The difference of the square of a number and 24 is equal to 5 times that number. Find the negative solution.

the "negative solution" is -3

Step-by-step explanation:

Represent the number by n.

Then n^2 - 24 = 5n

We rewrite this in standard quadratic form:

n^2 - 5n - 24 = 0

This factors as follows;  (n + 3)(n - 8) = 0

The roots are n = -3 and n = 8.  Thus, the "negative solution" is -3

side xy = 10

sin(x) = 4/5

cos(x) = 3/5

tan(x) = 4/3

step-by-step explanation:

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2