1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
I am Lyosha [343]
2 years ago
9

Find the value of the expression.

Mathematics
1 answer:
Aleks04 [339]2 years ago
5 0
The answer would be 6.
You might be interested in
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
Read 2 more answers
HELP DUE TODAY!!!!!!
larisa [96]

Answer:

x° is 66°  

Step-by-step explanation:

From the given diagram, we have;

∠JIH = 105° Given

∠IDJ = 39° Given

Therefore, we have;

∠JID and ∠JIH are supplementary angles, by the sum of angles on a straight line

∴ ∠JID + ∠JIH = 180° by definition of supplementary angles

∠JID + 105° = 180° by substitution property

∠JID = 180° - 105° = 75° by angle subtraction postulate

∠JID = 75°

∠IDJ + ∠JID + ∠IJD = 180° by the sum of interior angles of a triangle

∠IJD = 180° - (∠IDJ + ∠JID)  = 180° - (39° + 75°) = 66° angle subtraction postulate

∠IJD = 66°

∠x° ≅ ∠IJD, by vertically opposite angles

∴ ∠x° = ∠IJD = 66° by the definition of congruency

∠x° = 66°  

7 0
2 years ago
Read 2 more answers
List 3 equivalent ratios of 5/2
jek_recluse [69]
3 equivalent ratios or 5/2
10 /4
20/8
30/12
6 0
2 years ago
Read 2 more answers
In the figure YAZ = BAC by angle side angle which angles are congruent by CPCTC
Gelneren [198K]

Answer:

Step-by-step explanation

3 0
3 years ago
Multiplying decimals with models
Sidana [21]
1 is 0.0012. 2 is 3.25 and 3 is 3.25
6 0
3 years ago
Read 2 more answers
Other questions:
  • Luke is 5 years younger than 3 times Sydney’s age, s . in this situation , what does 3s represent?
    7·2 answers
  • Pls help i dont know how to do this​
    12·2 answers
  • If the perimeter of the semicircle is 10.28mm. What is the semicircles radius?
    11·1 answer
  • 3x-y=-5 <br> x=2y+5 <br> y=3/4x - 2 <br> y=-2/3x - 2
    5·1 answer
  • Explain why you can rewrite a division problem by moving the decimal points in the divisor and dividend the same number of decim
    9·1 answer
  • HELP ME!!! WHAT IS THIS?<br> 1+1
    14·2 answers
  • Solve each system by graphing:<br><br> 4x + 6y = -12<br> 2x + 3y = 6
    5·2 answers
  • A down arrow is drawn with its tip at (2, 0). Then it undergoes a translation described bythe directed line segment (−3, 1). Wha
    5·1 answer
  • PLEASE HELP WITH GEOMETRY QUESTION!! FIND H
    14·2 answers
  • Find the value of given expression<br><br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B230%20-%205%7D%20" id="TexFormula1" tit
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!