Understanding the rules for positive and negative numbers in mathematical operations helps to enhance your arithmetic skills significantly. Here’s a breakdown based on each operation: Addition Positive + Positive: The result is always positive. For example, 3 + 2 = 5. Negative + Negative: The result is always negative. For example, -3 + (-2) = … Read more
In triangle ABC, if line segment BD is both the altitude and the median, we can conclude that triangle ABC is an isosceles triangle with AB equal to AC. To understand this, let’s first break down what it means for BD to be an altitude and a median. An altitude is a line segment drawn … Read more
The exponent in a mathematical expression is a crucial element that tells us how many times the base number is used as a factor in multiplication. For instance, in the expression 34, the 3 is the base and the 4 is the exponent. This means that 3 is multiplied by itself 4 times: 3 x … Read more
Finding the Value of x in a System of Equations To solve for the value of x in the given system of equations: Equation 1: x * y = 3 Equation 2: 3 * x + 3 * y = 5 We will start by rearranging these equations. From Equation 1, we can express y … Read more
The integral of secant, denoted as ∫ sec(x) dx, can be derived through a clever manipulation involving trigonometric identities and substitution. The result is a bit surprising and showcases the beauty of calculus. To find the integral of sec(x), we can use the following identity: ∫ sec(x) dx = ln |sec(x) + tan(x)| + C … Read more
To solve the system of equations using substitution, let’s assume we have the following equations: Equation 1: y = 2x + 3 Equation 2: x + y = 10 We will follow these steps to find the value of y: Substitute one equation into the other: We can start with Equation 1, which expresses y … Read more
To find the solutions for the quadratic equation x² + 10x + 36 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a In this equation, a = 1, b = 10, and c = 36. Now, we will calculate the discriminant (the part under the square root): … Read more
To solve this problem, we need to first determine the highest common factor (HCF) of the numbers 56 and 72. The prime factorization of 56 is: 56 = 2^3 * 7^1 Now, for 72, the prime factorization is: 72 = 2^3 * 3^2 To find the HCF, we take the lowest power of each common … Read more
Finding the Domain and Range of a Rational Function A rational function is a function that can be expressed as the quotient of two polynomials, typically in the form: f(x) = P(x) / Q(x) where P(x) and Q(x) are polynomials. Step 1: Determine the Domain The domain of a rational function consists of all real … Read more
The minute hand of a clock completes a full rotation of 360 degrees every 60 minutes. To find the angle of rotation from 6:10 to 7:00, we first need to calculate the total minutes between these two times. From 6:10 to 7:00, the time difference is: From 6:10 to 6:59: 49 minutes From 6:59 to … Read more