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3 years ago

Find the value of x in this figure.

Mathematics

2 answers:

Serga [27]3 years ago

4 0

Answer:

Hello,

Step-by-step explanation:

$mes\ \widehat{QOP}=60^o\ since \ triangle \ OQM\ is\ isocele\\\\M=middle\ of\ [OP]\\\\x=90^o -60^o=30^o\\$

AleksAgata [21]3 years ago

3 0

Step-by-step explanation:

angle x is equal to 65

angles of triangle is equal to 180

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3 years ago

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Evaluate the expression when a=-3 and b=7 7a-b

melamori03 [73]

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3 years ago

Which choice shows the product of 22 and 39?

Yuliya22 [10]

Answer: (22)(39) = 858.

Step-by-step explanation:

Product of a number simply means that one has to multiply the numbers that are given. For example, if a student is told to find the product of 2 and 5, it simply means that 2 × 5 = 10.

Regarding the above question, the product of 22 and 39 is represented by: (22)(39) = 858. It should be noted that 22 × 39 = 858

8 0

3 years ago

Prove it. this question is from trigonometry

konstantin123 [22]

Answer:

See below for step-by-step proof.

Step-by-step explanation:

$\textsf{Given expression}:$

$\cos^6 \theta+\sin^6 \theta$

$\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:$

$\implies (\cos^2 \theta)^3+(\sin^2 \theta)^3$

$\textsf{Use the identity}\quad a^3+b^3=(a+b)^3-3ab(a+b):$

$\implies (\cos^2 \theta+\sin^2 \theta)^3-3 \cos^2 \theta\sin^2 \theta (\cos^2 \theta+\sin^2 \theta)$

$\textsf{Use the identity}\quad \sin^2 \theta + \cos^2 \theta=1:$

$\implies (1)^3-3 \cos^2 \theta\sin^2 \theta (1)$

$\implies 1-3 \cos^2 \theta\sin^2 \theta$

$\implies 1-3 (\cos \theta\sin \theta)^2$

$\textsf{Use the identity}\quad \sin 2 \theta=2 \sin \theta \cos \theta \implies \dfrac{1}{2}\sin 2 \theta= \sin \theta \cos \theta:$

$\implies 1-3 \left( \dfrac{1}{2}\sin 2 \theta\right)^2$

$\implies 1-\dfrac{3}{4} \sin^2 2 \theta$

$\textsf{Use the identity}\quad \sin^2 2\theta + \cos^2 2\theta=1 \implies \sin^2 2\theta=1-\cos^2 2\theta$

$\implies 1-\dfrac{3}{4} \left(1-\cos^2 2 \theta\right)$

$\implies 1-\dfrac{3}{4} +\dfrac{3}{4}\cos^2 2 \theta$

$\implies \dfrac{1}{4} +\dfrac{3}{4}\cos^2 2 \theta$

$\textsf{Factor out }\dfrac{1}{4}:$

$\implies \dfrac{1}{4}\left(1+3\cos^2 2 \theta\right)$

$\textsf{Use the identity}\quad \cos (4 \theta)=2 \cos^2 2\theta - 1 \implies \cos^2 2 \theta=\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}:$

$\implies \dfrac{1}{4}\left(1+3\left(\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}\right)\right)$

$\implies \dfrac{1}{4}\left(1+\dfrac{3}{2}\cos 4 \theta+\dfrac{3}{2}\right)$

$\implies \dfrac{1}{4}\left(\dfrac{5}{2}+\dfrac{3}{2}\cos 4 \theta\right)$

$\implies \dfrac{1}{4} \cdot \dfrac{1}{2}\left(5+3\cos 4 \theta\right)$

$\implies \dfrac{1}{8}\left(5+3\cos 4 \theta\right)$

6 0

2 years ago

PLZ HELP FIRST RIGHT GETS BRAINLEST

konstantin123 [22]

Answer:

$\frac{1}{8}$ or $\frac{9}{78}$

(see explanation)

Step-by-step explanation:

This problem is asking about compound probability, what is the probability of this even happening three times in a row.

Since there are 20 boy's names and 20 girl's names in the hat, one can say that half of the names in the hat. Assume that after drawing it from the hat, the name is put back into the hat. Therefore, on each night, there is a half-chance of the event happening. To find the probability of the event, one must multiply ( $\frac{1}{2}$ ) by itself (3) times,

$(\frac{1}{2})(\frac{1}{2})(\frac{1}{2})\\=\frac{1}{8}$

In this case, assume that after each drawing the name is not replaced into the hat. This means that after every draw, one must subtract (1) from both the numerator and denominator of the fraction when the fraction is in the un-simplified form.

$(\frac{1}{2})(\frac{19}{39})(\frac{18}{38})$

Simplify,

$(\frac{1}{2})(\frac{19}{39})(\frac{9}{19})$

$\frac{9}{78}$

6 0

3 years ago