Answer:
Aaron;s rate for mowing lawns is 0.5 acres per hour."as1.5 acres / 3 hours = 0.5 acres an hour2.5 acres / 5 hours = 0.5 acres an hour Option (B)
Step-by-step explanation:Aaron;s rate for mowing lawns is 0.5 acres per hour."as1.5 acres / 3 hours = 0.5 acres an hour2.5 acres / 5 hours = 0.5 acres an hour
Answer:
Step-by-step explanation:
{z - some integer}
2z+1 - the smallest number
7(2z+1) - seven times the smallest number
2z+1+2=2z+3 - the middle number
2z+3+2 = 2z+5 - the largest number
2(2z+5) - twice the largest number
7(2z+1) + 2(2z+5) - the sum of 7 times the smallest and twice the largest
7(2z+1) + 2(2z+5) = -91
14z + 7 + 4z + 10 = -91
-17 -17
18z = -108
÷18 ÷18
z = -6
2z+1 = 2(-6)+1 = -12 + 1 = -11
2z+3 = 2(-6)+3 = -12 + 3 = -9
2z+5 = 2(-6)+5 = -12 + 5 = -7
To solve this problem, we denote the smallest odd integer as 'x' and set up the equation 7x + 2(x+4) = -91. By solving this equation, we find that the smallest integer is -15.
To find the three consecutive odd integers, let us denote the smallest odd integer as x; therefore, the next two consecutive odd integers would be x + 2 and x + 4, respectively. The problem states that the sum of seven times the smallest integer and twice the largest integer equals to -91. So, we can translate this into the equation, 7x + 2(x+4) = -91. Solving this gives us x = -15. Hence the smallest integer is -15. The full solution is as follows:
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b. {2,2,4}
c. (1,2, sqrt of 3 wouldn't it be B because it has all even numbers?
The only set of numbers that could be the sides of a right triangle is **(b) {2, 2, 4}**.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Therefore, in order for a set of numbers to be the sides of a right triangle, the following equation must hold:
hypotenuse^2 = leg1^2 + leg2^2
Let's check each of the given sets:
(a) {2, 3, √13}
hypotenuse^2 = √13^2 = 13
leg1^2 = 2^2 = 4
leg2^2 = 3^2 = 9
13 ≠ 4 + 9
Therefore, {2, 3, √13} cannot be the sides of a right triangle.
(b) {2, 2, 4}
hypotenuse^2 = 4^2 = 16
leg1^2 = 2^2 = 4
leg2^2 = 2^2 = 4
16 = 4 + 4
Therefore, {2, 2, 4} can be the sides of a right triangle.
(c) {1, 2, √3}
hypotenuse^2 = √3^2 = 3
leg1^2 = 1^2 = 1
leg2^2 = 2^2 = 4
3 ≠ 1 + 4
Therefore, {1, 2, √3} cannot be the sides of a right triangle.
Therefore, the only set of numbers that could be the sides of a right triangle is **(b) {2, 2, 4}**.
Learn more about sides of a right triangle here:
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The set of numbers that could be the sides of a right triangle is {2,3, sqrt of 13}.
To determine whether a set of numbers could be the sides of a right triangle, we can use the Pythagorean theorem, which states that 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.
Let's check each set of numbers:
a. {2,3,√13}
b. {2,2,4}
c. (1,2,√3)
For set a, the sum of the squares of 2 and 3 is 13, which is equal to the square of √13. Therefore, set a could be the sides of a right triangle.
For set b, the sum of the squares of 2 and 2 is 8, which is not equal to the square of 4. Therefore, set b could not be the sides of a right triangle.
For set c, the sum of the squares of 1 and 2 is 5, which is not equal to the square of √3. Therefore, set c could not be the sides of a right triangle.
Therefore, the set of numbers that could be the sides of a right triangle is a. {2,3,√13}.
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