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Sati [7]
1 year ago
13

Estimate to compare. Select < or >. Round each number to the nearest whole number to estimate each sum.

Mathematics
1 answer:
Sauron [17]1 year ago
3 0
3+5=8
3+2=5
So your answer is 8 > 5
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If 180° &lt; α &lt; 270°, cos⁡ α = −817, 270° &lt; β &lt; 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
What is the recursive rule for this geometric sequence? 1/2, -2, 8, -32
Gnesinka [82]

Answer:

see explanation

Step-by-step explanation:

A recursive rule allows us to find the term in a sequence from the previous term.

From the given geometric sequence find r the common ratio

r = \frac{-2}{\frac{1}{2} } = \frac{8}{-2} = - 4

Hence recursive rule is

a_{n+1} = - 4a_{n} ( a₁ = \frac{1}{2} )

4 0
3 years ago
Equations
Flauer [41]

Answer:

Step-by-step explanation:

-3x + 4y = -18

8x - 4y =   28

5x = 10

x = 2

4 - y = 7

-y = 3

y = -3

(2, -3)

8 0
3 years ago
Read 2 more answers
Prove: An even plus an even is<br> an even<br> 2n + 2m = [? ](n + m)<br> = even
KonstantinChe [14]

Answer:

2(n + m)

Step-by-step explanation:

3 0
2 years ago
The probability of a biased coin landing on heads is 2/7 complete the tree diagram
mamaluj [8]

Answer:

The numbers needed to fill each box are in the image attached

Step-by-step explanation:

The probability of the coin landing on heads is 2/7, so the probability of it landing on tails is 1 - 2/7 = 5/7

The probability of landing heads 2 times is:

P = (2/7) * (2/7) = 4/49

The probability of landing heads and then tails is:

P = (2/7) * (5/7) = 10/49

The probability of landing tails and then heads is:

P = (5/7) * (2/7) = 10/49

The probability of landing tails 2 times is:

P = (5/7) * (5/7) = 25/49

The numbers needed to fill each box are in the image attached.

8 0
3 years ago
Read 2 more answers
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