Answer:
x = 48
Step-by-step explanation:
Supplementary angles sum to 180°
add the 2 angles and equate to 180
x + 3x - 12 = 180 ( add 12 to both sides )
4x = 192 ( divide both sides by 4 )
x = 48
For 1:
Use pythagorean theorem because of the radius tangent theorem(point of contact = 90 degrees)
12 is the hypotenuse (the right angle points at the hypotenuse)
Therefore:
(9)^2 + (x)^2 = (12)^2
81 + x^2 = 144
Subtract 81 from both sides of the equation
x^2 = 63
Square root both sides to get rid of square on x and isolate the variable
The square root of 63 = 7.93 (roughly)
Use algebra to set up 2 equations.
Assign c as number of tickets for CATS and w for number of tickets of WICKED
c + w = 2700
c / w = 7 / 11
Then solve for one of them in the first equation
c = 2700 - w
Then put this value for c into the 2nd equation
(2700 - w) / w = 7 / 11
Now cross multiply the numerator by denominator of both numerator and denominator pairs
7w = 11 x (2700 - w)
7w = 29700 - 11w
Now solve for w
7w = 26700 - 11w
Add +11w to both sides
18w = 29700
Now divide by 18 on both sides
w = 1650
Then c is the remainder of that ... 2700 - 1650 = 1050
You can also check because 7 / 11 = 1050 / 1650
The distance around a circle on the other hand is called the circumference :)