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. If the sum of the squares of two consecutive odd integers is 450, what is the largest of these two integers? Check Let the two consecutive odd integers be x and x + 2. Their squares can be represented as x^2 and (x + 2)^2. We have the following equation: x^2 + (x + 2)^2 = 450 Expanding and simplifying, we get: x^2 + x^2 + 4x + 4 = 450 2x^2 + 4x - 446 = 0 Now, we can factor the quadratic equation as (2x - 22)(x + 20) = 0, which gives us two possible values for x: x = 11 and x = -20. Since we want the largest integer, x = 11. Therefore, the largest of these two consecutive odd integers is x + 2 = 11 + 2 = 13. 2 / 5 2. The average age of a group of 6 students is 20 years old. If the oldest student is 25, what is the average age of the other 5 students? Check First, let's find the total age of all 6 students: Total age = average age * number of students = 20 * 6 = 120. Since the oldest student is 25 years old, we subtract this age from the total age: Total age of the other 5 students = 120 - 25 = 95 years. Now, we find the average age of the other 5 students: Average age = total age / number of students = 95 / 5 = 19 years. 3 / 5 3. The number of students in a math class is 30. If 5 students were added, the number of students would increase by what percent? Check First, find the total number of students after adding 5: 30 + 5 = 35 Now, find the increase in the number of students: 35 - 30 = 5 To find the percent increase, divide the increase by the original number of students and multiply by 100%: Percent increase = (5 / 30) * 100% Percent increase = 1/6 * 100% Percent increase ≈ 16.67% So, the number of students would increase by approximately 16.67%. 4 / 5 4. Given the function f(x) = 3x^2 + 2x - 5, find f(-2). Check We can find f(-2) by substituting -2 in for x in the function equation: f(-2) = 3(-2)^2 + 2(-2) - 5 f(-2) = 3(4) - 4 - 5 f(-2) = 12 - 4 - 5 f(-2) = 8 - 5 f(-2) = 3 So, f(-2) = 3. 5 / 5 5. If the slope of a line is -3/4 and the line passes through the point (6, 4), what are a and b in the equation of the line: ax+by = c? Check We can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. In this case, m = -3/4, x1 = 6, and y1 = 4. y - 4 = (-3/4)(x - 6) To avoid fractions, we can clear the fraction by multiplying both sides of the equation by 4: 4(y - 4) = -3(x - 6) 4y - 16 = -3x + 18 Now add 3x and 16 to both sides of the equation to put it in slope-intercept form: 3x + 4y = 34 The equation of the line is 3x + 4y = 34. Your score is 0% Restart Quiz