1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Pavel [41]
3 years ago
8

U.S. postal regulations require that a package can have a maximum combined length and girth (distance around) of 108 in. A shipp

ing carton is constructed so that it has a width of 14 in., a height of 12 in., and can be cut or folded to various lengths. What is the maximum length that can be used?
Mathematics
1 answer:
Eduardwww [97]3 years ago
4 0

Answer: The maximum length that can be used is 56 inches.

Step-by-step explanation:

Since we have given that

Width of package = 14 inch

Height of package = 12 inch

Let the length of package be 'l'.

Combined length and girth i.e. distance around = 108 inches.

So, According to question, we get that

l+2(w+h)=108\\\\l+2(14+12)=108\\\\l+2\times 26=108\\\\l+52=108\\\\l=108-52\\\\l=56\ inches

Hence, the maximum length that can be used is 56 inches.

You might be interested in
A rectangular bird sanctuary is being created with one side along a straight riverbank. the remaining three sides are to be encl
Mariana [72]
<span>2 km wide by 4 km long with the long side parallel to the river. So we can enclose a rectangular area using just 3 sides since the 4th side is provided free by the river. I'll use the variable L to represent the length of the side that's parallel to the river and W to represent the distance from the river that parallel side is. So the total perimeter of the fence will be 2W + L. Let's write down some equations. Area enclosed A = W * L Length of L expressed in terms of W 8 = 2W + L 8 - 2W = L Now substitute (8-2W) for L in the equation for the area. A = W * L A = W * (8-2W) A = 8W - 2W^2 Since we're looking for a maximum value, that will happen when the slope of the function is equal to 0. And the first derivative of the function tells you the slope at each point. So we need to calculate the first derivative. For simple functions such as what we have, we just need to multiply the coefficient of each term by the exponent of that term, then subtract 1 from the exponent. So let's calculate the first derivative of A = 8W - 2W^2 A = 8W - 2W^2 The term 8W has an implied exponent of 1 for W, so 8 * 1 = 8. And 1 - 1 = 0. So we have 8W^0. And since W^0 = 1, we have 8 as the 1st term of the derivative. The next term is -2W^2. So -2*2 = -4 and 2-1 = 1, giving us -4W^1. And we can get rid of the explicit exponent of 1 since that's assumed to exist giving us a term of -4W. So the first derivative becomes A' = 8 - 4W Now let's solve that equation for A' = 0. A' = 8 - 4W 0 = 8 - 4W 4W = 8 W = 2 So the ideal width of the fence is 2. And looking back at the equation 8 - 2W = L, we can calculate the length as 8 - 2*2 = 8 - 4 = 4, so the length of the fence is 4. So the dimensions of the sanctuary is 4 km parallel to the river and extended 2 km from the river for a total area of 4*2 = 8 km^2. To demonstrate that is the ideal size, let's show that if the width is either smaller or larger, then we'll have a smaller sanctuary. Let's show the smaller case. For this we'll introduce a variable called "e" which represents a very tiny, but non-zero amount of length. So we'll call the width W+e or 2+e and the length will be 8 - 2*(2+e) = 8 - 4 - 2e = 4 - 2e So the area is A = WL A = (2+e)(4-2e) A = 8 -4e + 4e - 2e^2 A = 8 - 2e^2 And as you can see, as long as e is none zero the area will be smaller than 8 km^2. Now let's try a width that's less than 2 by a tiny amount. Our width is now (2-e) and that makes our length (4+2e). So A = WL A = (2-e)(4+2e) A = 8 + 4e -4e - 2e^2 A = 8 - 2e^2 And once again, if the width is slightly smaller so the length is slightly longer, the area is once again, slightly smaller. So the absolute best side for the sanctuary is 2 km wide by 4 km long.</span>
6 0
3 years ago
Will the point of the arrow in Figure Bhave the same angle measure as the point of the arrow in Figure A? Explain your answer.
inn [45]

Rotation being a rigid transformation, does not alter the angle and side lengths after transformation.

The arrow in Figure B will have the same angle measure as Figure A

From the complete question (see attachment), we understand that:

Figure A is rotated 90 degrees clockwise around point (2,2)

Rotation is a rigid transformation

This means that: after the transformation

  • Figure A and figure B will have the same side lengths
  • Figure A and figure B will have the same measure of angles

The above highlights imply that, the arrow in Figure B will have the same angle measure as Figure A

Read more about rigid transformations at:

brainly.com/question/1761538

5 0
2 years ago
Select all that apply.
Ymorist [56]

Answer:

B

C

Step-by-step explanation:

B= one question equals one minute

C= one minute equals one question

3 0
3 years ago
What is the scale factor of two similar pyramids with volume of 13824 cubic feel and 216 cubic feet?
velikii [3]

Answer: The scale factor is 4

Step-by-step explanation:

We know that the pyramids are similar. The volume of one of these pyramids is  13,824 cubic feet and the volume of the other one is 216 cubic feet. Then:

V_1=13,824ft^3\\V_2=216ft^3

By Similar solids theorem, if two similar solids have a scale factor of \frac{a}{b}, then corresponding volumes have a ratio of \frac{a^3}{b^3}

Then:

\frac{V_1}{V_2}=\frac{a^3}{b^3}

Knowing this, we can find the scale factor. This is:

\frac{13,824}{216}=\frac{a^3}{b^3}\\\\\frac{13,824}{216}=(\frac{a}{b})^3\\\\\frac{a}{b}=\sqrt[3]{\frac{13,824}{216}}\\\\scale\ factor=\frac{a}{b}=4

3 0
3 years ago
Find the solution to the equation -2(x + 5) = -16. x =
Radda [10]

Answer:

x = 5/7 = 0.714

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Other questions:
  • 7 - 3 ( 5t - 10 ) = 67
    6·2 answers
  • How do I answer part A?
    9·1 answer
  • Which number goes in the box to make this a true number sentence?<br><br> 8 × (5 + 7) = 40 +
    12·1 answer
  • What is 66.087, 67, 66.87, and 66.6 from least to greaest
    8·1 answer
  • You play video games online. When you sign up with the game site, you get 200 points. You earn 20 more points for each hour that
    15·1 answer
  • A family of three children, what is the probability of 2 boys and 1 girl?
    8·1 answer
  • What’s the answer idk how to do this
    11·2 answers
  • 30 POINTS<br> 5x-3y=-1 2x+3y=8<br> Solve with elimination!<br> Show your work!
    14·1 answer
  • Write an equation for the trend line shown (please help thanks)
    13·1 answer
  • Identify parallel and perpendicular lines
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!