Solve each inequality. Give the solution set in interval notation. | 5/3 - (1/2) x | > 2/9

Solve each inequality. Give the solution set in interval notation. | 0.01x + 1 | < 0.01

Solve each equation. -2x² +11x = -21

Solve each equation using completing the square. x² - 2x - 2 = 0

Length of a Walkway A nature conservancy group decides to construct a raised wooden walkway through a wetland area. To enclose the most interesting part of the wetlands, the walkway will have the shape of a right triangle with one leg 700 yd longer than the other and the hypotenuse 100 yd longer than the longer leg. Find the total length of the walkway.

Solve each quadratic inequality. Give the solution set in interval notation. x²-x-6>0

Write each number in standard form a+bi. -6-√-24 / 2

Solve each quadratic inequality. Give the solution set in interval notation. x²-7x+10>0

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. P=2l+2w,for w (perimeter of a rectangle)

Explain why the equation | x | = √x² has infinitely many solutions.

Solve each equation or inequality. |4x + 3| - 2 = -1

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=96

Solve each equation using completing the square. 2x² + x = 10

Solve each quadratic inequality. Give the solution set in interval notation. 2x²-9x≤18

Solve each equation. (2x+1)(x-4) = x

Write each number in standard form a+bi. 10+ √-200 / 5

Solve each problem. See Examples 5 and 6. Formaldehyde is an indoor air pollutant formerly found in plywood, foam insulation, and carpeting. When concentrations in the air reach 33 micrograms per cubic foot (μg/ft³), eye irritation can occur. One square foot of new plywood could emit 140 μg per hr. (Data from A. Hines, Indoor Air Quality & Control.) A room has 100 ft² of new plywood flooring. Find a linear equation F that computes the amount of formaldehyde, in micrograms, emitted in x hours.

Solve each problem. See Examples 5 and 6. Formaldehyde is an indoor air pollutant formerly found in plywood, foam insulation, and carpeting. When concentrations in the air reach 33 micrograms per cubic foot (μg/ft^3), eye irritation can occur. One square foot of new plywood could emit 140 μg per hr. (Data from A. Hines, Indoor Air Quality & Control.) The room contains 800 ft^3 of air and has no ventilation. Determine how long it would take for concentrations to reach 33 μg/ft^3. (Round to the nearest tenth.)

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. F = GMm/r², for m (force of gravity)

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

Solve each quadratic inequality. Give the solution set in interval notation. 3x²+x≤4

Solve each equation or inequality. |8 - 3x| - 3 = -2

Solve each equation. x - √(2x+3) = 0

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 or inequality. |6 - 2x | + 1 = 3

Solve each equation. x²- √(5x) -1 = 0

Solve each equation using completing the square. -2x² + 4x + 3 = 0

Write each number in standard form a+bi. -3+ √-18 / 24

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. s = 1/2gt², for g (distance traveled by a falling object)

Solve each equation using completing the square. -3x² + 6x + 5 = 0