Formula Rearrangement Worksheets Grade 9

1. Solve for t: d = 4t² + 8t
2. Matiu is a conservation biologist studying a population of endangered birds. The population size, P, after t years can be modeled by the formula P = P0 * e^(kt), where P0 is the initial population and k is the growth rate constant. Matiu observes that an initial population of 15 birds grows to 45 birds in 6 years. Write an equation that represents this situation, and solve for the growth rate constant k, expressing your answer in exact form using natural logarithms.
3. Solve for x: 2(x - 4)² - 72 = 0

…and 5 more problems

1. Aisha is designing a triangular garden with sides that form a right triangle. The hypotenuse is 5 meters longer than the longer leg, and the longer leg is 2 meters longer than the shorter leg. Write an equation in terms of the shorter leg length x that represents this situation using the Pythagorean theorem, then solve for x to find the length of the shorter leg.
2. The formula for the surface area of a cylinder is S = 2πr² + 2πrh. Solve for h.
3. Tane is designing a rectangular solar panel for a school project. The length of the panel is 9 centimeters more than three times its width. If the area of the panel is 210 square centimeters, write an equation in terms of the width w that represents this situation, then solve for the width of Tane's solar panel.

…and 5 more problems

1. Solve for r: S = 2πr(r + h)
2. Liam is designing a rectangular garden with an area of 120 square meters. The length of the garden is 4 meters more than its width. Write an equation in terms of the width w that represents this situation, then solve for w to find the garden's dimensions.
3. Aisha is designing a triangular support structure for a bridge. The area of the triangular section is 84 square meters, and the base is 7 meters longer than the height. Write an equation in terms of the height h that represents this situation, then solve for the height of the triangular section.

…and 5 more problems