Regina has started making baby quilts to sell at a craft fair. the inside of each quilt will measure four feet by five feet and will be surrounded by a border of uniform width. she wants each quilt to have a total area (including the border) of 30 square feet. find the equivalent equations to find the width of the border given that the border is x. select all that apply.

1: (4+x)(5+x)=30
2: (4+2x)(5+2x)=30
3: 4x^2 + 20 = 30
4: 4x^2 +18x+20=30
5: (5+x)(4+x)=30
6: (x+4)(x+5)=30

Two positive integers are 3 units apart on a number line. their product is 108. which equation can be used to solve for m, the greater integer? m(m – 3) = 108 m(m + 3) = 108 (m + 3)(m – 3) = 108 (m – 12)(m – 9) = 108

What is the area of the trapezoid shown ?

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. which conclusion can be made from the given information? the volume of the triangular prism is half the volume of the cylinder. the volume of the triangular prism is twice the volume of the cylinder. the volume of the triangular prism is equal to the volume of the cylinder. the volume of the triangular prism is not equal to the volume of the cylinder.