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ruslelena [56]
3 years ago
14

Solve for x... need as fast as you can do it.

Mathematics
1 answer:
charle [14.2K]3 years ago
5 0

Answer:

6. 21.0°

7. 39.6°

8. 58.0°

9. 72.9°

Step-by-step explanation:

6. Reference angle (θ) = x°

Hypotenuse = 15

Adjacent = 14

Apply CAH:

Cos(\theta) = \frac{Adjacent}{Hypotenuse}

Plug in the values

Cos(x) = \frac{14}{15}

x = Cos^{-1}(\frac{14}{15})

x ≈ 21.0° (nearest tenth)

7. Reference angle (θ) = x°

Opposite = 19

Adjacent = 23

Apply TOA:

Tan(\theta) = \frac{Opposite}{Adjacent}

Plug in the values

Tan(x) = \frac{19}{23}

x = Tan^{-1}(\frac{19}{23})

x ≈ 39.6° (nearest tenth)

8. Reference angle (θ) = x°

Hypotenuse = 17

Adjacent = 9

Apply CAH:

Cos(\theta) = \frac{Adjacent}{Hypotenuse}

Plug in the values

Cos(x) = \frac{9}{17}

x = Cos^{-1}(\frac{9}{17})

x ≈ 58.0° (nearest tenth)

9. Reference angle (θ) = x°

Opposite = 43

Hypotenuse = 45

Apply SOH:

Sin(\theta) = \frac{Opposite}{Hypotenuse}

Plug in the values

Sin(x) = \frac{43}{45}

x = Sin^{-1}(\frac{43}{45})

x ≈ 72.9° (nearest tenth)

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blagie [28]
A.
5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
5x-4=-2 \times 3x-2 \times 2 \\
5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\
11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\
11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\
x=0

B.
3(2x-4)=5x-1 \\
6x-12=5x-1 \\
\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\
11x=11 \\
\boxed{x=11} \Leftarrow \hbox{the second mistake}

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\
x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  |\hbox{add 12 to both sides} \\
x=11
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3 years ago
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Answer:

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Step-by-step explanation:

Each triangle has the surface area of 1.5, because 1 * 3 = 3 / 2 = 1.5. You divide by two because it is half a rectangle instead of a full one. You multiply by four which would get you 1.5 * 4 = 6. The square in the middle has the surface area of 1 because 1 * 1 = 1. So you would get 7.

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You need to form an algebraic equation. 4.5+h=7.3 therefore h= 7.3 - 4.5 when you take 4.5 to the other side it becomes negative therefore the answer is 2.8.
7 0
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20x+30y= c(total cost of money)
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