To write the equation of a line given the slope and the y-intercept, you can use the slope-intercept form of a linear equation, which is expressed as: y = mx + b In this formula: y represents the dependent variable (the output of the function), x is the independent variable (the input), m is the … Read more
When a number is raised to the power of 1, it simply means that the number remains unchanged. Mathematically, this can be expressed as: a1 = a Where a is any real number. This property holds true for all numbers, whether they are integers, fractions, or decimals. For example: If you take the number 5, … Read more
To find the first five terms of the sequence defined by the formula a(n) = 1 + 4n, we need to substitute the values of n starting from 0 up to 4. Here’s how the calculation works: For n = 0: a(0) = 1 + 4(0) = 1 + 0 = 1 For n = … Read more
The divisor represented by the synthetic division notation you provided, which is written as 5 5 x 5 x 5, is referring to a polynomial being divided by the binomial (x – 5). In synthetic division, the coefficients of the polynomial are aligned with the value being used as the divisor, which in this case … Read more
The perimeter of a triangle is simply the sum of the lengths of all its sides. For triangle LMN, you would need to know the lengths of sides LM, LN, and MN. To calculate the perimeter, you can use the following formula: Perimeter (P) = LM + LN + MN Here’s a step-by-step guide on … Read more
A polygon is a flat shape consisting of straight lines that are joined to form a closed chain or circuit. Let’s examine the potential candidates to determine whether they are polygons: Triangle: Yes, a triangle has three straight sides and is a polygon. Rectangle: Yes, a rectangle has four straight sides and is a polygon. … Read more
To simplify the expression 7x + 34x² + 3x + 6, we start by identifying like terms. The expression can be broken down as follows: Terms with x²
To solve the equation described, we can break down the problem step by step. The statement says that four times the difference of a number (let’s call it x) and 7 is equal to 12. We can express this mathematically as: 4(x – 7) = 12 Now, let’s solve for x: First, divide both sides … Read more
To solve the absolute value inequality |2x – 4| < 14, we start by breaking it down into two separate inequalities. The absolute value inequality |a| < b means that -b < a < b. In this case, a is 2x – 4 and b is 14. So, we can rewrite the inequality as: -14 ... Read more
To solve the equation 28y + 6 = 02y + 5y + 14, let’s first simplify both sides of the equation. 1. Simplifying the right side: 02y + 5y can be simplified as follows: 02y = 2y, so we have 2y + 5y = 7y. This means that the equation now looks like this: 28y … Read more