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- Solve each equation using completing the square. See Examples 3 and 4. 2x^2 + x = 10
Problem 43
- (Modeling)Solve each problem. See Example 3.Height of a ProjectileA projectile is launched from ground level with an initial velocity of v_0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=-16t^2+v_0t. 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 v_0. Round answers to the nearest hun-dredth if necessary. v_0=96
Problem 43
- Solve each equation. (2x+1)(x-4) = x
Problem 43
Problem 43
Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. 2x2-9x≤18
Problem 43a
Write each number in standard form a+bi. 10+ √-200 / 5
Problem 43b
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)
Problem 44
- Solve each equation or inequality. |8 - 3x| - 3 = -2
Problem 44
- Solve each equation using completing the square. See Examples 3 and 4. 3x^2 + 2x = 5
Problem 44
Problem 44
Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. 3x2+x≤4
- Solve each equation or inequality. |6 - 2x | + 1 = 3
Problem 45
Problem 45
Solve each equation. See Examples 4–6. x - √(2x+3) = 0
- Solve each equation using completing the square. See Examples 3 and 4. -2x^2 + 4x + 3 = 0
Problem 45
- Solve each equation. x²- √5x -1 = 0
Problem 45
Problem 45a
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)
Problem 46
- Solve each equation or inequality. | 4 - 4x | + 2 = 4
Problem 46
- Solve each equation. (x+4)(x+2) = 2x
Problem 46
- Solve each equation using completing the square. See Examples 3 and 4. -3x^2 + 6x + 5 = 0
Problem 46
- Solve each equation or inequality. | 3x + 1 | - 1 < 2
Problem 47
Problem 47
Solve each equation. See Examples 4–6. √(3x+7) = 3x+5
- 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
Problem 47
Problem 47
Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x(x-1)≤6
- For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. y=(1/2)x-2
Problem 47
Problem 47a
Find each sum or difference. Write answers in standard form. (3+2i) + (9+3i)
- Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. z = x-μ/σ, for x (standardized value)
Problem 48
- Solve each equation or inequality. | 5x + 2 | - 2 < 3
Problem 48
Problem 48
Solve each equation. See Examples 4–6. √(4x+13) = 2x-1
- Solve each equation using completing the square. See Examples 3 and 4. 3x^2 - 9x + 7 = 0
Problem 48
Problem 48
Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x(x+1)<12