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The range of the function y = x² is the set of all possible output values (y-values) that the function can produce. To determine the range, we start by recognizing that this function is a quadratic function, and its graph is a parabola that opens upwards. In the case of y = x², regardless of … Read more

To solve for the missing number in the series 1, 4, 27, __, 3125, let’s first look for a pattern connecting the numbers. We can observe that: 1 = 13 4 = 23 27 = 33 __ = 43 3125 = 55 We note that the first three numbers represent cubes of integers: 1, 2, … Read more

To determine the next number in the sequence 6, 18, 20, 10, 30, 32, 16, we first need to analyze the pattern present in the numbers. Let’s break it down: Starting with 6, it is followed by 18. This is an increase of 12. The next number, 20, is an increase of 2 from 18. … Read more

To solve the question of what number is 14 of 12 of 15 of 200, we need to interpret what it means to find ’14 of 12 of 15 of 200.’ Let’s break it down step by step: Step 1: Calculate 12% of 200. This is calculated as follows: 12% of 200 = (12/100) * … Read more

To find the factors of the quadratic expression x² + 4x – 210, we can follow a systematic approach. Here’s how you can do it: Identify the Coefficients: The expression is in the standard form of ax² + bx + c, where: a = 1 (the coefficient of x²) b = 4 (the coefficient of … Read more

Calculating the Volume of a Sphere The formula to calculate the volume V of a sphere is: V = (4/3) × π × r³ In this formula, r represents the radius of the sphere. For a sphere with a radius of 3 inches, we can substitute r with 3: V = (4/3) × π × … Read more

To understand the derivative of an exponential growth function, we first need to define what an exponential growth function is. An exponential growth function typically has the form: f(x) = a * e^(bx) where: a is the initial amount (the value of the function at x = 0), e is the base of natural logarithms … Read more

To factor the quadratic expression 6x² + 11x + 10, we will first look for two numbers that multiply to the product of the coefficient of the quadratic term (6) and the constant term (10), which is 60 (6 * 10 = 60). At the same time, these two numbers must also add up to … Read more

To calculate the circumference of a circle, you can use the formula: C = πd Where: C is the circumference π (pi) is a constant approximately equal to 3.14159 d is the diameter of the circle In this case, the diameter of the circle is given as 22. Plugging this value into the formula gives … Read more