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3 years ago

Find the domain and range.

Mathematics

2 answers:

Kruka [31]3 years ago

8 0

Answer:

Domain: -5 < x ≤ 1

Range: -3 ≤ y ≤ 1

Step-by-step explanation:

For domain, the point on the most left is an open circle, meaning it is a greater than sign. The values of x is greater than -5 and less than or equal to 1.

For range, the lowest point is at -3, and the highest is at 1. Therefore, the range is greater than or equal to -3 and less than or equal to 1.

Advocard [28]3 years ago

4 0

Answer:

Domain: -5 < x ≤ 1

Range: -3 ≤ y ≤ 1

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3 years ago

1/3 and 3/5 as a decimal

DedPeter [7]

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3 years ago

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Prove it. this question is from trigonometry

konstantin123 [22]

Answer:

See below for step-by-step proof.

Step-by-step explanation:

$\textsf{Given expression}:$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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2 years ago

Hansika paid $9.25 for 2.8 pounds of pretzels. About how much did she pay for a pound of pretzels?

NeX [460]

Answer: $3.30

Explanation:
You set up a proportion where

9.25 X
------ = -----
2.8 1

Then you cross multiply and see that...
2.8X = 9.25
Then X = 9.25 / 2.8 = 3.30

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3 years ago

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How can I answer this question?

stiv31 [10]

She/he could use 2 12x3 in of wood and 1 4x2 so now we will take all of the numbers and see what we get when we calculat them so when we take the 2 12x3 we will get 72 and then we will add 72 to 4x2 after we multiply them so when we multiply the 4x2 we will get 8 and now will we add 72 to the 8 and we will get a 80 for your answer hope that is the right answer if it is not sorry

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4 years ago