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2 years ago

15

Find the domain of the function. (enter your answer using interval notation.) f(x) = x + 3 if x < −1 −2x if |x| ≤ 1 −2 if x &

gt; 1

1 answer:

Ivenika [448]2 years ago

4 0

The domain of the function is the union of all of the "if" parts of the function definition:

... (-∞, -1) ∪ [-1, 1] ∪ (1, ∞) = (-∞, ∞)

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What is the equation of the circle with center (0, 0) that passes through the point (5, -4)?

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The standard form of a circle is $(x-h) ^{2} +(y-k) ^{2} = r^{2}$ where h and k are the center and x and y are the coordinates you're given. We need to solve for the radius to finish this off correctly. Filling in, we have $(5-0) ^{2} +(-4-0) ^{2} = r^{2}$ and $25+16= r^{2}$ , giving us that $r^{2}=41$ . Therefore, our equation is $x^{2} + y^{2} =41$

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2 years ago

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Bethany has $3.10 in nickels and dimes. She has a total of 44 coins. What is the value of the nickels Bethany has?

lesantik [10]

0.05n + 0.1d = 3.10
n + d = 44

d = 44 - n

Substituting to the first equation:

0.05n + 0.1(44 - n) = 3.10
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-0.05n = 3.10 - 4.4
n = 26

Obtaining the value of nickels:
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Therefore, the value of nickels that Bethany has is $1.30

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