5. Find the length of a right triangle with legs of 5 ft. and 12 ft.
A 11 Ft
B 13 Ft
C 17 Ft
D 60 Ft
9. which of these nonterminating decimals can be converted into a rational number?
A 0.48907542...
b 0.02020202...
C 0.92589542...
D 0.10203040...
5.C
9.A
Thanks orange girl!
To find the length of a right triangle with legs of 5 ft. and 12 ft., we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the legs of the right triangle are 5 ft. and 12 ft. Let's call the length of the hypotenuse "c". According to the Pythagorean Theorem, we have the equation:
5^2 + 12^2 = c^2
Simplifying this equation, we get:
25 + 144 = c^2
169 = c^2
To find the length of the hypotenuse, we take the square root of both sides of the equation:
√(169) = √(c^2)
13 = c
So, the length of the hypotenuse (the right triangle) is 13 ft. Therefore, the correct answer is option B - 13 ft.
For the second question, to determine which of the nonterminating decimals can be converted into a rational number, we need to understand what a rational number is. A rational number is any number that can be represented as a fraction of two integers.
Looking at the given options:
A) 0.48907542... - This is a nonterminating decimal with repeating digits. Nonterminating decimals with repeating patterns can be converted into rational numbers by expressing them as fractions. For example, in this case, we can represent it as the fraction 48907542/99999999. Therefore, option A can be converted into a rational number.
B) 0.02020202... - This is a nonterminating decimal with a repeating pattern of "02". We can express it as the fraction 2/99. Therefore, option B can be converted into a rational number.
C) 0.92589542... - This is a nonterminating decimal without any repeating pattern. Such decimals cannot be converted into rational numbers. Therefore, option C cannot be converted into a rational number.
D) 0.10203040... - This is a nonterminating decimal without any repeating pattern. Similar to option C, it cannot be converted into a rational number.
Therefore, the correct answer is option A - 0.48907542... can be converted into a rational number.