Chapter 10

For the following problems, solve the equations, if possible. $$ 4 y^{2}=-4 y-2 $$

For the following problems, solve the equations, if possible. $$ 9 y^{2}=9 y+18 $$

For the following problems, find the solution. A study of the air quality in a particular city by an environmental group suggests that \(t\) years from now the level of carbon monoxide, in parts per million, in the air will be \(A=0.8 t^{2}+0.5 t+3.3\). (a) What is the level, in parts per million, of carbon monoxide in the air now? (b) How many years from now will the carbon monoxide level be at 6 parts per million?

Simplify \(\left(x^{4} y^{3}\right)^{2}\left(x y^{2}\right)^{4}\).

For the following problems, find the solution. A contractor is to pour a concrete walkway around a community garden that is 15 feet wide and 50 feet long. The area of the walkway and garden is to be 924 square feet and of uniform width. How wide should the contractor make it?

Write \(\left(x^{-2} y^{3} w^{4}\right)^{-2}\) so that only positive exponents appear.

For the following problems, find the solution. A ball thrown vertically into the air has the equation of motion \(h=144+48 t-16 t^{2}\) (a) How high is the ball at \(t=0 ?\) (b) How high is the ball at \(t=1 ?\) (c) When does the ball hit the ground?

Simplify \(\frac{\frac{1}{a}+\frac{1}{h}}{\frac{1}{a}-\frac{1}{b}}\).

For the following problems, find the solution. The length of a rectangle is 5 feet longer than three times its width. Find the dimensions if the area is to be 138 square feet.

For the following problems, find the solution. The area of a triangle is 28 square centimeters. The base is \(3 \mathrm{~cm}\) longer than the height. Find both the length of the base and the height.

Solve \((x+4)(3 x+1)=0\)

For the following problems, find the solution. The product of two consecutive integers is \(210 .\) Find them.

For the following problems, find the solution. The product of two consecutive negative integers is \(272 .\) Find them.

For the following problems, find the solution. A box with no top and a square base is to be made by cutting out 3 -inch squares from each corner and folding up the sides of a piece of cardboard. The volume of the box is to be 25 cubic inches. What size should the piece of cardboard be?