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tankabanditka [31]
3 years ago
14

What is the measure of ZY, in degrees?

Mathematics
1 answer:
ankoles [38]3 years ago
8 0
There is no picture/reference to go off of
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If tanA+sinA=m and tanA-sinA=n.prove that m^2-n^2=4√mn
mash [69]

Let a=\tan A and b=\sin A. Then

m^2-n^2=(a+b)^2-(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)=4ab

\implies m^2-n^2=4\tan A\sin A

and

mn=(a+b)(a-b)=a^2-b^2

\implies4\sqrt{mn}=4\sqrt{\tan^2A-\sin^2A}

The expression under the square root can be rewritten as

\tan^2A-\sin^2A=\dfrac{\sin^2A}{\cos^2A}-\sin^2A=\sin^2A\left(\dfrac1{\cos^2A}-1\right)=\sin^2A(\sec^2A-1)

Recall that

\sin^2A+\cos^2A=1\implies\tan^2A+1=\sec^2A

so that

\tan^2A-\sin^2A=\sin^2A\tan^2A

and assuming \sin A>0 and \tan A>0, we end up with

4\sqrt{\tan^2A-\sin^2A}=4\tan A\sin A

so that

m^2-n^2=4\sqrt{mn}

as required.

5 0
3 years ago
Write the equation of a line perpendicular to 5x−9y=−8 that passes through the point ​(−5​,8​).
Fantom [35]

Answer:  y = -(9/5)x - 1

Step-by-step explanation:

Rewrite the equation in standard form:  y = (5/9)x+(8/9).  [y=mx+b]

A line perpendicular to this would have a slope that is the negative inverse of the original slope (5/9), which would make it -(9/5).  The y-intercept would also change, but we don't know the value, yet.  For now, we'll use "b" for the y-intercept.  This results in a perpendicular line:

y = -(9/5)x + b

We can calculate b, the y-intercept, by using the point (-5,8) and solving for b.

8 = -(9/5)*(-5) + b

8 = (9) + b

b = -1

The line perpendicular to 5x−9y=−8 that passes through the point ​(−5​,8​) is

y = -(9/5)x - 1

7 0
3 years ago
In a lottery game, a player picks six numbers from 1 to 21. If the player matches all six numbers, they win 40,000 dollars. Othe
Darina [25.2K]

Answer:

The expected value of this game is -$0.26.

Step-by-step explanation:

Expected value:

Each possible earning/loss multiplied by it's probability.

Probability:

Number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the numbers are chosen is not important. So we use the combinations formula to solve.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Probability of winning:

Desired outcomes:

The 6 correct numbers, so D = 6

Total outcomes:

6 numbers from a set of 21. So

T = C_{21,6} = \frac{21!}{6!15!} = 54264

Probability:

p = \frac{1}{54265}

Expected value

\frac{1}{54265} probability of earning 40,000.

\frac{54264}{54265} probability of losing 1. So

E = \frac{40,000}{54265} - \frac{54264}{54265} = -0.26

The expected value of this game is -$0.26.

7 0
3 years ago
Choose each number that shows 1/2 % as an equivalent fraction, decimal, or percent. Select all that apply.
stepladder [879]

Answer:

(1/2)% = 0.5% =0.5/100 = 0.005

=> Option E is correct.

Hope this helps!

:)

7 0
3 years ago
Read 2 more answers
If y = -12 when x = 9, find u when x = -4
True [87]

Answer:

y should equal -25 if i did the math right

Step-by-step explanation:

-12 and 9 have a difference of -21 so if i subtract -21 from -4 it would equal -25.. hope this helps!!

4 0
3 years ago
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