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3 years ago

15

HELPPPPPPP !!!!! Select the statements that are true based on the following given information.

1 answer:

almond37 [142]3 years ago

7 0

the anwser is ]123[8D[

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If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

Find the circumference for 6 and 8

Naya [18.7K]

Answer:
6. 98.01
8. 32.04

5 0

2 years ago

Help plz !!!!!!!!!!!!!!!!! These are so hard

OlgaM077 [116]

Answer:

$m=\frac{4}{9}$

Step-by-step explanation:

Using the slope formula:

$m=\frac{1+7}{10+8}=\frac{8}{18}=\frac{4}{9}$

6 0

3 years ago

-4(-6+9+4v+7v) what is the answer

r-ruslan [8.4K]

First step:
simplify the values in the parenthesis:
-4(3+11v)
Second step:
apply the distributive property:
-12-44v
The final answer (simplified) is -44v-12

4 0

2 years ago

What is the answer to thiss

lana [24]

Hi Student!

This question is fairly simple because it gives us an equation and they also give us a value for the variable that is within the equation and they tell us evaluate the expression. So let's plug in the values and solve.

<u>Plug in the values</u>

$m^2 + 5$

$(9)^2 + 5$

<u>Factor out the exponent</u>

$(9*9) + 5$

$81 + 5$

<u>Combine</u>

$86$

Therefore, the final answer that we would get when substituting m with 9 in the given equation is that we get 86.

5 0

1 year ago