Answer: Conjecture: There is no triangle with side lengths N, 2N, and 3N (where N is a positive real number)
Proof:
We prove this by contradiction: Suppose there was an N for which we can construct a triangle with side lengths N, 2N, and 3N. We then apply the triangle inequalities tests. It must hold that:
N + 2N > 3N
3N > 3N
3 > 3
which is False, for any value of N. This means that the original choice of N is not possible. Since the inequality is False for any value of N, there cannot be any triangle with the given side lengths, thus proving our conjecture.
The lid will have a base area of 55 1/4 square inches. The long sides of the lid will each have an area of 17 square inches. The short sides of the lid will each have an area of 13 square inches. The total surface area of the lid will be 115 1/4 square inches.
So, for the base, you have w = 6.5 and l = 8.5. Area = 6.5 * 8.5 = 55.25 = 55 1/4.
For the long sides, you have l = 8.5 and h = 2. Area = 8.5 * 2 = 17
For the short sides, you have w = 6.5 and h = 2. Area = 6.5 * 2 = 13
For the total surface area, you have one base which is 55.25, you have two long sides which are 2 * 17 = 34, and you have two short sides which are 2 * 13 = 26. 55.25 + 34 + 26 = 115.25 = 115 1/4.
Given :
A meat market sells fajitas for $5.12 per pound.
To Find :
The cost of 3 - lbs of fajitas.
Solution :
Price of 1 pound fajitas, p = $5.12 .
So, price of 3 pounds of fajitas is :
P = 3 × p
P = 3 × 5.12
P = $15.36
Therefore, price of 3 pounds fajitas is $15.36 .
This shows that Marco can buy at most 5 pencils
<h3>Inequalities</h3>
- Let the price of each pencil Marco can buy be "x"
If the cost of markers is $4, and the cost of each lead pencil is $3 with at most $15 spent, hence;
Subtract 4 from both sides
3x ≤ 15
x ≤ 15/3
x ≤ 5
This shows that Marco can buy at most 5 pencils
Learn more on inequalities here:
brainly.com/question/24372553
