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3 years ago

What is the solution to this system of equations? y=22x + 42

Mathematics

1 answer:

irga5000 [103]3 years ago

3 0

Answer:

y=22x+42

y/x=22+42

y/x=64

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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

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

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

I’ll give brainliest, just help me please :)

Lemur [1.5K]

Answer:

V = 408 SA = 378

Step-by-step explanation:

To find the volume, you need to first find out the area and multiply it by overall length.

A = 1/2 (6)(8)

= 24

Volume = 24 x 17

= 408

Surface Area

SA = Front and Back + Right Side + Left Side + Bottom

= 2 [1/2 (6) (8)] + (17 x 10) + (3 x 8) + (17 x 8)

= 2 (24) + 170 + 24 + 136

= 48 + 170 + 24 + 136

= 378

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3 years ago

What is the area of a regular hexagon with a side length of 4 m? Enter your answer in the box. Round only your final answer to t

hichkok12 [17]

The area of a hexagon is
A= a^2 (3√3)/2
we replace a with 4
A=41.57

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3 years ago

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Find the value of sin 0<br>cos(90°- 0) + cos 0 sin(90°-0)

Step2247 [10]

Step-by-step explanation:

$sin \theta \: cos(90 \degree - \theta) + cos \theta \: sin(90 \degree - \theta) \\ = sin(\theta + 90 \degree - \theta) \\ = sin(90 \degree) \\ = 1$

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4 years ago

Need help please real fast will give brainlist

viktelen [127]

Answer:

-2

Step-by-step explanation:

Hope it helps

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3 years ago