To find an equation that is true for both x = 6 and x = 2, we can substitute these values into a general linear equation format, such as: y = mx + b Here, m is the slope and b is the y-intercept. The primary task is to determine if we can create an … Read more
To find the slope and the y-intercept of a line, you typically start with the equation of the line in the slope-intercept form, which is: y = mx + b In this equation: m represents the slope of the line. b is the y-intercept, the point where the line crosses the y-axis (where x is … Read more
In mathematics, any non-zero number raised to the power of zero is defined to be 1. This includes negative numbers as well. So, when we raise a negative number, such as -5, to the power of 0, the result is: -50 = 1 This rule stems from the properties of exponents. To understand why this … Read more
To solve the quadratic equation x² + 7x + 12 = 0, we can use the factoring method or the quadratic formula. Here, I’ll demonstrate both methods for clarity. Method 1: Factoring 1. First, we need to find two numbers that multiply to the constant term (12) and add up to the coefficient of the … Read more
To find the value of ‘a’ that varies jointly with ‘b’ and ‘c’, we can use the formula for joint variation: a = k * b * c where: a is the value we want to find, k is the constant of variation, b and c are the given values. In this problem, we know: … Read more
To calculate 60 percent of 20, you can follow these simple steps: First, understand that ‘percent’ means ‘per hundred.’ So, 60 percent can be expressed as a fraction: 60/100. Next, you can simplify this fraction. Dividing both the numerator and the denominator by 20 gives you: 3/5. Now, to find 60 percent of 20, multiply … Read more
A fraction in which the numerator is larger than the denominator is called an improper fraction. In an improper fraction, the value can be greater than 1. For example, consider the fraction 7/5. Here, the numerator (7) is greater than the denominator (5), making it an improper fraction. Improper fractions are commonly used in various … Read more
The shape that has four congruent sides and two sets of parallel sides is a square. A square is a special type of rectangle where not only are the opposite sides parallel (as is the case in all rectangles), but all four sides are of equal length, which gives it that congruence. In geometry, the … Read more
To solve the inequality 24 > 2x + 5x + 5, we will follow these steps: Step 1: Combine Like Terms First, we will combine the terms on the right side of the inequality. The terms 2x and 5x can be combined: 2x + 5x = 7x Therefore, we rewrite the inequality as: 24 > … Read more
The first step in constructing an angle bisector using a compass and straightedge is to start with your given angle. Let’s denote this angle as ∠ABC, where B is the vertex of the angle. Follow these steps: 1. **Place the Compass Point:** Position the compass point at the vertex of the angle, point B. 2. … Read more