Tom spent half of his allowance going to the movies. he washed the family car and earned 9 dollars. what is his weekly allowance if he ended with 13 dollars?

Let x = Tom’s allowance
Let x/2 = the amount he spent going to the movies.
So x – x/2 = the amount he has left after she went to the movies
he washed the car and earned nine dollars, so you’d add that amount in
x – x/2 + 9
the amount he has left over is 13 dollars
x – x/2 + 9 = 13
Now you solve for x
x – x/2 + 9 = 13
x/2 + 9 = 13
x/2 = 4
x = 8
His allowance is $8
To check your work, plug 8 into the equation:
8 – 8/2 + 9 = 13
8 – 4 + 9 = 13
13 = 13

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12