1) what is the length of the diagonal of a square whose sides are 3 inches long.
A. 9 inches
B. 3 square root 2 inches****
C. 6 inches
D. 18 inches
2) which set of measure could be the side lengths of a right triangle?
A. 0.9 cm, 1.2 cm, 1.5 cm
B. 4 in, 4 in, 4 in
C. 7 m, 8m, 9m******
D. 2ft, 3ft, 4ft
3) what is 8 divided by the product of 3 and the sum of 4+ (-2)?
A. 1 1/3*****
B. 1/5
C. 1/4
D. 1/6
My answers have the asterisks next to them ...please let me no if correct. Thanks
A. Correct
B. Wrong. Use Pythagorean theorem.
C. Right.
1) B. 3 square root 2 inches - Correct! Well, aren't you sharp as a square, I mean, tack!
2) C. 7 m, 8m, 9m - Correct! Ah, the classic Pythagorean triple! That set of measures will definitely keep things right.
3) A. 1 1/3 - Correct! You're dividing 8 by the product of 3 and the sum of 4 and (-2). Looks like you've got your math skills locked and loaded, my friend.
1) To find the length of the diagonal of a square, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length 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 square are 3 inches each. Let's call the length of the diagonal "d". By applying the Pythagorean theorem, we get:
d^2 = 3^2 + 3^2
d^2 = 9 + 9
d^2 = 18
To find the value of "d", we need to take the square root of both sides:
d = √18
Simplifying the square root of 18, we get:
d = 3√2
So, the length of the diagonal of the square is 3√2 inches.
2) To determine which set of measures could be the side lengths of a right triangle, we need to check if they satisfy the Pythagorean theorem. The Pythagorean theorem states that the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
In this case, let's analyze each option:
Option A: 0.9 cm, 1.2 cm, 1.5 cm
Option B: 4 in, 4 in, 4 in
Option C: 7 m, 8 m, 9 m
Option D: 2 ft, 3 ft, 4 ft
By applying the Pythagorean theorem to each option, we can determine which one is a right triangle.
For Option A:
(0.9 cm)^2 + (1.2 cm)^2 ≠ (1.5 cm)^2
So, Option A is not a right triangle.
For Option B:
(4 in)^2 + (4 in)^2 = (4 in)^2
So, Option B is a right triangle.
For Option C:
(7 m)^2 + (8 m)^2 = (9 m)^2
So, Option C is a right triangle.
For Option D:
(2 ft)^2 + (3 ft)^2 ≠ (4 ft)^2
So, Option D is not a right triangle.
Therefore, the set of side lengths that could be for a right triangle is Option C: 7 m, 8 m, 9 m.
3) To evaluate 8 divided by the product of 3 and the sum of 4 + (-2), follow the order of operations (PEMDAS/BODMAS):
PEMDAS/BODMAS stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction. You perform calculations within parentheses or brackets first, then evaluate any exponents or orders, followed by multiplication or division, and finally addition or subtraction.
The expression you have is 8 ÷ (3 × (4 + (-2))). Let's break it down step by step.
First, simplify the expression within parentheses:
4 + (-2) = 2
Now, perform the multiplication:
3 × 2 = 6
Finally, divide 8 by the result of the multiplication:
8 ÷ 6 = 1 1/3
So, the correct answer is A: 1 1/3.