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castortr0y [4]
1 year ago
7

Show all the stepsx: 3, 9, 13, 20y: 9, 27, 39, 60State whether the relationship between the variables in the table is a direct v

ariation, an inverse variation, or neither. If it is a direct or inverse variation, write a function to model it.
Mathematics
1 answer:
a_sh-v [17]1 year ago
6 0

By looking at the table, we can see that the y values are equal to the x values multiplied by 3.

3x = 3*3 = 9

3x =3*9 = 27

3x=3*13=39

3x= 3*20= 60

So, it is a direct variation and the function is y=3x

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segment YZ ≈ 19.4 in
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Explanation:

1) Given two side lenghts and one angle you can use sine law:

\frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c}

2) Using the sides with length 43 in and 40in, and the corresponding opposite angles, Z and 68°, that leads to:

\frac{sinZ}{43} = \frac{sin68}{40}

From which you can clear sinZ and get:

sinZ = 43 × sin(68) / 40 = 0.9967

⇒ Z = arcsine(0.9967) ≈ 85.36°


3) The third angle can be determined using 85.36° + 68° + X = 180°

⇒ X = 180° - 85.36° - 68° = 26.64°.

4) Finally, you can apply the law of sine to obtain the last missing length:

\frac{x}{sin(26.64)} = \frac{40}{sin(68)}

From which: x = 40 × sin(26.64°) /  sin(68°) = 19.34 in

The answer, then is:
segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°
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