9514 1404 393
Answer:
a. x, x+2, x+4
b. 10 ≤ 3x+6 ≤ 24
c. 6 ft, 8 ft, or 10 ft
Step-by-step explanation:
<u>Given</u>:
- The lengths of the sides of a certain triangle, in feet, are consecutive even integers.
- The perimeter of this triangle is between 10 feet and 24 feet inclusive.
<u>Find</u>:
a. Using one variable, write three expressions that represent the lengths of the three sides of the triangle.
b. Write a compound inequality to model this problem.
c. Solve the inequality. List all possible lengths for the longest side of the triangle.
<u>Solution</u>:
You have let x represent the shortest side. (Note that the question asks for the length of the longest side.)
a. The expressions for side lengths can be x, x+2, x+4 when x is the shortest side.
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b. Here is the compound inequality
10 ≤ x+(x+2)+(x+4) ≤ 24
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c. Here is the solution
10 ≤ 3x+6 ≤ 24 . . . . collect terms
4 ≤ 3x ≤ 18 . . . . . . . subtract 6
4/3 ≤ x ≤ 6 . . . . . . . . divide by 3
<em>Your working is correct, but incomplete</em>. The values of interest are the even integers x+4.
5 1/3 ≤ x+4 ≤ 10
The longest side may be 6 ft, 8 ft, or 10 ft.
Answer:
The height of the pyramid is 5m
Step-by-step explanation:
To calculate the heigth of a pyramid we have to use the following formula:
v = volume = 70 m³
w = width = 6 m
l = length = 7 m
h = height
v = (w * l * h) / 3
we replace the values that we know
70m³ = (6m * 7m * h) / 3
70m³ * 3 = 42m² * h
210m³ / 42m² = h
5m = h
The height of the pyramid is 5m
63 = 10 + m
hope this helps :)
Answer:
B. -2x2 + 6x + 6.
Step-by-step explanation:
(2x2 + 4x + 3) - (4x2 - 2x-3) Distribute negative over the parentheses:
= 2x2 + 4x + 3 - 4x2 + 2x + 3
= 2x2 - 4x2 + 4x + 2x + 3 + 3
= -2x2 + 6x + 6.
