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3 years ago

Find θ, 0° ≤ θ < 360°, given the following information.

Mathematics

1 answer:

ludmilkaskok [199]3 years ago

3 0

Answer:

210°

Step-by-step explanation:

Given

sinΘ = - $\frac{1}{2}$

Note taken the inverse sine of the positive value of the ratio, gives the related acute angle, that is

Θ = $sin^{-1}$ ( $\frac{1}{2}$ ) = 30° ← related acute angle

Thus the required angle in the third quadrant is

Θ = 180° + 30° = 210°

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Consider the two expressions 4b(b+1) and (2b+7)(2b-8). Compare their values if b=-3, b=-2, and if b=10. Is it true that for an v

frutty [35]

Answer:

FIRST EXPRESSION:

- If $b=-3$ , the value of $4b(b+1)$ is $24$

- If $b=-2$ , the value of $4b(b+1)$ is $8$

- If $b=10$ , the value of $4b(b+1)$ is $440$

SECOND EXPRESSION:

- If $b=-3$ , the value of $(2b+7)(2b-8))$ is $-14$

- If $b=-2$ , the value of $(2b+7)(2b-8))$ is $-36$

- If $b=10$ , the value of $(2b+7)(2b-8))$ is $324$

Yes, for any value of "b" the value of the first expression is greater than the value of the second expression.

Step-by-step explanation:

Substitute the given values of "b" into each expression and evaluate.

- For the first expression $4b(b+1)$ , you get:

If $b=-3$ → $4(-3)(-3+1)=24$

If $b=-2$ → $4(-2)(-2+1)=8$

If $b=10$ → $4(10)(10+1)=440$

- For the second expression $(2b+7)(2b-8))$ , you get:

If $b=-3$ → $(2(-3)+7)(2(-3)-8)=-14$

If $b=-2$ → $(2(-2)+7)(2(-2)-8)=-36$

If $b=10$ → $(2(10)+7)(2(10)-8)=324$

You can observe that for any value of "b" the value of the first expression is greater than the value of the second expression.

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3 years ago

Use the like bases property to solve the equation:<br> 16^x = 1/4<br> x=

gavmur [86]

Answer:-1/2

Step-by-step explanation:

16^x=1/4

(4^2)^x=4^(-1)

4^2x=4^(-1)

Base cancelled each other since they are the same

2x=-1

Divide both sides by 2

2x/2=-1/2

x=-1/2

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3 years ago