1. Equations & Inequalities

Which equation has two real, distinct solutions? Do not actually solve.

A. (3x-4)² = -9 B. (4-7x)² = 0 C. (5x-9)(5x-9) = 0 D. (7x+4)² = 11

Solve each equation in Exercises 15–34 by the square root property. $(x+3{)}^2=-16$

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) 3x² + 5x + 2 = 0

Solve each equation using the quadratic formula. (2/3)x² + (1/4)x = 3

Match the equation in Column I with its solution(s) in Column II. x² = -25

Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. -8x² + 10x = 7

Answer each question. Find the values of a, b, and c for which the quadratic equation. $a{x}^2+bx+c=0$ has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.)

$4,5$

Height of a Projected Ball An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 30 ft per sec. The height s of the ball in feet is given by the equations=-2.7t²+30t+6.5,where t is the number of seconds after the ball was thrown. (a) After how many seconds is the ball 12 ft above the moon's surface? Round to the nearest hundredth. (b) How many seconds will it take for the ball to hit the moon's surface? Round to the nearest hundredth.

Solve each equation using the square root property. (x - 4)² = -5

Dimensions of a Right Triangle The shortest side of a right triangle is 7 in. shorter than the middle side, while the longest side (the hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides.

Height of a Projectile A projectile is launched from ground level with an initial velocity of v₀ feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=-16t²+v₀t. In each exercise, find the time(s) that the projectile will (a) reach a height of 80 ft and (b) return to the ground for the given value of v₀. Round answers to the nearest hundredth if necessary. v₀=32

Solve each equation using completing the square. 3x² + 2x = 5

Solve the given quadratic equation using the square root property. $\(\left\)(x-\(\frac\)12\(\right\))^2-5=0$

Solve each equation. -2x² +11x = -21

Match the equation in Column I with its solution(s) in Column II. x² - 5 = 0