Solve Systems Approximately Worksheets Grade 9

1. Use technology to solve the system: y = 2x² - 3x + 1 and y = 4x - 5. Find the approximate solution where x > 2.
2. √(x² + 6x + 9) = 5
3. Noah is analyzing the profit from his online tutoring business. The monthly profit P(x) in hundreds of dollars is modeled by the quadratic function P(x) = -3x² + 36x - 81, where x is the number of students enrolled. Due to a new marketing campaign, the profit is also affected by a fixed monthly cost of 16 hundred dollars, represented by the horizontal line y = 16. Using graphing technology, find the approximate number of students enrolled when the profit first exceeds 16 hundred dollars. Round your answer to the nearest whole number.

…and 4 more problems

1. Matiu is studying the flight path of a toy rocket. The rocket's height above the ground (in meters) is modeled by the quadratic function h(t) = -4t² + 32t + 8, where t is time in seconds after launch. Meanwhile, a bird is flying at a constant height modeled by the linear function b(t) = 2t + 26. Using graphing technology, find the approximate time(s) when the rocket and the bird are at the same height. Round your answers to one decimal place.
2. Use technology to solve the system: y = x³ - 9x + 4 and y = 2x² - 7
3. Olivia is studying the spread of an invasive insect species in a forest. The area infested (in square kilometers) after t months is modeled by the exponential function I(t) = 9 × (1.7)^t. The forest service is deploying a pesticide treatment that reduces the infested area (in square kilometers) according to the quadratic function T(t) = -3t² + 27t + 15. Using graphing technology, determine approximately how many months (rounded to the nearest tenth) it will take for the infested area to equal the treated area.

…and 3 more problems

1. Use technology to solve the system: y = x³ - 3x + 1 and y = 2x - 5. Find the approximate solution (x, y) where x is positive.
2. Use technology to solve the system: y = x³ - 7x² + 14x - 8 and y = 3ˣ - 9. Find the approximate intersection point where x > 4.
3. Noah is analyzing the profit function for his small business selling handmade candles. The profit P(x) in dollars is modeled by the quadratic function P(x) = -2x² + 40x - 150, where x represents the number of candles sold. How many candles must Noah sell to maximize his profit?

…and 6 more problems