Answer:
1) x = 14°, y = 5°
2) x = 18.5°, y = 37°
Step-by-step explanation:
1) ∠AOC and ∠BOD are vertical angles, then ∠BOD = 25°
∠MOD = ∠MOB + ∠BOD = 90°
3x + 23° + 25° = 90°
3x = 90° - 23° - 25°
x = 42°/3
x = 14°
∠LOB = ∠LOM + ∠MOB = 90°
5y + 3x + 23° = 90°
5y = 90° - 23° - 3(14°)
y = 25°/5
y = 5°
2) ∠AOC and ∠BOD are vertical angles, then ∠BOD = 16°
∠EOB = ∠EOD + ∠DOB = 90°
2y + 16° = 90°
y = (90° - 16°)/2
y = 37°
∠DOF = ∠BOF + ∠DOB = 90°
4x + 16° = 90°
x = (90° - 16°)/4
x = 18.5°
a) The sum of your ages is F + (F+B) = 2F+B.
b) In 3 years, the sum of your ages will be (F+3)+(F+B+3) = 2F+B+6.
c) The difference of your ages at any time is B.
<u>Answer:</u>
3 miles 26 yards
<u>Step-by-step explanation:</u>
We are to perform subtraction on the following:
8 mi 133 yd 2 ft – 5 mi 107 yd 2 ft
We have to divide the amount of miles from miles, yards from yards and feet from feet. So a good idea is to write it this way in order to avoid any confusion:
8 mi 133 yd 2 ft
- 5 mi 107 yd 2 ft
_______________
3 mi 26 yd 0 ft
_______________
So we are left with 3 miles 26 yards.
Given:
The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).
To find:
The equation of the quadratic function.
Solution:
A quadratic function is defined as:
...(i)
It is passes through the point (0,11). So, substitute 
in (i).
Putting 
in (i), we get
...(ii)
The quadratic function passes through the point (5,31). So, substitute 
in (ii).
Divide both sides by 5.
...(iii)
The quadratic function passes through the point (3,11). So, substitute 
in (ii).
Divide both sides by 3.
...(iv)
Subtracting (iv) from (iii), we get
Putting 
in (iv), we get
Putting 
in (ii), we get
Therefore, the required quadratic equation is .
