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PtichkaEL [24]
2 years ago
11

If (x - 4) varies inversely as (y + 3) and x = 8 when y = 2, what is x when y = - 1?

Mathematics
1 answer:
denpristay [2]2 years ago
3 0

Answer:

x=14

Step-by-step explanation:

If two values are inversely proportional, their product must be maintained. That way, if one value goes up, the other goes down by the same extent.

Therefore, if (x-4) and (y+3) vary inversely, their product will be the same for all values of x-4 and y+3.

Let x=8 and y=2 as given in the problem. Substitute values:

(8-4)(2+3)=(4)(5)=20

Hence, the maintained product is 20.

Thus, we have the following equation:

(x-4)(y+3)=20

Substitute y=-1 to find the value of x when y=-1:

(x-4)(-1+3)=20,\\(x-4)(2)=20,\\x-4=10,\\x=10+4=\boxed{14}

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Grace was driving down a road and after 4 hours she had traveled 66 miles. At this speed, how many miles could Grace travel in 8
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Answer:

132 miles

Step-by-step explanation:

4 is half of 8 so you just have to multiple everything by 2 to get your answer

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Solve for y:<br>5(x + y) = 20 + 3x​
son4ous [18]
5(x+y)= 20+ 3x
5x+5y=20+3x
5x+5y-3x=20+3x-3x
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2x+5y-2x=20-2x
5y=-2x+20
5y/5=-2x/5+20/5
y=-2/5x+4

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A baseball team played 154 regular season games. The ratio of the number of games they won to the number of games they lost was
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Answer:

88 won and 66 lost

Step-by-step explanation:

Won = \frac{154}{4+3}×4 = 88 games

Lost = 154 - 88 = 66 games

7 0
3 years ago
What are the zeros of the polynomial function? f(x)=x2−16x+48
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X1 = 12
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3 years ago
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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.

6 0
3 years ago
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