Createa ratio tablefor making lemonade with juice to water ratio of 1: 3 how much lemon juice would be needed if you use 36 cups of water?

Juice:water is 1:3 so insert water and leave the juice blank. __:36. You can set these up as fractions: 1/3 = x/36. Cross multiply: 1 X 36= 36 and 36 divided by 3 is 12. Another way to figure this out is this: 3 divided by 3 is 1 (1:3) so 36 divided by 3 equals 12 (12:36) The answer is 12 cups of juice either way

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

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