Write 10 feet and 4 yards as a fraction in simplest form

1 answer:

5 0

⅚. You first find out how many feet are in a yard (three). Then you write the fraction- 10/12. Then you reduce. The number two can evenly go into both of those numbers. Ten divided by two is five. Twelve divided by two is six. So, your final answer is ⅚.

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Answer: Choice A) $3 \sqrt{26}$

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Work Shown:

$\text{The two points are } (x_1,y_1) = (6,7) \text{ and } (x_2,y_2) = (3,-8)\\\\d = \text{Distance between } (x_1,y_1) \text{ and } (x_2,y_2)\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} = \text{Distance Formula}\\\\d = \sqrt{(6-3)^2+(7-(-8))^2}\\\\d = \sqrt{(6-3)^2+(7+8)^2}\\\\$

$d = \sqrt{(3)^2+(15)^2}\\\\d = \sqrt{9+225}\\\\d = \sqrt{234}\\\\d = \sqrt{9*26}\\\\d = \sqrt{9}*\sqrt{26}\\\\d = 3\sqrt{26}\\\\$

When going from 234 to 9*26, the idea here is to factor where one factor is the largest perfect square possible. That way we can use the rule $\sqrt{x*y} = \sqrt{x}*\sqrt{y}$ to break up the root and simplify.