3x(x + 6) = -10 Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using the ± symbol. DESCRIBE AND JUSTIFY THE METHODS YOU USED TO SOLVE THE QUADRATIC EQUATION!

Step-by-step explanation:

Expand it:

Add 10 to both sides:

Divide both sides by 3:

Find a, b for

It’s

So, inserting it leads to:

Subtract b from both sides:

Apply square root to both sides and consider the two solutions:

Subtract 3 from both sides and you get

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.