Math Quiz - Grid questions Report a question What's wrong with this question? You cannot submit an empty report. Please add some details. Math Quiz - Grid questions 1 / 5 1. A quadratic function is given by f(x) = 2x^2 - 5x + 3. Find the x-coordinate of the vertex of the parabola. Check The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In general, the vertex coordinates are given by (h, k), where h = -b / (2a) and k = f(h). For the given quadratic function f(x) = 2x^2 - 5x + 3, the coefficients are a = 2 and b = -5. Calculate h: h = -(-5) / (2 * 2) = 5 / 4 Now, find k by substituting h back into the function: k = f(5/4) = 2(5/4)^2 - 5(5/4) + 3 k = 25/8 - 25/4 + 3 k = 25/8 - 50/8 + 24/8 k = -1/8 Therefore, the vertex of the parabola is (5/4, -1/8), and the x-coordinate of the vertex is 5/4. 2 / 5 2. A mixture of 20% alcohol solution is combined with a 40% alcohol solution to make a final mixture of 30% alcohol. If the final mixture is 10 liters, how many liters of the 20% alcohol solution were used? Check Let x be the number of liters of the 20% alcohol solution used. Then, (10 - x) liters of the 40% alcohol solution were used. Writing the equation for the mixture, we get: 0.20x + 0.40(10 - x) = 0.30 * 10 Simplifying, we have: 0.20x + 4 - 0.40x = 3 Combining like terms, we have: -0.20x = -1 Dividing both sides by -0.20, we get: x = 5 So, 5 liters of the 20% alcohol solution were used. 3 / 5 3. The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. If the area of a triangle is 48 square units and the base is 12 units, what is the height? Check Using the formula A = (1/2)bh, we can substitute the given values and solve for h: 48 = (1/2)(12)(h) Dividing both sides by 6, we get: 8 = h So, the height of the triangle is 8 units. 4 / 5 4. A train travels 360 miles in 6 hours. During this trip, it stops at a station for 30 minutes. What is its average speed in miles per hour during the entire trip, including the stop? Check The train travels 360 miles in 6 hours, but during this time, it stops for 30 minutes or 0.5 hours. So, the total time spent traveling, including the stop, is 6 hours + 0.5 hours = 6.5 hours. To find the average speed, we divide the total distance by the total time: Average Speed = 360 miles / 6.5 hours ≈ 55.38 miles per hour Thus, the average speed of the train during the entire trip, including the stop, is approximately 55.38 mph. 5 / 5 5. A factory produces x items per day at a cost of $5 each. The daily profit is $3 for each item produced. How much profit will the factory make after producing x items for 15 days (in terms of x such as ax, etc)? Check The profit made for each item is $3, so the total daily profit made from x items is 3x. Since the factory operates for 15 days, the total profit after 15 days is: Total Profit = 15 * daily profit = 15 * 3x = 45x Therefore, the factory will make a profit of 45x dollars after 15 days. Your score is 0% Restart Quiz