In Exercises 10–12, solve each inequality for x and write the solution in interval notation.
2x−5<11
−3x+4>−5
−3<2x−3<5
5≤1−2x≤7
|2x−1|≤7
|2x−3|≥5
Show that the triangle with vertices A(5,−2),B(6,5), and C(2, 2) is isosceles.
Sketch the graph of 4x2−9y2=0. [Hint:4x2−9y2=(2x+3y)(2x−3y).]
Show that the points (−3,−1),(2,4),(5,3), and (6, 2) lie on a circle with center (2,−1).
Find the center and radius of the circle with equation x2+y2−6x+4y+9=0.
In Exercises 17–22, find the slope–intercept form of the equation of the line satisfying the given condition.
Slope=−3;y-intercept 5
Slope=2;x-intercept 4
The line is perpendicular to y=2x+3 and passes through (2,−1).
The line is parallel to y=2x+3 and passes through (2,−1).
The line is the perpendicular bisector of the line segment joining (3,−1) and (5, 7).
The line is parallel to x=−2 and passes through (5, 7).
Find x, assuming that the line through (x, 5) and (5, 11) is parallel to a line with slope 2.
Find x, assuming that the line through (x, 3) and (3, 7) is perpendicular to a line with slope 12.
In Exercises 25–28, graph each equation.
12x=4y−6
x2−2x+y2−4y−4=0
f(x)=x+2−−−−−√+3
f(x)=−(x−1)2+4
Ms. Gutiérrez bought some used books for $1650. She kept 16 of the books and sold the rest at a profit of $10 each. If she recovered her original $1650 from this sale, how many books did she purchase initially?
The monthly note on a car that was leased for two years was $250 less than the monthly note on a car that was leased for a year and a half. The total expense for the two leases was $21,000. Find the monthly note for each lease.
Let f(x)=x+1−−−−−√−3.
Find the domain of f.
Find the intercepts.
Find f(−1).
Solve f(x)>0.
Let f(x)={−xx2if x<0if x≥0.
Find f(−2),f(0), and f(2).
Find the intervals on which f is increasing, decreasing, or constant.