What is a factor of a number?
A factor of a number is an integer that can be multiplied by another integer to produce the original number. In other words, if you can divide a number by another number without leaving a remainder, then the second number is a factor of the first. For example, let’s take the number 12. The factors […]
In the right triangle below, if tan(045) what is the approximate length of AB?
To find the approximate length of AB in a right triangle where the angle is 45 degrees (or tan(045)), we can use some basic trigonometric properties. In a right triangle with angles of 45 degrees, the ratios of the sides are equal. Specifically, for a 45-45-90 triangle, the lengths of the legs are equal, and […]
What is the equation in point slope form of the line passing through (0, 6) and (1, 3)?
To find the equation of the line in point-slope form that passes through the points (0, 6) and (1, 3), we first need to calculate the slope of the line. The slope (m) is calculated using the formula: m = (y2 – y1) / (x2 – x1) Here, (x1, y1) = (0, 6) and (x2, […]
What are the coordinates of the vertex for f(x) = x² + 6x + 13?
To find the coordinates of the vertex for the quadratic function f(x) = x² + 6x + 13, we can use the vertex formula. The vertex (h, k) of a parabola in the form f(x) = ax² + bx + c is given by: h = -b / (2a) Here, a = 1 and b […]
Factor the polynomial 4x^4 + 20x^2 + 3x^2 + 15 by grouping. What is the resulting expression?
To factor the polynomial 4×4 + 20×2 + 3×2 + 15 by grouping, we start by reorganizing the expression: (4×4 + 20×2) + (3×2 + 15) Now, we can factor out common factors from each group: From the first group 4×4 + 20×2, we can factor out 4×2: 4×2(x2 + 5) From the second group […]
What is the smallest angle of rotational symmetry for a square?
The smallest angle of rotational symmetry for a square is 90 degrees. A square has four equal sides and four equal angles, which allows it to be rotated around its center point. When you rotate a square by 90 degrees, it will look exactly the same as it did in its original position. This property […]
How many ways can you split 12 people into 3 teams of 4?
To determine how many ways you can divide 12 people into 3 teams of 4, we can follow these steps: First, we calculate the ways to choose the first team of 4 from 12 people. This can be done using the combination formula: C(n, k) = n! / (k!(n – k)!) For the first team: […]
Explain the Term Equation
An equation is a mathematical statement that asserts the equality of two expressions. It is composed of two sides, the left side and the right side, separated by an equal sign (=). For instance, in the equation 2x + 3 = 7, the left side consists of the expression 2x + 3 and the right […]
LCM of 23, 32 and 22, 33?
To find the least common multiple (LCM) of the given numbers, we first need to consider the prime factorization of each number: 23 is a prime number, so its factorization is simply 23. 32 can be expressed as 25 (since 32 = 2 × 2 × 2 × 2 × 2). 22 can be factored […]
The sum of a rational number and a rational number is rational
Yes, the sum of a rational number and a rational number is indeed a rational number. To understand why, we first need to clarify what rational numbers are. A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. This means that […]