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Gennadij [26K]
3 years ago
8

What is the surface area of the right prism given below?

Mathematics
2 answers:
mihalych1998 [28]3 years ago
7 0

For this case, we have that the area of the surface of the figure shown is given by:

A_{1}: The area of the upper rectangle (inclined)

A_{2}: The area of the two triangles.

A_{3}: The area of the base of the prism

A_ {4}: The area of the rear rectangle

We apply Pythagoras to know the length of the inclined side of the rectangle:

h = \sqrt {15 ^ 2 + 8 ^ 2}\\h = \sqrt {289}\\h = 17 \ units

Thus, the A_{1} is given by:

A_ {1} = 10 * 17\\A_ {1} = 170 \ units ^ 2

We look for the area given by the triangles, knowing that the area of a triangle is \frac {1} {2} b * h, then:

A_ {2} = \frac {1} {2} b * h + \frac {1} {2} b * h\\A_ {2} = b * h\\A _{2} = 15 * 8\\A_{2} = 120 \ units ^ 2

We look for the area of the base of the prism:

A_ {3} = 10 * 15\\A_ {3} = 150 \ units ^ 2

We look for the area of the posterior rectangle:

A_ {4} = 8 * 10\\\A_ {4} = 80 \ units ^ 2

Adding we have:

A_ {t} = (170 + 120 + 150 + 80) \ units ^ 2\\A_ {t} = 520 \ units ^ 2

Answer:

520 \ units ^ 2

Sloan [31]3 years ago
3 0

Answer:

10*15= 150

150 *8= 1,200

1,200 ÷ 2 = 600.

Step-by-step explanation:


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Solve the system using elimination. ''x-3y=9 and -x+3y=-9
DiKsa [7]

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's solve your system by elimination.

x−3y=9;−x+3y=−9

x−3y=9

−x+3y=−9

Add these equations to eliminate x:

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<u>Answer:</u>

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6 0
2 years ago
4x + 5y = 3 2x + 3y = 1Solve by elimination
Lesechka [4]

Answer:

The solution to the system of equations is:

x = 2, and y = -1

Explanation:

Given the pair of equations:

4x + 5y = 3 ..........................................................................(1)

2x + 3y = 1............................................................................(2)

To solve this by elimination:

Multiply equation (2) by 2, to eliminate x

Equation (2) becomes

4x + 6y = 2 .........................................................................(3)

Subtract equation (1) from (3)

4x - 4x + 6y - 5y = 2 - 3

y = -1 ....................................................................................(4)

Multiply equation (1) by 3 and equation (2) by 5 to eliminate y

Equation (1) becomes

12x + 15y = 9 .......................................................................(5)

Equation (2) becomes

10x + 15y = 5 ........................................................................(6)

Subtract equation (6) from (5)

12x - 10x + 15y - 15y = 9 - 5

2x = 4

Divide both sides by 2

x = 4/2 = 2 ............................................................................(7)

From equations (7) and (4)

x = 2, and y = -1

7 0
1 year ago
Is this correct?? if not pls tell me the correct answer
oee [108]

Step-by-step explanation:

<em>it's </em><em> </em><em>absolutely </em><em>correct </em><em>.</em><em>.</em>

6 0
3 years ago
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A blue boat and a red boat are on the same side of a lake and are 18 miles apart. The blue boat is 30 miles from a lighthouse on
rewona [7]

9514 1404 393

Answer:

  • red boat distance: 42 miles
  • angle at lighthouse: 22°

Step-by-step explanation:

The Law of Cosines can be used to find the distance from the red boat to the lighthouse.

  b² = l² +r² -2lr·cos(B)

  b² = 18² +30² +2·18·30·cos(120°) = 1764

  b = √1764 = 42

The distance from the red boat to the lighthouse is 42 miles.

__

The angle at the lighthouse can be found using the law of sines.

  sin(L)/l = sin(B)/b

  L = arcsin(l/b·sin(B)) = arcsin(18/42·sin(120°)) ≈ 21.79°

The angle between the boats measured at the lighthouse is about 22°.

8 0
3 years ago
What is the LCD of -3/14 and 1/10 is ?
White raven [17]

The least common denominator is 70 because both 14 and 10 go into 70.

8 0
3 years ago
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