Tossing two coins involves looking at all the possible outcomes that can result from the toss. The sample space for this event consists of all combinations of heads (H) and tails (T) that can occur when the two coins are tossed. When you toss two coins, the possible outcomes are: HH (both coins show heads) … Read more
An arithmetic sequence is defined by a specific formula that allows us to find any term in the sequence, given a value of n, which typically represents the position of the term in the sequence. In this case, the formula given is: a_n = 3 + 2n – 1 This can be simplified to: a_n … Read more
To determine whether the expression 2√3 + 2√6 is rational or not, we first need to understand what rational numbers are. A rational number can be expressed as the quotient of two integers, where the denominator is not zero. Let’s break down the expression: 2√3: This part represents 2 times the square root of 3. … Read more
Finding the Value of x in a Triangular Prism The volume of a triangular prism can be calculated using the formula: Volume = Base Area × Height In this case, we are given that the volume of the triangular prism is 54 cubic units. To find the value of x, we need additional information regarding … Read more
Finding Solutions to the Equation To solve the equation sec²(x) = 2tan²(x) within the interval [0, 2π], we start by rewriting the terms using the definitions of secant and tangent: sec(x) = 1/cos(x) tan(x) = sin(x)/cos(x) This allows us to express the equation in terms of sine and cosine: sec²(x) = 1/cos²(x) and tan²(x) = … Read more
To determine which binomial is a factor of the polynomial 9x² + 643x + 8, we first need to factor the expression. Factoring polynomials can often involve finding two numbers that multiply to a specific value, while also adding up to another value. In this case, we’re looking for factors of the form (ax + … Read more
To solve the inequality 2x + 20 < 37 + 62x, we’ll need to follow a series of steps to isolate x: Reorganize the inequality: Start by getting all the terms involving x on one side and the constants on the other. We can subtract 2x from both sides: Subtract 2x from both sides: This ... Read more
Two angles are said to be supplementary when the sum of their measures equals 180 degrees. If we have two angles, let’s call them A and B, both of which are supplementary to the same angle C, we can derive an important conclusion. In this case, since both angle A and angle B satisfy the … Read more
Solving the Equation x² – 24x + 80 by Completing the Square To solve the quadratic equation x² – 24x + 80 = 0 by completing the square, follow these steps: Rearrange the equation: Start with the original equation: x² – 24x + 80 = 0 Move the constant term (80) to the other side: … Read more
To find the exact value of cos(180) multiplied by sin(180), we start by calculating each trigonometric function individually. The value of cos(180) is determined using the unit circle, where the angle 180 degrees corresponds to the point (-1, 0). Therefore: cos(180) = -1 Next, we find sin(180). The angle 180 degrees also corresponds to the … Read more