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Hoochie [10]
3 years ago
13

What is the answer 5a - 3 = 8a + 6

Mathematics
2 answers:
earnstyle [38]3 years ago
7 0
Subtract 5a from both sides

-3=3a+6


Subtract 6 from both sides

-9=3a

Divide by three

a= -9/3 (which is -3)

Remember what you do to one side you must do to the other
Bingel [31]3 years ago
7 0
To find the answer you do:
5a-3=8a+6
5a-8a-3=8a-8a+6
-3a-3=6
-3a-3+3=6+3
-3a=9
-3a/-3=9/-3
a=-3
So a is equal to -3.
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In Triangle XYZ, measure of angle X = 49° , XY = 18°, and
marissa [1.9K]

Answer:

There are two choices for angle Y: Y \approx 54.987^{\circ} for XZ \approx 15.193, Y \approx 27.008^{\circ} for XZ \approx 8.424.

Step-by-step explanation:

There are mistakes in the statement, correct form is now described:

<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>

The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:

YZ^{2} = XZ^{2} + XY^{2} -2\cdot XY\cdot XZ \cdot \cos X (1)

If we know that X = 49^{\circ}, XY = 18 and YZ = 14, then we have the following second order polynomial:

14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}

XZ^{2}-23.618\cdot XZ +128 = 0 (2)

By the Quadratic Formula we have the following result:

XZ \approx 15.193\,\lor\,XZ \approx 8.424

There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:

XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y

\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}

Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)

1) XZ \approx 15.193

Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]

Y \approx 54.987^{\circ}

2) XZ \approx 8.424

Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]

Y \approx 27.008^{\circ}

There are two choices for angle Y: Y \approx 54.987^{\circ} for XZ \approx 15.193, Y \approx 27.008^{\circ} for XZ \approx 8.424.

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