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Heart of Algebra
Solve for x: 2x + 3 = 11 Solution: Subtracting 3 from both sides, we get: 2x = 8 Dividing both sides by 2, we get: x = 4 Answer: x = 4 . Problem Solving and Data Analysis A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer rents a car and drives it 150 miles, how much will they be charged? Solution: The total cost of renting the car is the sum of the flat fee and the cost per mile driven. The cost per mile is $0.20, so the total cost is: $30 + $0.20 * 150 = $30 + $30 = $60 Answer: $60 . Passport to Advanced Math Solve for x: 2x^2 - 5x + 3 = 0 Solution: We can solve this quadratic equation by factoring. We need to find two numbers that multiply to 2*3=6 and add to -5. These numbers are -2 and -3. We can then write the equation as: 2x^2 - 5x + 3 = (2x - 3)(x - 1) = 0 Setting each factor equal to zero and solving for x, we get: 2x - 3 = 0 or x - 1 = 0 2x = 3 or x = 1 x = 3/2 or x = 1 Answer: x = 3/2 or x = 1 . Additional Topics What is the area of a circle with radius 5? Solution: The formula for the area of a circle is A = πr^2, where r is the radius. Plugging in r = 5, we get: A = π * 5^2 = 25π Answer: 25π |