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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

To find the value of x, we first need to remember that for any regular polygon, the measure of each exterior angle can be calculated using the formula: Exterior Angle = 360° / n where n is the number of sides of the polygon. In our case, since we are dealing with a regular decagon, … Read more

To find the coordinates of the point that is equidistant from points A (2, 3) and C (5, 6), we can utilize the geometric concept of the midpoint of the line segment connecting these two points. The coordinates of the midpoint (M) can be calculated using the following formula: M = ((x1 + x2) / … Read more

To solve the system of equations 2x + 5y = 3 and x + 3y = 1, we can use either the substitution method or the elimination method. Here, we’ll use the elimination method for clarity. Step 1: Align the equations We start with the given equations: Equation 1: 2x + 5y = 3 Equation … Read more

To find the radius of the circle represented by the equation x² + y² – 8x – 6y – 21 = 0, we first need to rewrite this equation in standard form. The standard form of a circle’s equation is: (x – h)² + (y – k)² = r² where (h, k) is the center … Read more