What is the next number in the sequence: 11, 22, 13, 26, 15, 30, 17?
To determine the next number in the sequence, let’s break down the pattern in the provided numbers. The series alternates between two different sequences: Odd indexed positions: 11, 13, 15, 17 Even indexed positions: 22, 26, 30 In the odd indexed positions, the numbers increase by 2: 11 to 13 (increase by 2) 13 to […]
What is the inverse function for f(x) = x^2?
To find the inverse function of f(x) = x2, we start by replacing f(x) with y: y = x2 Next, we swap x and y. This gives us: x = y2 Now, we solve for y: y = √x However, we need to consider the domain of the original function. The function f(x) = x2 […]
Which ordered pair makes both inequalities true y x + 2?
To find an ordered pair that satisfies both inequalities y < 2x + 3 and y > x + 2, we can start by graphing the lines represented by the equations y = 2x + 3 and y = x + 2. The first inequality y < 2x + 3 indicates that we are looking […]
Solve for x in the equation x² – 20x + 100 = 36, x + 16 or x – 4, x – 10, x – 8, x – 4 or x – 16
To solve the equation x² – 20x + 100 = 36, we first rearrange it: x² – 20x + 100 – 36 = 0 This simplifies to: x² – 20x + 64 = 0 Next, we can apply the quadratic formula, which is: x = (-b ± √(b² – 4ac)) / 2a In our equation, […]
How to Express 10010 in Simplest Form?
To express the number 10010 in its simplest form, we first need to understand what is meant by ‘simplest form’. In mathematics, we often simplify a number when it can be factored down into smaller components or when it can be expressed in a more digestible format. The number 10010 is already a whole number […]
A quadrilateral has no pairs of parallel sides which name best describes the figure?
The figure you are describing is best called a trapezium (or a trapezoid in some regions, like the United States). In geometry, a trapezium is defined as a four-sided polygon, or quadrilateral, that does not have any sides that are parallel. Unlike its counterpart, the trapezoid, which does have at least one pair of parallel […]
What are the roots of f(x) = x² – 48?
To find the roots of the function f(x) = x² – 48, we need to solve the equation f(x) = 0. This means we set the equation: x² – 48 = 0 Next, we can isolate x²: x² = 48 Now, to find x, we take the square root of both sides: x = ±√48 […]
Which number doesn’t belong to the series: 1, 1, 2, 3, 4, 5, 8, 13, 21?
The number that doesn’t belong to this series is 4. This sequence is actually the beginning of the Fibonacci series, where each number is the sum of the two preceding ones. The series starts like this: 1 (first) 1 (second) – 1 + 0 = 1 2 – 1 + 1 = 2 3 – […]
How to Find the Area of a Circle with Circumference
To find the area of a circle when you have the circumference, you can follow these steps: First, recall the formulas involved. The circumference (C) of a circle is given by the formula: C = 2πr, where r is the radius. From the circumference, you can solve for the radius: r = C / (2π) […]
What is the result of dividing x³ 6 by x²?
To simplify the expression of dividing x³ 6 by x², we start by rewriting it in a more manageable form: We can express this division as: x³ * 6 ÷ x² Next, we can break this down step by step. First, we focus on the division of the variables: x³ ÷ x² Using the property […]