Tutor profile: Aditya Y.

Solve nABC with C = 1078, B = 258, and b = 15.

First find the angle: A 5 1808 2 1078 2 258 5 488. By the law of sines, you can write} a sin 488 5} 15 sin 258 5} c sin 1078 . } a sin 488 5} 15 sin 258 Write two equations, each with one variable. } c sin 1078 5} 15 sin 258 a 5} 15 sin 488 sin 258 Solve for each variable. c 5} 15 sin 1078 sin 258 a ø 26.4 Use a calculator. c ø 33.9 c In nABC, A 5 488, a ø 26.4, and c ø 33.9.

Find the distance between the parallel lines
and m whose equations are y

1 3
x
3 and y

1 3
x
1 3
, respectively.

First, write an equation of a line p perpendicular to
and m. The slope of p is the opposite reciprocal of
1 3
, or 3. Use the y-intercept of line
, (0, 3), as one of the endpoints of the perpendicular segment. y y1 m(x x1) Point-slope form y (3) 3(x 0) x1 0, y1 3, m 3 y  3 3x Simplify. y 3x 3 Subtract 3 from each side Next, use a system of equations to determine the point of intersection of line m and p. m: y
1 3
x 
1 3
p: y 3x 3 The point of intersection is (1, 0). Then, use the Distance Formula to determine the distance between (0, 3) and (1, 0). d (x
2 x1)
2  (y
2 y1)
2 Distance Formula
(0 1)
2  (
3 0)
2 x2 = 0, x1 = 1, y2 = 3, y1 = 0 10
Simplify. The distance between the lines is 10
or about 3.16 units.

Solve x2 2 2x > 15 algebraically.

First, write and solve the equation obtained by replacing > with 5. x2 2 2x 5 15 Write equation that corresponds to original inequality. x2 2 2x 2 15 5 0 Write in standard form. (x 1 3)(x 2 5) 5 0 Factor. x 5 23 or x 5 5 Zero product property The numbers 23 and 5 are the critical x-values of the inequality x2 2 2x > 15. Plot 23 and 5 on a number line, using open dots because the values do not satisfy the inequality. The critical x-values partition the number line into three intervals. Test an x-value in each interval to see if it satisfies the inequality