The area of the conference table in Mr. Nathan’s office must be no more than 175 ft2. If the length of the table is 18 ft more than the width, x, which interval can be the possible widths?

Answer 1

x(x+18) <= 175
x^2+18x-175 <= 0
(x+25)(x-7) <= 0
So, -25 <= x <= 7
Or, for real-world tables,

0 <= x <= 7
There is probably a minimum positive width for a useful table.

Answer 2

The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle

Answer 3

A small rock falling from the top of a 124-ft-tall building with an initial downward velocity of –30 ft/sec is modeled by the equation h(t) = –16t2 – 30t + 124, where t is the time in seconds. For which interval of time does the rock remain in the air?

Answer 4

boy what the hell boy

Answer 5

pop