Chapter 1

Find the equation of the line through the given points. $$(4,3) and (2,-1)$$

The net revenues of Pepsico were \(\$ 26,971\) million in 2003 and \(\$ 32,562\) million in 2005 . Estimate the net revenue in 2004 .

Use the quadratic formula to solve the equation. $$x^{2}+2 x-1=0$$

Find the equation of the line through the given points. $$(6 / 5,3 / 5) and (1 / 5,3)$$

Determine whether the point is on the graph of the given equation. $$(2,-1) ; 3 x-y-5=0$$

Use the quadratic formula to solve the equation. $$x^{2}+6 x+7=0$$

Find the equation of the line through the given points. $$(6,7) and (6,15)$$

Determine whether the point is on the graph of the given equation. $$(2,-1) ; x^{2}+y^{2}-6 x+8 y=-15$$

Use the quadratic formula to solve the equation. $$x^{2}+4 x-3=0$$

Determine whether the point is on the graph of the given equation. $$(6,2) ; 3 y+x=12$$

Draw a picture on the number line of the given interval. $$(0,8]$$

Use the quadratic formula to solve the equation. $$x^{2}+6=2 x$$

Graph the equation. Label all intercepts. $$2 x-3 y=12$$

Determine whether the point is on the graph of the given equation. $$(1,-2) ; 3 x+y=12$$

Use the quadratic formula to solve the equation. $$x^{2}+11=6 x$$

Graph the equation. Label all intercepts. $$2 y-x=2$$

Determine whether the point is on the graph of the given equation. $$(1,-4) ;(x-2)^{2}+(y+5)^{2}=4$$

Draw a picture on the number line of the given interval. $$[-2,1]$$

Use the quadratic formula to solve the equation. $$4 x^{2}+4 x=7$$

Graph the equation. Label all intercepts. $$4 x+5 y=-10$$

Determine whether the point is on the graph of the given equation. $$(1,-1) ; \frac{x^{2}}{2}+\frac{y^{2}}{3}=1$$

Draw a picture on the number line of the given interval. $$(-1,1)$$

Use the quadratic formula to solve the equation. $$4 x^{2}-4 x=11$$

Graph the equation. Label all intercepts. $$3 x-2 y=0$

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$x^{2}-6 x+y+5=0$$ CAN'T COPY THE GRAPH

Draw a picture on the number line of the given interval. $$(-\infty, 0]$$

Use the quadratic formula to solve the equation. $$4 x^{2}-8 x+1=0$$

Graph the equation. Label all intercepts. $$2 x+6 y=0$$

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$x^{2}-2 x y+3 y^{2}=1$$ CAN'T COPY THE GRAPH

Draw a picture on the number line of the given interval. $$[-2,7)$$

Use the quadratic formula to solve the equation. $$2 t^{2}+4 t+1=0$$

Determine whether the line through \(P\) and \(Q\) is parallel or perpendicular to the line through \(R\) and S or neither.\(P=(2,5), Q=(-1,-1)\) and \(R=(4,2), S=(6,1)\)

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$(x-2)^{2}+y^{2}=9$$

Use interval notation to denote the set of all real numbers \(x\) that satisfy the given inequality. $$5 \leq x \leq 10$$

Solve the equation by any method. $$x^{2}+9 x+18=0$$

Determine whether the line through \(P\) and \(Q\) is parallel or perpendicular to the line through \(P=(0,3 / 2), Q=(1,1)\) and \(R=(2,7), S=(3,9)\)

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$(x+1)^{2}+(y-2)^{2}=4$$

Use interval notation to denote the set of all real numbers \(x\) that satisfy the given inequality. $$-2 \leq x \leq 7$$

Solve the equation by any method. $$3 t^{2}-11 t-20=0$$

Determine whether the line through \(P\) and \(Q\) is parallel or perpendicular to the line through \(P=(-3,1 / 3), Q=(1,-1)\) and \(R=(2,0), S=(4,-2 / 3)\)

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$9 x^{2}+24 x y+16 y^{2}+90 x-128 y=0$$

Use interval notation to denote the set of all real numbers \(x\) that satisfy the given inequality. $$-3

Solve the equation by any method. $$4 x(x+1)=1$$

Determine whether the line through \(P\) and \(Q\) is parallel or perpendicular to the line through \(P=(3,3), Q=(-3,-1)\) and \(R=(2,-2), S=(4,-5)\)

Use interval notation to denote the set of all real numbers \(x\) that satisfy the given inequality. $$7

Solve the equation by any method. $$25 y^{2}=20 y+1$$

Determine whether the lines whose equations are given are parallel, perpendicular, or neither. \(2 x+y-2=0 \quad\) and \(\quad 4 x+2 y+18=0\)

The graph on the next page, which is based on data from the Actuarial Society of South Africa and assumes no changes in current behavior, shows the projected new cases of AIDS in South Africa (in millions) in coming years \((x=0\) corresponds to 2000 ). (a) Estimate the number of new cases in 2010 . (b) Estimate the year in which the largest number of new cases will occur. About how many new cases will there be in that year? (c) In what years will the number of new cases be below \(7,000,000 ?\) CAN'T COPY THE GRAPH

Use interval notation to denote the set of all real numbers \(x\) that satisfy the given inequality. $$x \geq-9$$

Solve the equation by any method. $$2 x^{2}=7 x+15$$