Answer:
the area of the hexagon is approx. 187.1 in²
Step-by-step explanation:
Picture this regular polygon as being a hexagon made up of six equilateral triangles of side 12 in. We find the area of one such triangle and then multiply that by 6 to obtain the total area of the hexagon.
One such equilateral triangle has three sides all of length 12 in, and all the interior angles are 60°. The height of one such triangle is
h = (12 in)sin 60°, or
√3
h = (12 in) -------- = 6√3 in
2
So, with base 12 in and height 6√3 in, the area of one such equilateral triangle is
A = (1/2)(12 in)(6√3 in) = 36√3 in²
and the total area of the hexagon is 6(36)√3 in², or approx. 187.1 in²
Answers:
Part A: 12y² + 10y – 21
Part B: 4y³ + 6y² + 6y – 5
Part C: See below.
Explanations:
Part A:
For this part, you add Sides 1, 2 and 3 together by combining like terms:
Side 1 = 3y² + 2y – 6
Side 2 = 4y² + 3y – 7
Side 3 = 5y² + 5y – 8
3y² + 2y – 6 + 4y² + 3y – 7 + 5y² + 5y – 8
Combine like terms:
3y² + 4y² + 5y² + 2y + 3y + 5y – 6 – 7 – 8
12y² + 10y – 21
Part B:
You have the total perimeter and the sum of three of the sides, so you just need that fourth side value, which we can call d.
P = 4y³ + 18y² + 16y – 26
Sides 1, 2 & 3 = 12y² + 10y – 21
Create an algebraic expression:
12y² + 10y – 21 + d = 4y³ + 18y² + 16y – 26
Solve for d:
12y² + 10y – 21 + d = 4y³ + 18y² + 16y – 26
– 12y² – 12y²
10y – 21 + d = 4y³ + 6y² + 16y – 26
– 10y – 10y
– 21 + d = 4y³ + 6y² + 6y – 26
+ 21 + 21
d = 4y³ + 6y² + 6y – 5
Part C:
If closed means that the degree that these polynomials are at stay that way, then yes, this is true in these cases because you will notice that each side had a y², y and no coefficient value except for the fourth one. This didn't change, because you only add and subtract like terms.
Normally you would only solve by completing the square if a is 1 and b is even. But the answer would be half of b. So half of 9 is 4.5 or 4(1/2).
Answer:
259.80 dollars was deposited from his last pay check and he will have saved 6235.20 dollars in total
Step-by-step explanation:
Answer:
- after the raise, her salary is $1755 per month
- this is a +17% change from her original salary
Step-by-step explanation:
The multiplier of her original salary to her reduced salary is ...
(1 - 10%) = 0.90
The multiplier of her reduced salary after her raise is ...
(1 +30%) = 1.30
The multiplier of her raised salary from her original salary is ...
(0.90)(1.30) = 1.17 = (1 +17%)
Her salary after the 17% raise is ...
1.17·1500/mo = $1755/mo
