<h3>Answer: A. 5/12, 25/12</h3>
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Work Shown:
12*sin(2pi/5*x)+10 = 16
12*sin(2pi/5*x) = 16-10
12*sin(2pi/5*x) = 6
sin(2pi/5*x) = 6/12
sin(2pi/5*x) = 0.5
2pi/5*x = arcsin(0.5)
2pi/5*x = pi/6+2pi*n or 2pi/5*x = 5pi/6+2pi*n
2/5*x = 1/6+2*n or 2/5*x = 5/6+2*n
x = (5/2)*(1/6+2*n) or x = (5/2)*(5/6+2*n)
x = 5/12+5n or x = 25/12+5n
these equations form the set of all solutions. The n is any integer.
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The two smallest positive solutions occur when n = 0, so,
x = 5/12+5n or x = 25/12+5n
x = 5/12+5*0 or x = 25/12+5*0
x = 5/12 or x = 25/12
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Plugging either x value into the expression 12*sin(2pi/5*x)+10 should yield 16, which would confirm the two answers.
The slant height is 5.19615 in
Hey there!
The distance on a number line is the distance that a point is from 0.
For example, if you were looking at a number line and there was a point on the number 5, that point would be 5 units away from 0.
Opposite numbers are related because they are the same distance away from 0. For example -3 and 3 are both 3 units away from the number 0.
I hope this helped! :-)
First answer: 12
Second answer: 6
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How to get these answers
She uses 1/3 of a cup for 1 cake, so we have this ratio
1/3 cup : 1 cake
Multiply both sides by 3 and we end up with
1 cup : 3 cakes
Then multiply both sides by 4 to change "1 cup" to "4 cups" and we have
4 cups : 12 cakes which is the answer to the first part
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For part 2, we'll follow the same steps as before, but instead of multiplying both sides by 4, we do 2 instead because we're dealing with 2 cups of oil.
1/3 cup : 1 cake
3*(1/3 cup) : 3*(1 cake)
1 cup : 3 cakes
2*(1 cup) : 2*(3 cakes)
2 cups : 6 cakes which is the answer to the second part
Answer:
10 + 4(-8q - 4)
= 10 + 4 * (-8q) + 4 * (-4) (Distribute 4)
= 10 - 32q - 16 (Expand)
= -32q - 6 (Combine like terms)
