To solve the problem, we need to find a number that, when multiplied by 3 and then divided by 4, results in 24. Let’s denote the unknown number as x. We can set up the equation as follows: 3x / 4 = 24 To isolate x, we will first eliminate the denominator by multiplying both … Read more
To find the x-intercepts of the function f(x) = 2×2 + 3x – 20, we need to determine the points where the graph of the function intersects the x-axis. This occurs when the value of the function is equal to zero. So, we set the function equal to zero: 2×2 + 3x – 20 = … Read more
Finding the Sum of the Polynomials To find the sum of the two polynomials mn3 and mn4, we need to simply add them together. Step-by-Step Calculation Identify the two polynomials: mn3 and mn4. Since both polynomials share the common factor ‘mn’, we can combine them quite easily. The expression becomes: mn3 + mn4. Now, we … Read more
To determine the probability of getting exactly 1 head when flipping a coin 3 times, we need to consider the total possible outcomes and the successful outcomes for our case. When flipping a coin, each flip has two possible outcomes: heads (H) or tails (T). Thus, when flipping the coin 3 times, the total number … Read more
To find the zeros of the function f(x) = x² + 5x + 5, we can use the quadratic formula, which is given by: x = (-b ± sqrt(b² – 4ac)) / 2a In this case, the coefficients are: a = 1 (the coefficient of x²) b = 5 (the coefficient of x) c = … Read more
To convert an angle from degrees to radians, you can use the following formula: Radians = Degrees × (π / 180) For example, let’s say you have an angle of x degrees. To find its radian measure, you simply multiply x by π / 180. This conversion is essential because many mathematical functions and applications, … Read more
To find coterminal angles, we need to understand that two angles are coterminal if they differ by a multiple of 2π (360 degrees). For an angle given in radians, such as 3π/4, we can find coterminal angles by either adding or subtracting 2π. Let’s start with the given angle: 3π/4 Now, we can find two … Read more
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, a prime number has exactly two divisors: 1 and itself. Looking for prime numbers between 40 and 50, we can check each number individually: 41: This number can only be divided evenly … Read more
Trigonometric Ratios for Specific Angles Understanding the values of trigonometric ratios for key angles is essential in trigonometry. Below are the values for the angles 120°, 135°, 150°, 180°, and 270° for all six trigonometric ratios. 1. Angle: 120° Sine (sin): √3/2 Cosine (cos): -1/2 Tangent (tan): -√3 Cosecant (csc): 2/√3 Secant (sec): -2 Cotangent … Read more
To express a complex number in trigonometric form, we typically use the format: z = r (cos θ + i sin θ) where: r is the modulus (magnitude) of the complex number θ is the argument (angle) of the complex number Let’s break down the steps to express the complex number 3 + 3i in … Read more