Write an expression for the perimeter of the triangle shown below: a triangle is shown with side lengths labeled 2.3x plus 14, 2x, and negative 0.2x plus 15. 4.1x + 29 4.1x − 29 4.5x + 29 4.5x − 29

Afurniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply

50 plz, given the system of equations, match the following items. x + 3 y = 5 x - 3 y = -1 a) x-determinant b) y-determinant c) system determinant match the following to the pictures below.

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =