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Masja [62]
3 years ago
10

Samantha wants to wrap this unassembled box with paper. The base of the box measures 3 inches by 6 inches. When the box is assem

bled it measures 9 inches tall. If Samantha wraps the box with paper, how many square inches will she need?

Mathematics
1 answer:
kotegsom [21]3 years ago
6 0

Answer:

198 in.^2

Step-by-step explanation:

You need the area of the net that is shown.

The long horizontal rectangle made up of 4 smaller rectangles has length 3 in. + 9 in. + 3 in. + 9 in. = 24 in. Its width is 6 in.

Then there are two congruent rectangles with length 9 in. and width 3 in.

area of rectangle = length * width

total area = 24 in. * 6 in. + 2 * 9 in. * 3 in.

total area = 198 in.^2

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A power line is to be constructed from a power station at point A to an island at point C, which is 1 mi directly out in the wat
Alchen [17]

Answer:

  point S is 3 1/4 miles from point A

Step-by-step explanation:

We assume you want to find point S that minimizes the power line cost.

Let k = 5000/3000 = 5/3 represent the ratio of construction cost underwater to construction cost downshore. Then the total cost will be proportional to ...

  cost ~ k(CS) + SA

The distance BS can be found from the Pythagorean theorem. In miles, the relation is ...

  BS² +BC² = CS²

  BS² +1 = CS²

So our cost is ...

  cost ~ k(CS) +BA -BS = k√(BS² +1) +BA -BS

__

To minimize the cost, we want to find BS that makes the derivative d(cost)/dBS = 0.

  d(cost)/dBS = kBS/√(BS² +1) -1 = 0

  kBS = √(BS² +1) . . . . . . add 1, multiply by the root

  k²BS² = BS² +1 . . . . . . . square

  (k² -1)BS² = 1 . . . . . . . . . subtract BS² and factor

  BS = 1/√(k² -1) . . . . . . . . divide by the coefficient of BS² and square root

Please note that this can be considered to be a generic solution to problems of this sort. BS is measured as a multiplier of distance BC, which in this case is 1 mile.

__

Filling in the value we have for k, the downshore length BS is ...

  BS = 1/√((5/3)² -1) = 1/√(16/9) = 3/4

The distance from point A to S is 4 miles -3/4 miles = 3 1/4 miles.

8 0
3 years ago
the frost burg truth bus travels on a straight road from Frostburg mall to sojourner truth park. The mall is 3 miles west and 4
Goshia [24]

9514 1404 393

Answer:

  10.8 miles

Step-by-step explanation:

The distance between (-3, -4) and (3, 5) can be found using the distance formula.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = √((3 -(-3))^2 +(5 -(-4))^2) = √(6^2 +9^2) = √117

  d ≈ 10.8

It is about 10.8 miles from the mall to the park.

3 0
3 years ago
Select all the pieces of the triangle that are marked as congruent in the following picture
nikitadnepr [17]

Answer:

C. D. E. is the correct answer.

Step-by-step explanation:

Hope this helps you. Have a nice day. If you have doubt then please ask in comments.

Please mark as brainliest. It helps a lot.

5 0
2 years ago
Read 2 more answers
Which graph shows a line with an x-intercept of -5?
Finger [1]

Answer:

The answer is A.

Step-by-step explanation:

The only option is A. since an intercept of (-5,0)

Option B has y-int: (0,-5)
Option C has y-int: (0,5)

Option D has x-int(5,0)

8 0
2 years ago
Please help, i don’t know how to work this out!!
victus00 [196]

Answer:

40 degrees

Step-by-step explanation:

so, a triangle is 180 degrees. you know that one angle is 60 degrees.

180= 60+ 2x + x

this is the equation of the triangle

120=3x

simplify

40=x

x= 40 degrees

hope this helps :)

5 0
2 years ago
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