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Elenna [48]
3 years ago
5

Geometry, please answer question ASAP

Mathematics
1 answer:
lesya [120]3 years ago
7 0

Answer:

D) 12.2

Step-by-step explanation:

EH is median

FH = HG

6x - 1.1 = 4x + 1.3

Add 1.1 to both sides

6x = 4x + 1.3 + 1.1

6x = 4x + 2.4

Subtract 4x from both sides

6x - 4x = 2.4

2x = 2.4

Divide both sides by 2

x = 2.4/2

x = 1.2

FH = 6x - 1.1

    = 6*1.2 - 1.1

    = 7.2 - 1.1

    = 6.1

FG = 6.1 + 6.1 = 12.2

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Miguel wants to build a container out of sheet metal that has a volume of about 320 cubic inches . He
ZanzabumX [31]

Answer:

  cylinder, has the least surface area

Step-by-step explanation:

We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.

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We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.

<h3>Rectangular Prism</h3>

The relevant formulas are ...

  V = LWH

  A = 2(LW +H(L +W))

for length L, width W, and height H.

<u>a)</u><u> prism 1</u>

The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...

  V = (8 in)(8 in)(5 in) = 320 in³

  A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²

<u>b)</u><u> prism 2</u>

The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...

  V = (10 in)(8 in)(4 in) = 320 in³

  A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²

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<h3>Cylinder</h3>

The relevant formulas are ...

  V = πr²h

  A = 2πr(r +h)

for radius r and height h.

c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...

  V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³

  A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²

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<h3>Square Pyramid</h3>

The relevant formulas are ...

  V = 1/3s²h

  A = s(s +2H)

for base side dimension s, vertical height h, and slant height H.

d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...

  V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³

  A = (10 in)(10 in + 2×14 in) = 380 in²

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<h3>Summary</h3>

The proposed figures have volume and area (rounded to the nearest unit) as follows:

  \begin{tabular}{|c|c|c|c|}\cline{1-4}&shape&V (in^3)&A (in^2)\\\cline{1-4}a&rect prism&320&288\\b&rect prism&320&304\\c&cylinder&314&\bf283\\d&pyramid&333&380\\\cline{1-4}\end{tabular}

The proposed <em>cylinder</em> requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.

_____

<em>Additional comment</em>

For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.

3 0
2 years ago
To solve a system of inequalities, you just need to graph each inequality and see which points are in the overlap of the graphs.
Juli2301 [7.4K]
The answer is true. Apex
6 0
3 years ago
Read 2 more answers
Please help im almost done​
irga5000 [103]

Answer:

1/4

Step-by-step explanation:

the numerator is 12 because there are 12 possible outcomes.  The numerator is 3 because there are 3 numbers in this set that are greater than 9.  You get 3/12 which then simplifies to 1/4

8 0
3 years ago
Gavin invests $5,000 in a savings account that pays 3.75% simple interest. How much will be in the account after 6 years if Gavi
ivolga24 [154]

Answer:

$6261.62

Step-by-step explanation:

A=Pe^rt forumla

A=5000e^0.0375(6)=6261.612633

I rounded e to 2.71828 for calculator reasons

and I rounded the number two places since it is a monetary value.

I tried hope it helps!!!

8 0
3 years ago
A family wants to rent a car to go on vacation. Company a charges $70.50 and $.50 per mile. Company B charges $35.50 and nine ce
Naddik [55]

Answer:

Company A is 1.99 times B.

Step-by-step explanation:

Company A charges:

A=70.50+0.50=\$71/mile  

Company B charges:

B=35.50+0.09=\$35.59/mile

We just need to divide A by B:

x=A/B=1.99

Therefore, company A is 1.99 times B.

I hope it helps you!

     

5 0
3 years ago
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