The municipal swimming pool in nicetown has three different ways of paying for individual open swimming. todd is trying to decide which way to pay. • early pay: pay $70 before memorial day; swim any number of days • deposit plus: $15 deposit plus $4.00 per day • daily pay: $6.00 per day answer the following questions: 1. write an equation for each method of payment. write your equations in slope-intercept form so that x is the number of days and y is the cost. a. early pay: b. deposit plus: c. daily pay:

Sllope intercept form is y=mx+b
m is the slope , b is the y itnercept

so early pay
cost=70 flat rate
x=infinity
the equation would be y=70

deposit pluss
you have to pay an initial one time payment of 15 so
y=mx+15
then 4 dollars per day
4 times number of days
y=4x+15

daily pay is 6 dollars per day so 6 times number of days
y=6x

1.
a. y=70
b. y=4x+15
c. y=4x

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