!!!!!!!!

Answers

Answer:

[tex]b= \frac{-4}{7} a - \frac{52}{7}[/tex]

Step-by-step explanation:

1st, isolate b.

7b=-4a-52

Next, divide both sides by 7.

b=(-4a/7)-(52/7)

May You Please Help Me With This Problem

Answers

Answer:

x² + x - 8

Step-by-step explanation:

(f . g)(x) is same with (f(g(x))

so insert the g(x) equation into f(x) and change the x on it

f(g(x)) = g(x) - 2

f(g(x)) = (x² + x - 6) - 2 = x² + x - 6 - 2 = x² + x -8

so

(f.g)(x) is x² + x - 8

Given that 3m=2c-5k,express c in terms of k and m.

Answers

Answer:

The answer is

[tex]c = \frac{3m + 5k}{2} [/tex]

Step-by-step explanation:

You have to move all the unrelated terms to the other side :

[tex]3m = 2c - 5k[/tex]

[tex]3m + 5k = 2c[/tex]

[tex]2c = 3m + 5k[/tex]

Next you have to divide it by 2 :

[tex]c = \frac{3m + 5k}{2} [/tex]

you can use a change to separate c.so,c=(3m+5k)/2

Can someone please help me with the slope?

Answers

Answer:

1/2

Step-by-step explanation:

For each two units that this line moves to the right, it rises one. This means that it has a slope of 1/2. Hope this helps!

Circle T is shown. Line segments T S, T R, T Q, and T P are radii. Lines are drawn to connect points S and R and points P and Q to form secants. Angles R T S and Q T P are congruent. What is true regarding two adjacent arcs created by two intersecting diameters? They always have equal measures. The difference of their measures is 90°. The sum of their measures is 180°. Their measures cannot be equal.

Answers

Answer: the sum of their measures is 180 degrees

Step-by-step explanation:

I just got it right

The angles R T S and Q T P are vertically opposite angles. So that they always have equal measures.

Circle :

In given circle, T is center of circle .

and RP and SQ are diameter of circle which are intersecting at center T.

The diagram of circle is attached below.

In the diagram of circle, Angles R T S and Q T P are congruent.

So that,  [tex]\angle RTS=\angle QTP\\\\[/tex]

Since, both diameter are crossing each other.

So that, Angles R T S and Q T P are vertically opposite angles.

Therefore, they always have equal measures.

Learn more about the diameter of circle here:

https://brainly.com/question/1649593

Solve each equation and check your solution:
A) -2w=26
B)3n-3=17
C)15 - w = 45
D) 5c- 7c= 32
E) 6+ 6h = 2h -5
F) 2.5x - 4 + 1.2x = 3.5

Answers

Answer:

A. w = 26/2 = -13

B. 3n = 20

     n = 20/3

C. -w = 30

     w = -30

D. -2c = 32

       c = -16

E. 4h = -11

     h = -11/4

F. 3.7x = 7.5

        x = 75/37

Answer:

    x = 75/37

Step-by-step explanation:

they paid $13 for each pepperoni pizza and $11for each plain pizza the club bought total of 18 pizzas for the party and paint a total of $212 Drag and drop the numbers to the boxes to create an equation which models this situation if x=the number of pepperoni pizza and y=the numbers of plain pizza boght

Answers

Complete question;

A booster club paid for pizzas for an  end of season party. They paid $13  for each pepperoni pizza and $11 for  each plain pizza. The club bought a

total of 18 pizzas for the party and  paid a total of $212.

Drag and drop the numbers to the  boxes to create an equation which  models this situation if x = the  number of pepperoni pizzas and y =  the number of plain pizzas bought.

Answer:

13x + 11y = 212

Step-by-step explanation:

They bought 2 different recipe of pizza. The first is the pepperoni pizza and the second kind is the plain pizza. The pepperoni pizza cost $13 each while the  plain Pizza cost $11 each. The total number of pizza bought is 18 in number.

The total cost of the pizza is also $212.

number of pizza bought = 18

total cost of pizza = $212

x = the  number of pepperoni pizzas

y =  the number of plain pizzas

The number of pepperoni pizzas multiply by the cost for each will give the cost of the pepperoni pizzas. This same method is applied to get the cost of the plain pizzas.

Therefore, adding the individual cost of the kinds of pizza will give the total cost of the pizzas.

13x + 11y = 212

Jeremy’s bank account started at a balance of $124 this week. Since then, he wrote a check, which decreased his balance by $147. Jeremy was then charged an overdraft fee, decreasing his balance by $32. Finally, he deposited a paycheck, which increased his balance by $567. What is Jeremy’s ending balance after these transactions, in dollars?

Answers

Answer:

$512

Step-by-step explanation:

His bank account started at a balance of $124.

He wrote a check, which decreased his balance by $147. His new balance is:

124 - 147 = -$23

Jeremy was then charged an overdraft fee, decreasing his balance by $32. That is:

-23 - 32 = -$55

He deposited a paycheck, which increased his balance by $567. His account balance will become:

-55 + 567 = $512

His account balance after those transactions is $512.

A right circular solid cone of base radius 42cm and height 84cm has the same volume as a solid cylinder of height 112cm find the radius of the cylinder

Answers

Answer:

21 cm

Step-by-step explanation:

Volume of cone is given by [tex]1/3(\pi r^2h)[/tex]

volume of cylinder is given by [tex]\pi r^2h[/tex]

where r is the radius of base and h is the height

_________________________________

For cone

radius = 42cm

height = 84

volume = [tex]1/3(\pi *42^2*84)[/tex]  (1)

________________________________

For cone

radius = to find let it be r

height =112

volume = [tex]\pi *r^2*112[/tex]  (2)

_______________________________________

since , volume of both solid are same

thus, equation 1 = equation 2

[tex]1/3(\pi *42^2*84) = \pi *r^2*112\\=> r^2 = 1/3((\pi *42^2*84) / 112*\pi \\=> r^2 = 1/3(42*42*84/112) = 441\\=> r = \sqrt{441} \\=> r = 21[/tex]

Thus, radius of cylinder is 21 cm

PLEASE HELP RIGHT NOW I WILL MARK AS BRAINIEST!!!!!!!!!!!!!!!!
Select three (3) TRUE statements ABOUT quadrilaterals.

a.) A quadrilateral is a polygon with 4 sides and 4 angles.
b.) The sum of the angle measurements in a quadrilateral are 180 degrees.
c.) A rectangle is a parallelogram with 4 right angles.
d.) A square is a rectangle with all 4 equal sides.
e.) A quadrilateral is not a polygon.
f.) All the angles measures in a quadrilateral have to be right angles.

Answers

Answer:

A, B and E

Step-by-step explanation:

In a box-and-whisker plot, the interquartile
range is a measure of the spread of the
middle half of the data. Find the interquartile
range for the data set: 10, 3, 7, 6, 9, 12, 13.

Answers

Answer:

IQR=8

Step-by-step explanation:

write numbers in ascending order

3 6 9 10 12 13

find the middle, in this case, it's two numbers (10 and 12)

3 6 are on the left, find the middle between them; 3+6/2

4.5

12 and 13 are on the right, find the middle between them;

12+13/2

12.5

IQR=12.5-4.5

Find the value of 5!
O A. 120
O B. 20
O C. 15
O D. 25

Answers

Answer:

A: 120

Step-by-step explanation:

5! means 5 factorial

the factorial of a number is the number times every whole number until 1

in this case,

5 * 4 * 3 * 2 * 1

5 * 4 = 20 , 3 * 2 * 1 = 6

20 * 6 = 120 (option A)

If this helps. please consider giving me brainliest.

Answer:

a 120

Step-by-step explanation:

Which number is less than 0.37? A. 0.72 B. 0.5 C. 0.35 D. 0.41

Answers

Answer:

0.35 is less than 0.37 because 35 < 37.

Answer:

C is the correct answer

Step-by-step explanation:

1)In an year the value of a motorcycle depreciates by 10% of its value at the beginning of that year.What is its value after two years if the purchased price was $7200?
2)When John Short increases the spend at which he motors from an average of 40mph to 50mph,the number of miles travelled per gallon decreases by 25%.If he travels 36 miles on each gallon when his average speed is 30 mph how many miles per gallon can he execpt at an average speed of 50mph? ​

Answers

Answer:1. $5760

Step-by-step explanation:

Answer:

the answer is 1,200 thats what i got

Step-by-step explanation:

The product of a number and its ___________ is
A).opposite
B)reciprocal
C)factor
D)quotient

Answers

Reciprocal

Explanation:
I know what I know and this is one of those things

Answer:

Most definitely reciprocal

g(x)=x^3+6x^2+12x+8 determine

Answers

g(-1) = 1

g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8

g(-1) = 1

Answer:

g(-1) = 1

Step-by-step explanation:

g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8

g(-1) = 1

A company is evaluating a new reading program that is supposed to improve test scores. The box plots show the results of reading tests given before and after using the program. With this data, what is the most reasonable answer to the question: Does the program improve test scores 20 pts

Answers

Answer:

Yes, because the median test score increased 5 points.

Step-by-step explanation:

Answer:

Yes, because the median test score increased 5 points

good luck and have a great day

Divide $1200 in the ratio 5:3:2

Answers

Answer:

Step-by-step explanation:

16

Please help me with my math question!!

Answers

Answer: A

Step-by-step explanation:

Using sohcahtoa you can figure out that the missing side length is 5.98 :)

Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!!

Answers

Answer:

Multiply 5 to both sides to get

(x+3)^2 = 100

Step-by-step explanation:

Please refer to the picture above.

Simplify the equation by aiming to eliminate the fraction in the right hand side of the equation by multiplying the denominator to both sides of the equation in step 2

Answer:

[tex](x + 3)^{2}[/tex] = 100

Step-by-step explanation:

The final velocity, V, of an object under constant acceleration can be found using the formula v2=v2+2as, where v is the initial velocity (in meters per second), a is acceleration (in meters per second), and s is the distance (in meters). What is the formula solved for a?

Answers

Answer: a = (V^2 - v^2)/2s

Step-by-step explanation:

The equation for the final velocity is:

V^2 = v^2 + 2*a*s

where V is the final velocity, v is the initial velocity, a is the acceleration and s is the distance.

Now, we want to solve this formula for a, this would mean isolate a in one side of the equation, this is pretty simple, first we pass subtract v^2 in both sides.

V^2 - v^2 = v^2 + 2*a*s - v^2

V^2 - v^2 = 2*a*s

now we can divide by 2*s in both sides:

(V^2 - v^2)/2s = 2*a*s/2s = a

a = (V^2 - v^2)/2s

what is the equation of the line? please help !!!! first and correct answer will get brainesttt

Answers

Answer:

y=1/2x-4

Step-by-step explanation

somebody come help me I'm stuck in this problem how do I simplify it using exponent rule ​

Answers

Answer:

-5x^4y^3

Step-by-step explanation:

so you divide -25 by 5 and the rule is if it is division for exponents then you subtract the exponent so 6-2=4, 7-4=3, 3-3=0. z^0 is 1 so we don't have to write it out.

screenshot below-mathematics ,help please!!

Answers

Answer:

(a) range = difference between highest

mark and lowest mark

range of marks = 10 - 6

= 4

(b) total students = marks × frequency

(6×5)+(7×4)+(8×7)+(9×10)+(10×4)

= 30+28+56+90+40

= 244 students

(c) total frequency = 5+4+7+10+4

= 30

mean mark = total students/total

frequency

= 244/30

= 8.133

Answer:range-4 , no. of students-30, mean mark is 26

Step-by-step explanation:

Here’s a graph of a linear function. Write the equation that describes that function. Express it in slope intercept form.

Answers

Answer:   y = (1/2)x+3

slope = 1/2,  y intercept = 3

==============================================================

Work Shown:

Pick any two points you want on the line.

I'll pick the two points (0,3) which is the y intercept and also the point (2,4).

------

Find the slope of the line through (x1,y1) = (0,3) and (x2,y2) = (2,4)

m = (y2 - y1)/(x2 - x1)

m = (4 - 3)/(2 - 0)

m = 1/2 is the slope

slope = rise/run = 1/2

rise/run = 1/2 means rise = 1 and run = 2.

This means we go up 1 unit each time we move to the right 2 units.

-----

Since the slope is m = 1/2 and the y intercept is b = 3, we can say

y = mx+b

y = (1/2)x+3

this is the same as y = 0.5x+3 since 1/2 = 0.5

Veronica wants to check her work after evaluating -108 divided by (-6). What steps can she follow to verify her answer? A. Divide her answer by –6 and see if the result is –108. B. Divide her answer by –108 and see if the result is –6. C. Multiply her answer by –6 and see if the result is –108. D. Multiply her answer by –108 and see if the result is –6.

Answers

Answer:

C. Multiply her answer by –6 and see if the result is –108.

Step-by-step explanation:

Answer:

The answer is c

Step-by-step explanation:

hope this helps c:

What would the base be to the solution to
4^8*4^2?

Answers

Answer:

It can would be 4

Step-by-step explanation:

When you multiply exponents you add the exponents

so you get 4^10

What is the solution of the equation 6x - 3 = -51?
OA.
-9
OB.
-8
O c.
00
OD.
9

Answers

Answer:

x = -8

Step-by-step explanation:

6x - 3 = -51

Add 3 to each side

6x - 3+3 = -51+3

6x = -48

Divide each side by 6

6x/6 = -48/6

x = -8

Answer:

x = -8

Step-by-step explanation:

[tex]6x - 3 = -51?\\To - find-x- collect-like-terms.\\6x=-51+3\\6x =-48\\Divide-both-sides-of-the-equation-by-6\\\frac{6x}{6} = \frac{-48}{6} \\x = -8[/tex]

how to write 70 persent as fraction

Answers

Answer:

70/100 or 7/10

Step-by-step explanation:

As a percentage 70 percent is 70%.

As a fraction because 70 is out of 100 it would obviously be 70/100 but you can simplify to 7/10 and it is still equal to 70%

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