Appearance
question:The tornado picked up the Smith's car and transported it 200 feet in the air before dropping it into the neighbors' pool. Also in the pool was a lawn chair that had been blown twice as far as the car had been transported. And the pool also contained a birdhouse that had flown through the air three times farther than the lawn chair had been blown. How far, in feet, far had the birdhouse flown?
answer:The car was transported 200 feet in the air by the tornado. The lawn chair was blown twice as far as the car, so it was blown 200 x 2 = 400 feet. The birdhouse was flown three times farther than the lawn chair, so it was flown 400 x 3 = 1200 feet. Therefore, the birdhouse had flown 1200 feet. 1200 The answer is: 1200
question:What is the product of the solutions to the equation |y| = 2(|y| - 1)?
answer:We start by simplifying the equation |y| = 2(|y| - 1). If y ge 0, then |y| = y, so the equation becomes y = 2(y-1). Solving for y, we find y = 2. If y < 0, then |y| = -y, so the equation becomes -y = 2(-y-1). Solving for y, we find y = -2. So the solutions to the equation are y = 2 and y = -2. The product of the solutions is 2 cdot -2 = boxed{-4}. The answer is: -4
question:Francis and Kiera had breakfast at a cafe. Muffins cost 2 each, and fruit cups cost 3 each. Francis had 2 muffins and 2 fruit cups. Kiera had 2 muffins and 1 fruit cup. How much did their breakfast cost?
answer:Francis had 2 muffins, so that's 2 x 2 = 4 for muffins. Francis also had 2 fruit cups, so that's 2 x 3 = 6 for fruit cups. In total, Francis's breakfast cost 4 + 6 = 10. Kiera had 2 muffins, so that's 2 x 2 = 4 for muffins. Kiera also had 1 fruit cup, so that's 1 x 3 = 3 for a fruit cup. In total, Kiera's breakfast cost 4 + 3 = 7. Therefore, their breakfast together cost 10 + 7 = 17. 17 The answer is: 17
question:What is the solution for x in the equation log_2 x + log_4 x = 6?
answer:Since log_4 x = frac{log_2 x}{log_2 4} = frac{log_2 x}{2}, we can rewrite the equation as log_2 x + frac{log_2 x}{2} = 6. Combining the logs, we get frac{3log_2 x}{2} = 6. Dividing both sides by frac{3}{2} gives log_2 x = 4. Exponentiating both sides with base 2, we get x = 2^4 = boxed{16}. The answer is: 16