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
scZoUnD [109]
3 years ago
8

Solve for x. x = __°

Mathematics
1 answer:
Luba_88 [7]3 years ago
6 0
Total inner angles add up to 720 because its a hexagon. so,
160 + 108 + 113 + 132+ 75+ x = 720
answer should be : 132°
You might be interested in
Picture below need answer fast
IRINA_888 [86]
Ok can you help me with this 137x8 multiply with expanded form please???? I will help with yours
7 0
2 years ago
What is the area of the circle represented by the equation x^2+y^2-6y=16
saveliy_v [14]

Answer: 12.56 (insert units)

Step-by-step explanation:

radius = 2

so pi x r^2 = 3.14 x 2^2 = 12.56

(Units were not mentioned)

3 0
3 years ago
Question (c)! How do I know that t^5-10t^3+5t=0?<br> Thanks!
astra-53 [7]
(a) By DeMoivre's theorem, we have

(\cos\theta+i\sin\theta)^5=\cos5\theta+i\sin5\theta

On the LHS, expanding yields

\cos^5\theta+5i\cos^4\theta\sin\theta-10\cos^3\theta\sin^2\theta-10i\cos^2\theta\sin^3\theta+5\cos\theta\sin^4\theta+i\sin^4\theta

Matching up real and imaginary parts, we have for (i) and (ii),


\cos5\theta=\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta
\sin5\theta=5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta

(b) By the definition of the tangent function,

\tan5\theta=\dfrac{\sin5\theta}{\cos5\theta}
=\dfrac{5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta}{\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta}

=\dfrac{5\tan\theta-10\tan^3\theta+\tan^5\theta}{1-10\tan^2\theta+5\tan^4\theta}
=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}


(c) Setting \theta=\dfrac\pi5, we have t=\tan\dfrac\pi5 and \tan5\left(\dfrac\pi5\right)=\tan\pi=0. So

0=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}

At the given value of t, the denominator is a non-zero number, so only the numerator can contribute to this reducing to 0.


0=t^5-10t^3+5t\implies0=t^4-10t^2+5

Remember, this is saying that

0=\tan^4\dfrac\pi5-10\tan^2\dfrac\pi5+5

If we replace \tan^2\dfrac\pi5 with a variable x, then the above means \tan^2\dfrac\pi5 is a root to the quadratic equation,

x^2-10x+5=0

Also, if \theta=\dfrac{2\pi}5, then t=\tan\dfrac{2\pi}5 and \tan5\left(\dfrac{2\pi}5\right)=\tan2\pi=0. So by a similar argument as above, we deduce that \tan^2\dfrac{2\pi}5 is also a root to the quadratic equation above.

(d) We know both roots to the quadratic above. The fundamental theorem of algebra lets us write

x^2-10x+5=\left(x-\tan^2\dfrac\pi5\right)\left(x-\tan^2\dfrac{2\pi}5\right)

Expand the RHS and match up terms of the same power. In particular, the constant terms satisfy

5=\tan^2\dfrac\pi5\tan^2\dfrac{2\pi}5\implies\tan\dfrac\pi5\tan\dfrac{2\pi}5=\pm\sqrt5

But \tanx>0 for all 0, as is the case for x=\dfrac\pi5 and x=\dfrac{2\pi}5, so we choose the positive root.
3 0
3 years ago
Order 1.09,1.9,and 1.1 from least to greatest
zysi [14]
1.09, 1.1, 1.9 Hope I helped
6 0
3 years ago
Read 2 more answers
In the given figure x = 145°. What theorem can be used to prove the lines p and q are parallel?
Gemiola [76]
C alternate exterior angles converse theorem

When two lines are parallel the alternate exterior angles are congruent
4 0
2 years ago
Other questions:
  • Given A = {a, b, c, d} and B = {1, 2, 3, 4} , sets A and B can be defined as?
    13·1 answer
  • A circle has a circumference of \blue{18}18start color #6495ed, 18, end color #6495ed. It has an arc of length 666.
    11·2 answers
  • Represent the quadratic polynomial 2x2 + x – 6 using algebra tiles and determine the equivalent factored form. The number of zer
    5·1 answer
  • 13 The circumference of the circle and the perimeter of the rectangle are equal.
    6·1 answer
  • Mrs. Ryan has a toy model car that represents her real car. 2 centimeters
    12·2 answers
  • What is the measure of the angle complementary to an angle that is 66 degrees?
    13·1 answer
  • Which equation matches the table<br> ​
    9·2 answers
  • What is the circumference of my circle
    15·1 answer
  • Use any method to multiply (3a + 2b - c)(a - b + 2c).
    10·1 answer
  • PLEASE HELP FAST) A ship travels 10 miles from Point A to Point B, makes a turn of 112, and
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!