which of these is a rational number?
A) PI
B) √3
C) √2
D) 1.3
James attached a diagonal brace across a rectangular frame the measures 6 feet by 8 feet. what is the length of the diagonal brace?
A) 20ft
B) 10ft
C) 14ft
D) 48ft
Ok, for the first one, a rational number is a number that can be written as a fraction. A? No. B? No. C? No. D? Yes. If a number can't be written as a fraction, or doesn't have repeating decimals, it's called an irrational number.
For the second one, this requires using the Pythagorean Theorem which is a^2+b^2=c^2. A and B are the side lengths of a right triangle and C is the digonal of the right triangle. Plug values in to get 6^2+8^2=c^2. Solving that gets you c=10. So the diagonal is 10ft.
Do my explanations make sense? Let me know if you are still stuck.
And you think the answers are ... ?
idk. thats why im asking for help
thank you so much! i understand now
To determine which of the options is a rational number, we need to understand what a rational number is. A rational number is a number that can be expressed as a fraction, where both the numerator and the denominator are integers.
A) PI: Pi is an irrational number, meaning it cannot be expressed as a fraction. Therefore, it is not a rational number.
B) √3: The square root of 3 is an irrational number because it cannot be expressed as a fraction. Therefore, it is not a rational number.
C) √2: Like the square root of 3, the square root of 2 is also an irrational number and cannot be expressed as a fraction. Thus, it is not a rational number.
D) 1.3: This number can be expressed as a fraction, specifically 13/10. Therefore, it is a rational number.
So, the rational number among the options is D) 1.3.
To find the length of the diagonal brace, we can use the Pythagorean theorem, which states that in a right-angled 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 two sides of the rectangle form a right-angled triangle, with the diagonal brace being the hypotenuse. The length of one side is 6 feet, and the length of the other side is 8 feet.
Using the Pythagorean theorem, we can calculate the length of the diagonal brace:
(diagonal brace)^2 = (6 feet)^2 + (8 feet)^2
(diagonal brace)^2 = 36 + 64
(diagonal brace)^2 = 100
Taking the square root of both sides gives us:
diagonal brace = √100
diagonal brace = 10 feet
Therefore, the length of the diagonal brace is B) 10ft.