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S_A_V [24]
3 years ago
8

The surface area of rectangular prism is 48 ft.². The area of its front is 4 ft.², and the area of one side is 10 ft.². What is

the area of the top of the prism?
Mathematics
1 answer:
DaniilM [7]3 years ago
3 0
I think the answer is 20.
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Use Cramer’s Rule to solve system of equation.
alisha [4.7K]

\left\{\begin{array}{ccc}5x+2y=4\\3x+4y+2z=6\\7x+3y+4z=29\end{array}\right\\\\A=\left[\begin{array}{ccc}5&2&0\\3&4&2\\7&3&4\end{array}\right]\\\\\det A=5\cdot4\cdot4+3\cdot3\cdot0+2\cdot2\cdot7-7\cdot4\cdot0-3\cdot2\cdot5-3\cdot2\cdot4=54\\W_x=\left[\begin{array}{ccc}4&2&0\\6&4&2\\29&3&4\end{array}\right]\\\det W_x=4\cdot4\cdot4+2\cdot2\cdot29+6\cdot3\cdot0-29\cdot4\cdot0-3\cdot2\cdot4-6\cdot2\cdot4=108

W_y=\left[\begin{array}{ccc}5&4&0\\3&6&2\\7&29&4\end{array}\right]\\\det W_y=5\cdot6\cdot4+3\cdot29\cdot0+4\cdot2\cdot7-7\cdot6\cdot0-29\cdot2\cdot5-3\cdot4\cdot4=-162\\W_z=\left[\begin{array}{ccc}5&2&4\\3&4&6\\7&3&29\end{array}\right]\\\det W_z=5\cdot4\cdot29+3\cdot3\cdot4+6\cdot2\cdot7-7\cdot4\cdot4-3\cdot6\cdot5-3\cdot2\cdot29=324\\\\x=\dfrac{\det W_x}{\det A}=\dfrac{108}{54}=2\\\\y=\dfrac{\det W_y}{\det A}=\dfrac{-62}{54}=-3\\\\z=\dfrac{\det W_z}{\det A}=\dfrac{324}{54}=6

5 0
3 years ago
Shelly Ann Fraser Pryce ran the 100m in 10.7 seconds. If she runs at a constant pace, how long will it take her to run 1/2 Km?
kvv77 [185]

Answer:53.5 Seconds ;)

3 0
3 years ago
Tony solves the linear equation 3(x - 3) + 2x + 9 = 2x + 2(x - 1) using the step shown below.
Natasha_Volkova [10]

Answer:

D.)

Step-by-step explanation:

because when you have numbers inside the parentheses, you have to multiply both of those numbers by the number to the right of the parentheses, not just the X.

8 0
3 years ago
Can someone solve this for me please.
nika2105 [10]

Answer:

  • The value of PR is 21 ft.

Step-by-step explanation:

<u>We know that:</u>

  • 3(PQ + QT + TP) = PR + RS + SP
  • PQ = 7 ft.
  • QT = 4 ft
  • RS = 12 ft.

<u>Work:</u>

  • 3(PQ + QT + TP) = PR + RS + SP
  • => 3(7 + 4 + TP) = PR + 12 + SP
  • => 21 + 12 + 3TP = PR + 12 + SP
  • => 21 + 3TP = PR + SP
  • => 21 + SP = PR + SP                                                                       [3TP = SP]
  • => 21 = PR

Hence, <u>the value of PR is 21 ft.</u>

Hoped this helped.

BrainiacUser1357

6 0
2 years ago
Need help with a math problem
Greeley [361]
The answer would be $159.85
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