If John can paint half of a room in two-thirds of an hour, what part of the room can he paint in a full hour?

0.75(3/4) part of the room

Step-by-step explanation:

Step one:

given data

we can express the given data mathematically as

John can paint 0.5room in 2/3 hours

let the part of the room he can paint in an hour be x

so

if he takes 2/3 hours to paint 0.5 room

then he will take 1 hour to paint x

cross multiply we have

x= 0.5/2/3

x=0.5*3/2

x= 1.5/2

x=0.75 part of the room

75/100= 15/20=3/4 part

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