91Ó°ÊÓ

Graph each line by hand. Give the \(x\)- and y-intercepts. \(x+y=4\)

Exercises 27 and 28 involve octane rating of gasoline, a measure of its antiknock qualities. In one measure of octane, a standard fuel is made with only two ingredients: heptane and isooctane. For this type of fuel, the octane rating is the percent of isooctane. An actual gasoline blend is then compared with a standard fuel. For example, a gasoline with an octane rating of 98 has the same antiknock properties as a standard fuel that is \(98 \%\) isooctane. How many gallons of 92-octane and 98 -octane gasoline should be mixed together to provide 120 gallons of 96 -octane gasoline?

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$\frac{x-2}{4}+\frac{x+1}{2}=1$$

Solve each problem. Women against the Men For the men's Olympic 100-meter freestyle swimming event, winning times in seconds during year \(x\) can be approximated by the formula \(F(x)=-\frac{5}{44} x+276.18,\) where \(1948 \leq x \leq 2008\) (Assume that \(x\) is a multiple of 4 because the Olympics occur every 4 years.) (a) Evaluate \(F(2008)\) and interpret the result. (b) In 2008 the women's Olympic winning time for the 100 -meter freestyle was about 53 seconds. Determine the years when this time would have beaten or tied the men's winning times. (IMAGE CAN'T COPY)

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(0,5)$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(4,1),(3,-5),(-2,3),(3,7)\\}$$

Graph each line by hand. Give the \(x\)- and y-intercepts. \(3 x-y=6\)

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$\frac{1}{2}(x-3)=\frac{5}{12}+\frac{2}{3}(2 x-5)$$

Graph each line by hand. Give the \(x\)- and y-intercepts. \(2 x-3 y=6\)

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$\frac{7}{3}(2 x-1)=\frac{1}{5} x+\frac{2}{5}(4-3 x)$$