The two angles form a straight line which is equal to 180 degrees. This makes the angles supplemtary.
To find x, add the two angles together to equal 180:
7x + x+20 = 180
Combine like terms:
8x + 20 = 180
Subtract 20 from both sides:
8x = 160
Divide both sides by 8:
X = 20
Answer:
(i) The name of the part of the circle, OQ is a radius
(ii) The radius of the sector QOR is 21 cm
Step-by-step explanation:
The given figure is a sector of the circle O
∵ Any sector of a circle formed from 2 radii and an arc
∴ OQ is a radius
(i) The name of the part of the circle, OQ is a radius
The rule of the length of an arc of a circle is L = 
× 2 π r, where
- α is the angle of the sector
- r is the radius of the circle
∵ The length of the arc QR is 22 cm
∴ L = 22
∵ The measure of the angle of the arc is 60°
∴ α = 60°
∵ π = 
→ Substitute them in the rule above
∵ 22 = 
× 2 × × r
∴ 22 = 
r
→ Divide both sides by
∴ 21 = r
(ii) The radius of the sector QOR is 21 cm
Given :
On the first day of ticket sales the school sold 10 senior tickets and 1 child ticket for a total of $85 .
The school took in $75 on the second day by selling 5 senior citizens tickets and 7 child tickets.
To Find :
The price of a senior ticket and the price of a child ticket.
Solution :
Let, price of senior ticket and child ticket is x and y respectively.
Mathematical equation of condition 1 :
10x + y = 85 ...1)
Mathematical equation of condition 2 :
5x + 7y = 75 ...2)
Solving equation 1 and 2, we get :
2(2) - (1) :
2( 5x + 7y - 75 ) - ( 10x +y - 85 ) = 0
10x + 14y - 150 - 10x - y + 85 = 0
13y = 65
y = 5
10x - 5 = 85
x = 8
Therefore, price of a senior ticket and the price of a child ticket $8 and $5.
Hence, this is the required solution.
He didn’t multiply by 4 first
The equations without a solution are A, B, and D since if you were to simply multiply out the equations with FOIL, you would receive X's that cancel out on both sides. I am not sure if you are looking for one solution but here's my input
