Answer:
12 noodles
Step-by-step explanation:
If each child is given x amount of noodles, and there are 276 noodles to split among 23 students, set up the equation as seen below:
276÷23=12
276 noodles divided by 23 children = 12 noodles per child.
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Equation
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y = -3x - 9
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Option 1
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If I substitute x = -9, I should get y = 0
When x = -9
y = -3 (-9) - 9
= 18 (I did not get 0, wrong)
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Option 2
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If I substitute x = -3, I should get y = 0
y = -3(-3) - 9
y = 9 - 9
y = 0 (Yes, I got 0, correct)
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Option 3
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If I substitute x = 0, I should get y = -3
y = -3 (0) - 9
y = 0 - 9
y = -9 (I did not get -3, wrong)
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Option 4
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If I substitute x = 0, I should get y = -9
y = -3 (0) - 9
y = 0 - 9
y = -9 (Yes, I got -9, correct)
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Answer: (-3, 0) and (0, 9) are ordered pairs of the equation (Answer B, D)
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For this case we must simplify the following expression:
![\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B64%20%2A%20a%20%5E%206%20%2A%20b%20%5E%207%20%2A%20c%20%5E%209%7D)
We rewrite:
So:
![\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B4%20%5E%203%20%2A%20%28a%20%5E%202%29%20%5E%203%20%2A%20%28b%20%5E%202%29%20%5E%203%20%2A%20b%20%2A%20%28c%20%5E%203%29%20%5E%203%7D%20%3D%5C%5C%5Csqrt%20%5B3%5D%20%7B4%20%2A%20a%20%5E%202%20%2A%20b%20%5E%202%20%2A%20c%20%5E%203%29%20%5E%203%20%2A%20b%7D%20%3D)
By definition of properties of powers and roots we have:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
So:
![4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}](https://tex.z-dn.net/?f=4a%20%5E%202b%20%5E%202%20c%20%5E%203%20%5Csqrt%20%5B3%5D%20%7Bb%7D)
Answer:
Option B
X2<span> - 25 = x</span>2<span> - 5</span>2<span> = (x - 5)(x + 5)
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