Theo started to solve the quadratic equation (x + 2)2 – 9 = –5. he added 9 to both sides and the resulting equation was (x + 2)2 = 4. next, he took the square root of each side. which was the resulting equation of that step?

There is a line with slope 1/a going through the point (a, a²). find the equation of the line perpendicular to this line at this point. (don’t let this problem intimidate you! solve the problem as you would if i’d given you specific values. just use variables instead.)

In a certain pentagon, the interior angles are a, b,c, d,e where a, b,c, d,e are integers strictly less than 180. ("strictly less than 180" means they are "less than and not equal to" 180.) if the median of the interior angles is 61 and there is only one mode, then what are the degree measures of all five angles?

Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.