Chapter 1

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree. $$\sqrt{2} x-\sqrt{3}$$

Find the domain of the expression. $$\frac{\sqrt{2 x}}{x+1}$$

Write an equation that expresses the statement. \(A\) is proportional to the square of \(t\) and inversely proportional to the cube of \(x.\)

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$-4 x \geq 10$$

Find the slope of the line through \(P\) and \(Q .\) $$P(-1,-4), Q(6,0)$$

Determine an appropriate viewing rectangle for the equation, and use it to draw the graph. $$y=-100 x^{2}$$

Express the given quantity in terms of the indicated variable. The total rent paid for an apartment if the rent is \(\$ 795\) a month; \(n=\) number of months.

The given equation is either linear or equivalent to a linear equation. Solve the equation. $$5 x-3=4$$

State the property of real numbers being used. $$(x+a)(x+b)=(x+a) x+(x+a) b$$

Find the sum, difference, or product. $$(12 x-7)-(5 x-12)$$

Simplify the rational expression. $$\frac{3(x+2)(x-1)}{6(x-1)^{2}}$$

Write an equation that expresses the statement. \(V\) is jointly proportional to \(l, w,\) and \(h.\)

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$2 x-5>3$$

A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$(0,8),(6,16)$$

Express the given quantity in terms of the indicated variable. The area (in \(\mathrm{ft}^{2}\) ) of a rectangle that is three times as long as it is wide; \(w=\) width of the rectangle (in \(\mathrm{ft}\) ).

The given equation is either linear or equivalent to a linear equation. Solve the equation. $$\frac{1}{2} x-8=1$$

State the property of real numbers being used. $$2 x(3+y)=(3+y) 2 x$$

Find the sum, difference, or product. $$(5-3 x)+(2 x-8)$$

Simplify the rational expression. $$\frac{4\left(x^{2}-1\right)}{12(x+2)(x-1)}$$

Write an equation that expresses the statement. \(S\) is jointly proportional to the squares of \(r\) and \(\theta\).

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$3 x+11<5$$

(a) Sketch lines through \((0,0)\) with slopes \(1,0, \frac{1}{2}, 2\) and \(-1\) (b) Sketch lines through \((0,0)\) with slopes \(\frac{1}{3}, \frac{1}{2},-\frac{1}{3},\) and 3.

Determine an appropriate viewing rectangle for the equation, and use it to draw the graph. $$y=0.3 x^{2}+1.7 x-3$$

A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$(-2,5),(10,0)$$

Express the given quantity in terms of the indicated variable. The perimeter (in \(\mathrm{cm}\) ) of a rectangle that is \(5 \mathrm{cm}\) longer than it is wide; \(w=\) width of the rectangle (in cm )

The given equation is either linear or equivalent to a linear equation. Solve the equation. $$3+\frac{1}{3} x=5$$

State the property of real numbers being used. $$7(a+b+c)=7(a+b)+7 c$$

Find the sum, difference, or product. $$\left(3 x^{2}+x+1\right)+\left(2 x^{2}-3 x-5\right)$$

Simplify the rational expression. $$\frac{x-2}{x^{2}-4}$$

Write an equation that expresses the statement. \(R\) is proportional to \(i\) and inversely proportional to \(P\) and \(t\).

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$7-x \geq 5$$

A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$(-3,-6),(4,18)$$

Express the given quantity in terms of the indicated variable. The distance (in mi) that a car travels in 45 min; \(s=\) speed of the car (in \(\mathrm{mi} / \mathrm{h}\) ).

The given equation is either linear or equivalent to a linear equation. Solve the equation. $$-7 w=15-2 w$$

Evaluate each expression. (a) \(-3^{2}\) (b) \((-3)^{2}\) (c) \(\left(\frac{1}{3}\right)^{4}(-3)^{2}\)

Rewrite the expression using the given property of real numbers. Commutative Property of addition, \(x+3=\) ______

Find the sum, difference, or product. $$\left(3 x^{2}+x+1\right)-\left(2 x^{2}-3 x-5\right)$$

Simplify the rational expression. $$\frac{x^{2}-x-2}{x^{2}-1}$$

Write an equation that expresses the statement. \(A\) is jointly proportional to the square roots of \(x\) and \(y\).

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$5-3 x \leq-16$$

A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$(-1,-1),(9,9)$$

Express the given quantity in terms of the indicated variable. The time (in hours) it takes to travel a given distance at \(55 \mathrm{mi} / \mathrm{h} ; d=\) given distance (in \(\mathrm{mi}\) )

The given equation is either linear or equivalent to a linear equation. Solve the equation. $$5 t-13=12-5 t$$

Evaluate each expression. (a) \(5^{4} \cdot 5^{-2}\) (b) \(\frac{10^{7}}{10^{4}}\) (c) \(\frac{3}{3^{-2}}\)

Rewrite the expression using the given property of real numbers. Associative Property of multiplication, \(7(3 x)=\) _____

Find the sum, difference, or product. $$\left(x^{3}+6 x^{2}-4 x+7\right)-\left(3 x^{2}+2 x-4\right)$$

Simplify the rational expression. $$\frac{x^{2}+6 x+8}{x^{2}+5 x+4}$$

Express the statement as an equation. Use the given information to find the constant of proportionality. \(y\) is directly proportional to \(x .\) If \(x=6,\) then \(y=42\).

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$2 x+1<0$$

A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$(6,-2),(-6,2)$$