W= width
l= length= 2w-3
Area= length * width
A= lw
substitute l=2w-3 for l
54= (2w-3)(w)
54= 2w^2 - 3w
subtract 54 from both sides
0= 2w^2 - 3w - 54
factor the polynomial
0= (2w + 9)(w - 6)
Set each set of parentheses equal
to 0 and solve for width.
0=2w+9
-9=2w
-4.5= w NEGATIVE VALUE
0=w-6
6 cm=w
-4.5 is not the answer because it has a negative value. You cannot have a negative side of a photograph. So substitute 6 in to find length.
length= 2w-3
l= 2(6)-3
l= 12-3
l= 9 cm
CHECK:
w= 6cm
l= 9cm
Area= length * width
54= 6*9
54= 54
ANSWER: width= 6cm; length= 9cm
Hope this helps! :)
they could only be changed under certain circumstances
I believe the answer is cos^2 theta. Sec^2 theta on the right side of the equation is the inverse of Cos^2 theta, so multiplying the two together will get you 1. Cos^2 theta * Tan^2 theta = Sin^2 theta, and Cos^2 theta * 1 = Cos^2 theta. This all leads to the third and last step in the picture above.
Earl is incorrect
let x be the number of discount tickets sold
then the number of regular tickets sold is 6x
the total tickets sold is 1456, thus
x + 6x = 1456
7x = 1456 ( divide both sides by 7 )
x = 208
number of discount tickets sold = 208
≠ 208
but 
= 208
Earl is incorrect , dividing by 7 gives the amount sold
