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Setler [38]
3 years ago
5

In Triangle XYZ, measure of angle X = 49° , XY = 18°, and

Mathematics
1 answer:
marissa [1.9K]3 years ago
6 0

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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-8b-32 what is the answer with work?
Crank
Well the LCM (lowest common multiples) for 8 and 32 would be 4. So plug 4 into "b" -8×4-32. -8×4=32. -32-32. Since you can't subtract 32 and 32 you add! Which gives you -64.

Hope this helps (:
7 0
3 years ago
Calculate the new balance of an account that has been sitting for three years with a 1.5% interest rate and had an initial depos
maksim [4K]

Answer:

$5225

Step-by-step explanation:

Use the formula for the amount after simple interest: A = P(1 + rt)

"A" is the final amount, or balance.

"P" is the principal, or the starting amount.

"r" is the rate of interest in decimal form.

"t" is the time.

What we know:

P = 5000

t = 3

r = 1.5%

Convert the rate to decimal form by dividing by 100, or moving the decimal place two places to the left.

1.5% => 0.015 = r

Substitute what we know into the formula:

A = P(1 + rt)

A = 5000(1 + (0.015)(3))     <=simplify

A = 5000(1 + 0.045)

A = 5000(1.045)

A = 5225     <= new balance

The new balance of an account is $5225.

4 0
3 years ago
HOW MANY BASEBALLS CAN FIT INTO THE TRACTOR TRAILER. THE TRAILER DIMENSIONS ARE 301.5"L X 96.99"W X 105.04"H AND CIRCUMFERENCE R
Shkiper50 [21]
Volume of tractor = length x width x height = 301.5 x 96.99 x 105.04 = 3,071,630.624

For baseballs of 9 inches:
9=2\pi r \\  \\ r= \frac{9}{2\pi}

Volume = \frac{4}{3} \pi r^3= \frac{4}{3} \pi \left( \frac{9}{2\pi} \right)^3=12.31

Number of 9 inches baseballs = \frac{3,071,630.624}{12.31} = 249,513

For baseballs of 9.25 inches:
9.25=2\pi r \\  \\ r= \frac{9.25}{2\pi}

Volume = \frac{4}{3} \pi r^3= \frac{4}{3} \pi \left( \frac{9.25}{2\pi} \right)^3=13.37

Number of 9.25 inches baseballs = \frac{3,071,630.624}{13.36} = 229,824

Therefore, the tractor can contain between 229,824 and 249,513 baseballs.
8 0
2 years ago
HELP PLEASEEE. I DONT UNDERSTAND
Shtirlitz [24]

Answer:

D

Step-by-step explanation:

So we have the equation:

x^2-6x+58=0

And we want to solve for x.

We can solve it by completing the square.

First, subtract 58 from both sides:

x^2-6x=-58

Divide the b term by 2 and square it:

(-6)/2=-3\\(-3)^2=9

So, add 9 to both sides:

(x^2-6x+9)=-58+9

On the left, the perfect square trinomial pattern. Add on the right. So:

(x-3)^2=-49

Take the square root of both sides:

x-3=\pm \sqrt{-49}

The square root of -49 is 7i:

x-3=\pm 7i

Add 3 to both sides:

x=3\pm 7i

So, our answer is D.

And we're done!

4 0
2 years ago
Please HELP QUICK!!!!!!!!!!!!!!!!!!
aleksklad [387]

Answer:

so the answer is 0.2

1/5 = 0.2

5 0
2 years ago
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