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MAXImum [283]
3 years ago
8

Name the intersection of lines r and s

Mathematics
1 answer:
Rudiy273 years ago
5 0
The two lines intersect at point B, hope this helps.
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Can anybody show me how to do this half angle identity problem STEP BY STEP? I always seem to be missing something
klio [65]

Answer:   \bold{-\dfrac{7\sqrt2}{10}}

<u>Step-by-step explanation:</u>

It is given that θ is between 270° and 360°, which means that θ is located in Quadrant IV ⇒ (x > 0, y < 0).  Furthermore, the half-angle will be between 135° and 180°, which means the half-angle is in Quadrant II ⇒ cos\ \dfrac{\theta}{2}

It is given that sin θ = -\dfrac{7}{25}  ⇒  y = -7 & hyp = 25

Use Pythagorean Theorem to find "x":

x² + y² = hyp²

x² + (-7)² = 25²

x² + 49 = 625

x²         = 576

      x   =  24    

Use the "x" and "hyp" values to find cos θ:

cos\ \theta=\dfrac{x}{hyp}=\dfrac{24}{25}    


Lastly, input cos θ into the half angle formula:

cos\bigg(\dfrac{\theta}{2}\bigg)=\pm \sqrt{\dfrac{1+cos\ \theta}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{1+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{25}{25}+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{49}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{49}{50}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\.\qquad \quad =\pm \dfrac{7\sqrt2}{10}

Reminder: We previously determined that the half-angle will be negative.

6 0
3 years ago
Translate into an inequality.
Alex787 [66]
5x-1 is greater than or equal to -11
5 0
3 years ago
Read 2 more answers
What is the unit rate of 15 and 2
Katena32 [7]
Https://www.khanacademy.org/math/in-sixth-grade-math/ratio-and-proportion/unitary-method/v/finding-unit-rates
4 0
4 years ago
a dance team has 80 dancers.The ratio of seventh-grade dancers to all dancers is 5:16.Find the number of seventh-grade dancers o
PSYCHO15rus [73]

Answer:

  25

Step-by-step explanation:

Each of the 16 "ratio units" representing all 80 dancers must stand for ...

  (80 dancers)/(16) = 5 dancers

Then 5 "ratio units" representing seventh-grade dancers will stand for ...

  5 × 5 dancers = 25 dancers

___

Another way to figure this is to write the proportion ...

  (seventh-grade dancers)/(all dancers) = 5/16

  seventh-grade dancers = (all dancers)×(5/16) = 80×5/16

  seventh-grade dancers = 25

5 0
3 years ago
A veterinarian weighs three cats. The American Shorthair weighs 13.65 pounds. The Persian weighs 13.07 pounds, and the Maine Coo
Alex_Xolod [135]

Answer:

Persian, Maine Coon, American Shorthair

13.07, 13.6, 13.65

Step-by-step explanation:

I hope this helped!

7 0
3 years ago
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