Answer:
x = 12
Step-by-step explanation:
The mistake made here is in making 130 = 9x + 7. They are not the same.
The central angle = 130 degrees.
Any angle sharing the endpoints of the central angle and having it's vertex on the same side of the central angle is 1/2 the central angle.
1/2 the central angle = 130 /2 = 65
Cyclic quadrilaterals (those with all 4 points touching a circle's circumference) have opposite angles supplementary.
65 + 9x + 7 = 180 Combine like terms on the left
72 + 9x = 180 Subtract 72 from both sides
72 - 72 + 9x = 180-72 Combine
9x = 108 Divide by 9
9x/9 = 108/9
x = 12
The line needs to be 8.06 m long
Explanation
Given that the ladder is 7 feet tall and the bottom of the slide should be 4 m away from the ladder.
The ladder,slide and the ground connecting them makes the sides of a right angled triangle with ladder as the height and ground as the base.
base=4m
height=7m
hypotenuse can be determined using pythagoras law
Answer:
$11,130.47
Step-by-step explanation:
The amortization formula can be used. It tells you the monthly payment amount A for some principal P, interest rate r, and n payments.
A = P(r/12)/(1 -(1 +r/12)^(-n))
Filling in your values, we get ...
200 = P(.03/12)/(1 -(1 +.03/12)^-60) = P(.0025)/(1 -1.0025^-60)
P = 200(1 -1.0025^-60)/.0025 ≈ 200×55.6523577
P ≈ 11,130.47
The present value of the loan is $11,130.47.
9514 1404 393
Answer:
- square: 12 ft sides
- octagon: 6 ft sides
Step-by-step explanation:
This problem can be worked in your head.
If the perimeters of the square and regular octagon are the same, the side length of the 4-sided square must be the same as the length of 2 sides of the 8-sided octagon. Since the side of the square is 6 ft more than the side of the octagon, each side of the octagon must be 6 ft, and each side of the square must be 12 ft.
__
We can let s represent the side length of the octagon. Then we have ...
8s = perimeter of octagon
4(s +6) = perimeter of square
These are equal, so ...
4(s +6) = 8s
s +6 = 2s . . . . . . divide by 4
6 = s . . . . . . . . . . subtract s
The octagon has 6-ft sides; the square has 12-ft sides.
