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nexus9112 [7]
3 years ago
5

Hannah and anthony are siblings who have ages that are consecutive odd integers. The sum of there ages is 92. Which equations co

uld be used to find Hannahs age, h, if she is the older sibling?
Mathematics
1 answer:
horsena [70]3 years ago
5 0
If you would like to know the equation that could be used to find Hannah's age, you can calculate this using the following steps:

h ... Hannah's age ... h = a + 2
a ... Anthony's age ... a = h - 2

a + h = 92
h - 2 + h = 92
2 * h - 2 = 92
2 * h = 92 + 2
2 * h = 94       /2
h = 94 / 2 = 47

<span>a = h - 2 = 47 - 2 = 45
</span>
The correct result could be <span>h - 2 + h = 92.</span>
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The first method is simplifying the root. While this doesn't give you an exact value, it reduces the number inside the root.

Find the prime factorization of 864:

\sqrt{864} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3}

Take any number that is repeated twice in the square root, and move it outside of the root:

\sqrt{864} = \sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3}

\sqrt{2 \cdot 2} = \sqrt{4} = 2

\sqrt{3 \cdot 3} = \sqrt{9} = 3

\sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3} = \sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3}

\sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3} = (2 \cdot 2 \cdot 3) \sqrt{2 \cdot 3} = \boxed{12 \sqrt{6}}

The simplified form of √864 will be 12√6.

The second method is evaluating the root. Using a calculator, we can find the exact value of √864.

Plugged into a calculator and rounded to the nearest hundredths value, √864 is equal to 29.39. Because square roots can be negative or positive when evaluated, this means that √864 is equal to ±29.39.

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Answer:

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