Bank A charger a 4$ service fee and $0.25 for each check written. Bank B charges $5 and $0.20 for each check written . How many checks does a person need to write each month for the two banks to charge the same amounts in fees. Which account would cost less if a person were to write 10 checks in a month?

1. A person would need to write 20 checks each month for the two banks to charge the same amount in fees.
2. The account from Bank A would cost less if a person were to write 10 checks in a month.

Explanation:
1. Bank A = 0.25x + 4, Bank B = 0.2x + 5

0.25x + 4 = 0.2x + 5
0.05x = 1
x = 20

2. Bank A = 0.25(10) + 4 = $6.5
Bank B = 0.2(10) + 5 =$7
Therefore, it would cost less to write 10 checks from Bank A.

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