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Ivenika [448]
3 years ago
7

Use what you know about triangles to classify this triangle.

Mathematics
1 answer:
Leya [2.2K]3 years ago
8 0

Answer:

obtuse scalene triangle

Step-by-step explanation:

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Save me the headache
maxonik [38]

(9\sin2x+9\cos2x)^2=81

Taking the square root of both sides gives two possible cases,

9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1

or

9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1

Recall that

\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta

If \alpha=2x and \beta=\dfrac\pi4, we have

\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}

so in the equations above, we can write

\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1

Then in the first case,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi

(where n is any integer)

\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi

\implies x=n\pi\text{ or }\dfrac\pi4+n\pi

and in the second,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi

\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi

\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi

Then the solutions that fall in the interval [0,2\pi) are

x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4

5 0
3 years ago
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At noon Ada and Kent had gallons of lemonade left at their lemonade stand. The next 3/8 customer bought of the remaining lemonad
Stolb23 [73]

Answer:

2

Step-by-step explanation:

Which represents the solution set of the inequality 5x-9 < 21? a. x < 12/5 b. x > 12/5 c. x > 6 d. x < 6

5 0
3 years ago
What is the volume of the right cone shown below? 10 O A. 7577 units3 B. 100n units3 C. 1507 units3 375 units3​
arsen [322]

Answer:

168

Step-by-step explanation:

6 0
3 years ago
Which property is shown below?
Tpy6a [65]

Answer:

C

Step-by-step explanation:

The identity property for addition tells us that zero added to any number is the number itself.

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3 years ago
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One Solution, Many (infinite) solutions, No solutions.
tensa zangetsu [6.8K]

Answer:

System A the answer is: One solution

System B the answer is: Many infinite solution

System C the answer is: No solution

Step-by-step explanation:

Hope this helps you :)

3 0
3 years ago
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