The sum of three consecutive even integers is −246. Find the three integers.
1 answer:
Answer:
-83, -82, and -81
Step-by-step explanation:
Step 1: Declare your variable
Let x represent the largest of the 3 consecutive integer
Integer 1: x
Integer 2: x + 1
Integer 3: x + 2
Step 2: Create an equation
(x) + (x + 1) + (x + 2) = -246
Step 3: Solve
x + x + 1 + x + 2 = -246
3x + 3 = -246
3x = -249
x = -83
FInd the other 2 numbers
Integer 1: -83
Integer 2: -82
Integer 3: -81
Step 4: Therefore Statement
Therefore the 3 consecutive numbers are -83, -82, and -81
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Answer:
Step-by-step explanation:
1. Area of base
The radius given is that of the circumcircle.
The general formula for the edge length a of a regular polygon is
a = 2Rsin(π/n)
So,
a = 2 × 5 × sin(π/5) = 10sin0.6283 = 10 × 0.5878 = 5.878 in
The general formula for the area of a regular polygon is
A = ¼na²cot(π/n)
So,
A = ¼ × 5 × 5.878²cot(π/5) = ¼ × 5 × 5.878² × 1.376 = 59.44 in²
2. Lateral area
The general formula for the lateral area L of regular prism is
L = nah
So,
L = 5 × 5.878 × 12 = 352.7 in²
3. Total area
Total surface area = lateral area + 2×base area
S = L + 2B = 352.7 + 2 × 59.44 = 471.6 in²
Answer:
x = 72
Step-by-step explanation:
Start by multiplying 16 to both sides
16s on the left-hand cancel
we can simplify that expression