The mean of four numbers is 7. Three of the numbers are 5, 7, and 7. What is the fourth number? Explain your reasoning.

9

Step-by-step explanation:

The mean is equal to the sum of all numbers divided by the amount of numbers there are. If we represent the mean as m, sum as s, and number of numbers as n, we can write our equation as

m = s/n

Therefore, as we know the mean (7) and number of numbers (4), we can plug those in to find the sum.

7 = s / 4

Multiply both sides by 4

28 = s

We then have our sum. Because we know 3 numbers, and there are 4 total, there is one number left to figure out. Our current sum is 5+7+7 = 19, and we need a sum of 28. The difference between the sums, equivalent to the fourth number, is 28-19=9.

the co-ordinates of the transformed rectangle are:

d. (0, 0), (0, 3), (-3, 3), (-3, 0)

step-by-step explanation:

from the columns of the given matrix, the co-ordinates of the rectangle before transformation are:

(0, 0), (0, 3), (3, 3), (3, 0)

r =

transformed matrix can be obtained by multiplying the given matrix by r:

columns of the transformed matrix are:

0   0   -3   -3

0   3     3     0

from the columns of the resulted matrix, we can see that the vertices of the transformed triangle are:

(0, 0), (0, 3), (-3, 3), (-3, 0)