Mathematics High School

A shipping company offers various sized shipping boxes to its customers. Some of these boxes are cube-shaped, with equal height, width, and depth. As part of an upcoming sales promotion, the company will offer two cube-shaped boxes for the price of one.
a. Write an expression to represent the total volume of two different sized boxes as a sum of cubes if one of the boxes has sides with a length of 1 foot and the other has sides with a length of x feet.
b. Factor the sum of cubes.
c. Calculate the total volume of the two boxes if x = 3 feet.

Answers

Answer 1
A cube shaped box of side length equal to m foot has volume 
[tex]m*m*m= m^{3} [/tex]  foot cubed.

a.
Let v1 be the volume of the box with side length 1 ft. 
and v2 be the volume of the box with side length x ft.

[tex]V1=1^{3}=1[/tex] (foot cubed)
[tex]V2=x^{3}[/tex] (foot cubed)

Vtotal=[tex]V1+V2=1+x^{3}[/tex] feet cubed

b. 

by the "sum of cubes" identity:

[tex]x^{3}+1=(x+1)( x^{2} -x+1) [/tex],

this identity can be derived by dividing [tex]x^{3}+1[/tex] by (x+1), by long division.

c. Vtotal when x=3 feet is:

          Vtotal=[tex]V1+V2=1+3^{3}=1+27=28[/tex]   (feet cubed)

Related Questions

lady runs 20 miles in 4 hours. write an equation representing the direct relationship between distance and time

Answers

d=rt
20=40t
divide by 20 
t=2
d=10

Practice writing linear equations in different forms. Line AB goes through the points A (0, –4) and B (6, 2). Which equation represents line AB?  y – 4 = 3x y – 2 = 3(x – 6) y + 4 = x y + 6 = x - 2

Answers

(0,-4)(6,2)
slope = (2 - (-4) / (6 - 0) = 6/6 = 1

y = mx + b
slope(m) = 1
(0,-4)..x = 0 and y = 4
sub and find b
4 = 1(0) + b
4 = b

equation is : y = x + 4...or x - y = -4
or  y + 4 = 6(x - 0) ...or y - 2 = 6(x - 6)

the answer is c . y + 4 = x

Emily is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 14 km/h. After nine hours, the velocity of the cyclist is 4 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 10 hours? (5 points)


Answers

Assume that Emily starts from rest so that the velocity is zero at 0 hours.

Define the function v(t) for velocity in km/h, and t in hours.

Part A
From t=0 to t=4, v changes from 0 to 14.
Let v(t) = mt + b
The slope is
  m = 14/4 = 3.5, and the y-intercept is
  b = 0.
Therefore
v(t) = 3.5t,  for 0 ≤ t ≤ 4

Fromt=4 to t=9,  changes from 14 to 4.
Let v(t) = mt + b
The slope is
  m = (4 - 14)/(9 - 4) = -2
Therefore
  v = -2t + b
When t=4, v=14, therefore
 14 = -2*4 + b = -8 + b
 22 = b
v(t) = -2t + 22, for 4 < t ≤ 9.

Answer:
The equation for the velocity is
v(t) = 3.5t,  0 ≤ t ≤ 4
      = -2t + 22,  4 < t ≤ 9

Part B
The equation for velocity is a piecewise function that is graphed as shown below. If we assume that the second part of the equation is valid at t=10, then
v(10) = -2*10 + 22 = 2 km/h

A chocolate bar measures 40 mm wide, 80 mm long, and 5 and 1 over 2 mm high. Will’s Wrapping Company is making a wrapper to cover the chocolate bar. Use the correct net and determine how much paper will be needed to make the wrapper

Answers

The amount of the wrapper that is needed in order to wrap completely the chocolate bar is equal to the surface area of the bar. 

The surface area of the rectangular prism is calculated through the equation,
                   SA = 2LW + 2WH + 2LH

Substituting the known values,

      SA = (2)(80 mm)(40 mm) + 2(40 mm)(5.5 mm) + 2(80 mm)(5.5 mm)
                 SA = 6400 mm² + 440 mm² + 880 mm²
                    SA = 7720 mm²

Thus, the least area needed to completely cover or wrap the chocolate bar is 7720 mm². 

Answer:

Will’s Wrapping Company needs 7,720 mm of paper to wrap the chocolate bar.

Please HELP
1-) Solve the equation using the Properties of Equality.

11 − c = −17
2-)Solve the equation using the Properties of Equality.
1/2y + 1/5=1/2

Answers

Problem 1:
11-c = -17
First, we need to isolate the term with the variable. We can simply do that by subtracting 11 from both sides as follows:
11-11-c = -17-11
-c = -28
Then, we will multiply both sides by -1 to get the positive value of c as follows:
-c x -1 = -28 x -1
c = 28

Problem 2:
1/2 y + 1/5 = 1/2
First, we need to isolate the term with the variable by subtracting 1/5 from both sides as follows:
1/2 y = 1/2 - 1/5 = 3/10
Then, we will get rid of the coefficient in the term with variable by dividong both sides with 1/2, this will give the following output:
y = 3/5

what would be the measure of angle DGF, if segment DG is a bisector of angle G




30 degrees.60 degrees.90 degrees.None of the choices are correct.

Answers

check the picture below.

a bisector, means, it "cuts in two equal halves".

A card is chosen at random from a standard deck of 52 playing cards. What is the probability that the chosen card is a jack or a queen?

Answers

since there are 4 jacks and 4 queens in a deck, there are a total of 8 jacks and queens in 52 cards. this translates to 8/52, ( simplified 2/13 ) or 15%.

Find the midpoint of the segment below

Answers

1.
If we are given 2 points A(a, b) and B(c, d), 

the midpoint M, of segment AB has coordinates:

[tex]M_A_B=( \frac{a+c}{2} , \frac{b+d}{2} )[/tex]

2.
We are given the points A(2, 3) and B(10, 3)

the midpoint of AB, is given by the above formula:

[tex]M_A_B=( \frac{2+10}{2} , \frac{3+3}{3} )=(6, 3)[/tex]

3. 
Remark, since the segment is horizontal, that is the y-coordinate of both points is 3, the y coordinate of the midpoint will also be 3.

While the x coordinate is still found by [tex]\frac{2+10}{2}[/tex]

Answer: (6, 3)

An ostrich that is 108 inches tall is 20 inches taller than 4 times the height of a kiwi. What is the height of a kiwi in inches?

Answers

Let the height of the Kiwi be 'x'

'4 times the height of a kiwi' = 4x
'20 inches taller than 4 times the height of a kiwi' = 4x + 20

An ostrich is 108 inches tall and this is EQUAL to 4x + 20

108 = 4x + 20
108 - 20 = 4x
88 = 4x
88 ÷ 4 = x
x = 22

The height of the kiwi is 22 inches

The perimeter of a rectangle is 42 m. the length of the rectangle is 3 m more than twice the width. find the dimensions of the rectangle.

Answers

42/2 = 21

 21 = w +2w+3

21 = 3w +3

18 =3w

w = 18/3 = 6

 width is 6

 length = 6x2=12+3 = 15

6+6+15+15 = 42


 width = 6 m

 length = 15 m

Which of the following is an identity? A. sin2x sec2x + 1 = tan2x csc2x B. sin2x - cos2x = 1 C. (cscx + cotx)2 = 1 D. csc2x + cot2x = 1



Edit: no one answered but I figured out that the right answer is A

Answers

There are three 'Pythagorean' identities that we can look at and they are

sin²(x) + cos²(x) = 1
tan²(x) + 1 = sec²(x) 
1 + cot²(x) = csc²(x)

We can start by checking each option to see which one would give us any of the 'Pythagorean' identities as its simplest form

Option A:

sin²(x) sec²(x) + 1 = tan²(x) csc²(x)

Rewriting sec²(x) as 1/cos²(x)
Rewriting tan²(x) as sin²(x)/cos²(x)
Rewriting csc²(x) as 1/sin²(x)

We have

[tex]sin^{2}(x)[ \frac{1}{ cos^{2}(x) }]+1=[ \frac{ sin^{2}( x)}{ cos^{2} (x)}][ \frac{1}{ sin^{2}(x) } ][/tex]
[tex] [\frac{ sin^{2}(x) }{ cos^{2}(x) } ]+1= \frac{1}{ cos^{2}(x) } [/tex]
[tex] tan^{2}(x)+1= sec^{2}(x) [/tex]

Option B:

sin²(x) - cos²(x) = 1

This expression is already in the simplest form, cannot be simplified further

Option C:

[ csc(x) + cot(x) ]² = 1

Rewriting csc(x) as 1/sin(x)
Rewriting cot(x) as cos(x)/sin(x)

We have

[tex][ \frac{1}{sin(x)}+ \frac{cos(x)}{sin(x)}] ^{2} =1[/tex]
[tex] \frac{1}{sin^2(x)}+2( \frac{1}{sin(x)})( \frac{cos(x)}{sin(x)})+ \frac{cos^2(x)}{sin^2(x)}=1 [/tex][tex]csc^2(x)+2csc^2(x)cos(x)+cot^2(x)=1[/tex]

Option D:

csc²(x) + cot²(x) = 1

Rewriting csc²(x) as 1/sin²(x) and cot²(x) as cos²(x)/sin²(x)

[tex] \frac{1}{sin^2(x)}+ \frac{cos^2(x)}{sin^2(x)}=1 [/tex]
[tex] \frac{1+cos^2(x)}{sin^2(x)} =1[/tex]
[tex]1+cos^2(x)=sin^2(x)[/tex]
[tex]1=sin^2(x)-cos^2(x)[/tex]

from our working out we can see that option A simplified into one of 'Pythagorean' identities, hence the correct answer

Answer: A is the correct answer.

Step-by-step explanation:

Just did the question, followed OP's advice since no one answered. Good luck.

which of the following fractions will convert to repeating decimals?

a. 1/3
b. 1/6
c. 1/4
d. 3/8
e. 1/5

Answers

Well, that's odd. both a and b are repeating decimals.

a. 1/3 = 0.33333333
b. 1/6 = 0.16666666
c. 1/4 = 0.25
d. 3/8 = 0.375
e. 1/5 = 0.2

Use the information in the figure. If m∠F = 76°, find m∠E

Answers

52 because the whole triangle is 180 if you subtract that by 76 you get 102 since both sides equal each other the angles equal each other so you devide that by 2 you get 52

Answer:

m∠E=52°.

Step-by-step explanation:

The given triangle has two sides equal. In isosceles triangle two sides are equal and base angles are equal.m∠E=m∠D.

Let m∠D=m∠E= x

The sum of angles in any triangle is 180°.

Or,

x+x+76= 180

Addling like terms :

2x+76=180

Subtracting 76 both sides,

2x=104.

Dividing by 2:

x=52.

m∠E= 52°.


What is the solution set of the following equation? 3x2 - 6x = 0

Answers

The solutions are x=0 and x=2 because you have to find the gcf first and factor it. The gcf is 3x so, the factor is 3x(x-2)=0. When you solve that you get x=0 and x=2 for the solutions. 3x=0 divide both sides by 3 and you get x=0 and x-2=0 add 2 on both sides and you get x=2. Thanks for letting me help you.

To make lemonade, you used one gallon of water, four quarts of lemon juice, and 32 ounces of honey. How much lemonade did you make?

Answers

We know that 1 gallon = 4 quarts and 1 quart = 32 ounces.
We have 4 quarts of lemon and it is 1 gallon ( and we also have 1 gallon of water ). Also we have 32 ounces of honey, which is 1 quart more.
4 quart + 4 quart + 1 quart = 9 quarts = 2 gallons 1 quart
Answer:
There is 9 quarts or 2 gallons and 1 quart of lemonade.

Find the number of permutations of the first 8 letters of the alphabet taking 4 letters at a time.

Answers

The permutations of the first letters of alphabet taking 4 letters at once will be given by:
8P4
using the calculator this will give us:
8P4=1,680
This tells us that there are more than 1,680 different ways that the leteers will be selected.

0.43 is 10 times as mush as what

Answers

The correct answer is 0.043. Thanks for asking and have a great day!

The number that is 10 times less than 0.43 is 0.043, found by dividing 0.43 by 10.

To find the number that 0.43 is 10 times as much as, we need to divide 0.43 by 10. This is the same as multiplying by 10 raised to the power of -1, which is a division by 10.

The operation looks like this:

0.43*10^{-1} = 0.043.

Therefore, 0.43 is 10 times as much as 0.043

The perimeter of a triangle is 510 ft and the sides are in the ratio of 11:16:24. Find the area of the triangle. Need help, is there a specific formula for this?

Answers

1.
The side lengths are in the ratio 11:16:24, so let them be

11k, 16k, and 24k for some number k.

11k+16k+24k=510 
k(11+16+24)=510
51k=510
k=10

so the actual sides are 110, 160 and 240 feet.

2.
There is a famous formula, called Heron's formula, which calculates the area of a triangle, given its sides a, b and c.

we first calculate the half perimeter, which we usually denote by u:

[tex]u= \frac{a+b+c}{2} [/tex]

then the theorem states that the area A is as follows:

[tex]A= \sqrt{u(u-a)(u-b)(u-c)} [/tex]

3.

In our case:

[tex]u= \frac{a+b+c}{2} =\frac{110+160+240}{2} = \frac{510}{2} [/tex]

[tex]u-a= \frac{510}{2} -110= \frac{510-220}{2} = \frac{290}{2} [/tex]

[tex]u-b= \frac{510}{2} -160= \frac{510-320}{2} = \frac{190}{2} [/tex]

[tex]u-a= \frac{510}{2} -240= \frac{510-480}{2} = \frac{30}{2} [/tex]


[tex]A= \sqrt{\frac{510}{2}*\frac{290}{2}* \frac{190}{2} * \frac{30}{2}} =7,258.745[/tex]  feet squared


Answer:D 7,258.745 ft squared

Final answer:

To find the area of a triangle with sides in a given ratio, first find the value of x by setting up and solving an equation using the perimeter. Then, multiply each side by x to find the base and height of the triangle. Finally, substitute the base and height into the formula for the area of a triangle.

Explanation:

To find the area of a triangle, we can use the formula: Area = 1/2 × base × height. In this case, we don't know the base and height directly, but we do know that the sides of the triangle are in the ratio of 11:16:24. Let's assume the sides are 11x, 16x, and 24x. The perimeter of the triangle is 510 ft, which means 11x + 16x + 24x = 510. Simplifying this equation, we get 51x = 510. Therefore, x = 10. Now we can find the base and height of the triangle by multiplying the corresponding sides by 10. The base is 11x * 10 = 110 ft and the height is 16x * 10 = 160 ft.

Now we can substitute these values into the formula to calculate the area of the triangle. Area = 1/2 × base × height = 1/2 × 110 ft × 160 ft = 8800 square feet.

200 gallon tank fills at 3 gallons/minute and loses 2 gallons/minute how long does it take to fill up

Answers

it fills at 3 gallons per minute, but loses 2 gallons per minute

 3-2 =1, so it fills at 1 gallon per minute

200 gallons at 1 gallon per minute = 200 minutes,

200/60 = 3 hours and 20 minutes

The sum of three interior angles of a convex Pentagon is 420°.if the remaining angles are equal how much does each angle measure?

Answers

The sum of interior angles of any polygone is:

Sum of angles = (n-1)x180°, where n is the number of sides. For the pentagone n = 5, then Sum of angles of a PENTAGONE = (5-1)x180° = 720°.
Already the sum of 3 angles is 420°, the measure of the 2 remaining one is 
720° - 420° = 300°. Since the remaining angles are equal, hence each one will have a measure of 300°/2 = 150°

Each one of the remaining angles measures 60°.

How much does each angle measure?

We know that the sum of the interior angles of a closed figure of n sides is given by:

(n - 2)*180°.

A pentagon has 5 sides, so we use n = 5 and we get:

(5 - 2)*180° = 540°

Now we know that 3 angles add up to 420°.

Then the other two angles must add up to:

540° - 420° = 120°

And those two angles are equal, then each one measures:

120°/2 = 60°.

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

https://brainly.com/question/17972372

A square prism has a base length of 5 m, and a square pyramid of the same height also has a base length of 5 m. Are the volume the same?

Answers

No.  the square prism has volume of 5x5xheight
The square pyramid has a volume of
5x5xheight/3

Find the value of x in the equation √ x + 5 = √ x + 45.

Answers

there is no solution since 5 doesn't equal 45

In a 45-45-90 triangle, the length if the hypotenuse is 11. Find the length of one of the legs

Answers

the answer is B, picture shows how to solve it although the answer is written slightly different

Answer:

[tex] \frac{11\sqrt{2}}{2}[/tex]

Step-by-step explanation:

In a 45-45-90 triangle, the length if the hypotenuse is 11

WE use the common ratio of 45-45-90 degree triangle

common ration is x: x: x sqrt(2)

x sqrt(2) is the length of the hypotenuse

[tex]x\sqrt{2} = 11[/tex]

Divide by sqrt(2) on both sides

[tex]x= \frac{11}{\sqrt{2}}[/tex]

To rationalize the denominator, multiply by sqrt(2) at the top and bottom

sqrt(2) * sqrt(2) = 2

[tex]x= \frac{11\sqrt{2}}{2}[/tex]

Zeus Industries bought a computer for $2011. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 5 years?

Answers

The value of the computer after five years will be as follows;
Value after 1 year:
24/100*2011
=$482.64
2011-482.64
=$1528.36
or
76/100*2011
=$1528.26

Value after 2nd year:
76/100*1528.36
=$1,161.55

Value after 3rd year:
76/100*1,161.55
=$882.78

Value after 4th year:
76/100*882.78
=$670.91

Value after 5th year:
76/100*670.91
=$509.89
hence the value after five years will be: $509.90

HELP
If f(x)=-6x+12, then f^-1(x)=?

Answers

The inverse is (x-12)/-6

10-2v=-5-50
+5 +5
10-3v=-50
+3 +3
10=47

Answers

hello : 
10-2v=-5-50
add : 5
 10 - 2v  + 5 = 5 - 5 - 50
15 -2v = -50
add : -15
-15 +15 -2v = -15 -50
-2v =-65
v = 65/2

Carissa is budgeting for her next semester at college. She spent $50 on gas this month. Economists are predicting gas prices to rise 8% per month for the next 6 months. How much should she budget for gas if classes start next month and are 4 months long?

The answer is D.243.33
(I looked up the question and couldnt find it so i thought i'd post it for anyone who needed it)

Answers

Spent on gas this month = $50.

Predicted spent of gas next month = $50 * 1.08

Predicted spent of gases for the four months:

$50 * 1.08
$50 * 1.08^2
$50 * 1.08^3
$50 * 1.08^4

Total spent for the four months:  $50 (1.08 + 1.08^2 + 1.08^3 + 1.08^4) = $50 * (4.8666) = $243.33, which is the option D. 243.33

PLEASE HELP!!!
How can one thirdx − 2 = one fourthx + 11 be set up as a system of equations?

3y − x = −6
4y − x = 44

3y + x = −6
4y + x = 44

3y − 3x = −6
4y − 4x = 44

3y + 3x = −6
4y + 4x = 44

Answers

y=1/3x-2
3y=x-6
3y-x=-6
y=1/4x+11
4y=x+44
4y-x=44

Answer: Hello!

we have that:

one third x − 2 = one fourth x + 11

this means:

(1/3)x - 2 = (1/4)x + 11

if this are equal numbers, we can write it as:

(1/3)x - 2 = y =  (1/4)x + 11

now we have the system of equations:

(1/3)x - 2 = y

(1/4)x + 11 = y

if we "simplify" the rational therm in each equation, we get:

3*(1/3)x - 3*2 = 3y

x - 6 = 3y

and

4*(1/4)x + 4*11 = 4y

x + 44 = 4y

Then our system of equations is:

x - 6 = 3y

x + 44 = 4y

Now we can subtract x in each side of both equations:

-6 = 3y - x

44 = 4y - x

Then the right option is the first one.

3y - x = -6

4y - x = 44

Find the measure of an angle whose supplement is 9 times the measure of its complement

Answers

if the angle is x , then

180 - x = 9(90-x)
180-x = 810 - 9x
8x = 630
x = 78.75 degrees

The equation is 180 - x = 9 (90 - x).Then the measure of the angle will be 78.75 degrees.

What is an angle?

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

Let 'x' be the angle. Then the equation is given as,

180 - x = 9 (90 - x)

180 - x = 810 - 9x

8x = 630

x = 78.75 degrees

The measure of the angle will be 78.75 degrees.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ5

A polygon with 12 sides is called a/an

Answers

In geometry, a dodecagon or 12-gon is any twelve-sided polygon.


hope this helps!


A polygon with 12 sides is called a dodecagon.
Other Questions
Which food item is ideal for bacterial growth? A maintenance electrician would likely specialize in one kind of work if he is employed in a large A. industrial plant. B. hospital. C. apartment house. D. office building.ANSWER IS A. just took the test. Kenji wants to divide 48.6 by 0.15. What is the first step that Kenji must complete? Multiply the divisor and dividend by 10.Multiply the divisor and dividend by 100.Divide the divisor and dividend by 100.Divide the divisor and dividend by 10. A solution with a hydrogen ion concentration of 3.25 10-2 m is ________ and has a hydroxide concentration of _______ The length of a screw produced by a machine is normally distributed with a mean of 0.65 inches and a standard deviation of 0.01 inches. What percent of screws are between 0.61 and 0.69 inches?HELP A. 65% B. 68% C. 99.7% D. 99.9936% Lisa and Kate are playing a card game, and a total of 900 points has been scored. Lisa scored 250 more points than Kate. If you let l=l=the number of points that Lisa scored, and k=k= the number of points that Kate scored, then the problem can be represented by the system:l+k=900l+k=900 and l=k+250l=k+250Graph the system. How many points did each of them score?Select one:a. Kate = 575 and Lisa = 325b. Kate = 250 and Lisa = 650c. Kate = 450 and Lisa = 450d. Kate = 325 and Lisa = 575 The nurse is administering intravenous amiodarone to a patient in the emergency department. which task would the nurse need to prioritize? When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm divided by min0.02 cm/min. at what rate is the plate's area increasing when the radius is 4040 cm? What would it be like if you were deaf,blind, and couldn't feel anything? What news do we learn about rebecca nurse? Earth's climate has been stable throughout its history. True False Sadie the dog is sitting on the roof of his doghouse, 4.5 ft off the ground. He is watching a cat that is 16 ft away from the base of the doghouse. What is the angle of depression from the roof of the doghouse to the cat? Round to the nearest hundredth. I watched the lesson but it all just went over my head, can someone simplify the explanation of how these problems work? How many moles of H2O can be formed when 4.5 moles of NH3 react with 3.2 moles of O2?4NH3 + 5O2 yields 4NO + 6H2OA)3.8 mol H2OB) 4.8 mol H2OC) 6.4 mol H2OD) 6.8 mol H2O The floor of a rectangular room will be tiled with square tiles that measure 3 inches on each side. The room is 109 inches long and 103 inches wide. How many tiles, including parts of tiles, are needed to complete the job? ?the management of zilo toys inc., a toy manufacturing company, believes that the longer the customers spend deciding what to purchase, the less likely they are to purchase more items. in order to determine the average time customers spend in purchasing toys from the store, the management employees time to observe the customers as they discuss which toys to buy. he then reports his findings to the management. in this scenario, tim is engaging in _____. What does the narrator do to the first cat after it bites him on the hand Which of these powers does the constitution deny the federal government Software that allows the application software to interact with the computer is called __________. Select the answer that properly completes the sentence.Our presentation is nothing compared to _____theirs.theirs.theirs.their. In a 36 minute gym period, 24 boys want to play basketball. if only 10 can play at the same time, and each boy plays the same amount of time, how many minutes does each boy play Steam Workshop Downloader