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The expression 4×2 + 19x + 5 is a quadratic equation in the standard form ax2 + bx + c, where: a = 4 b = 19 c = 5 To determine the properties of this quadratic equation, we can analyze its coefficients: 1. Parabola Orientation: Since the coefficient of x2 (which is 4) is … Read more

To solve the equation a² = 4, we will take the following steps: Understand the Equation: The equation states that a squared is equal to 4. We need to find the values of a that satisfy this equation. Isolate the Variable: To find a, we can take the square root of both sides of the … Read more

To find the vertex of the quadratic function f(x) = 3x² + 6x + 3, we can use the formula for the vertex of a parabola given in the standard form f(x) = ax² + bx + c. The coordinates of the vertex (h, k) can be found using the formulas: h = -b / … Read more

To complete the square for the quadratic equation x² + 12x – 11, we need to focus on the quadratic and linear terms, which are x² + 12x. Here’s a step-by-step process to determine the number to add: Take the coefficient of the linear term (which is 12 in this case) and divide it by … Read more

To find the length of one side of a square when given its perimeter, you can use the formula for the perimeter of a square, which is: Perimeter = 4 × side length In this case, we know that the perimeter is 36. So we can set up the equation: 36 = 4 × side … Read more

The relative maximum and minimum points of a function can be found by analyzing its critical points. A critical point occurs when the first derivative of the function is zero or undefined. Let’s go through the steps to find the critical points of the function f(x) = 2x³ + x² + 11x. Step 1: Find … Read more

To find the number of onto functions (surjective functions) from set A to set B, we can use the concept from combinatorial mathematics involving Stirling numbers of the second kind and inclusion-exclusion principle. Assuming that set A has m elements and set B has n elements, where m >= n, the formula for the number … Read more

To solve the problem of finding the probability of rolling exactly one ‘3’ when a fair 6-sided die is rolled three times, we can apply the binomial probability formula. The situation can be modeled as a binomial experiment, where: ‘n’ (the number of trials) = 3 rolls of the die ‘k’ (the number of successes … Read more

To graph a line with a given slope and a specific point, you can follow a simple process. In this case, the slope (m) is 7, and the point through which the line passes is (2, 9). Step 1: Understand the Slope The slope of a line measures how steep the line is, calculated as … Read more