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2 years ago

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

umka2103 [35]

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
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3 years ago

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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

Fittoniya [83]

Answer:

88 won and 66 lost

Step-by-step explanation:

Won = $\frac{154}{4+3}$ ×4 = 88 games

Lost = 154 - 88 = 66 games

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3 years ago

What are the zeros of the polynomial function? f(x)=x2−16x+48

posledela

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 $XZ \approx 8.424$ .

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3 years ago