Colleen compared the ratios 3:8 and One-half. Her work is shown below. Write the ratios as fractions: Three-eighths and One-half
The common denominator is 8.
Write each fraction using the common denominator: Three-eighths and One-eighth
Compare the numerators: 3 > 1
Write the correct statement: Three-eighths > One-half

Where did Colleen make her first mistake?
The common denominator should be 4 rather than 8.
The numerators are compared incorrectly.
The fraction One-half should have been rewritten as StartFraction 6 Over 8 EndFraction.
The fraction One-half should have been rewritten as StartFraction 4 Over 8 EndFraction.

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

Where is the table?