Aphotograph has a length that is 6 inches longer than its width, x. so its area is given by the expression x(x+6) square inches. if the area of the photograph is 112 square inches, what is the width of the photograph?

The width of the photograph is 8 inches

let

width of the photograph = x

length of the photograph = 6 + x

Area  = x(6 + x)

112 =  x(6 + x)

112 = 6x + x²

x² + 6x - 112 = 0

x² - 8x + 14x - 112 = 0

x(x - 8) + 14(x - 8) = 0

(x + 14)(x - 8)

x = -14 or 8

x = 8

x cannot be negative so we use only 8.

width of the photograph = 8 inches

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the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.