To solve the system of equations, we have the following two equations: 1. 2x + 4y = 12 2. y = 3x We can use the substitution method since the second equation expresses y in terms of x. Let’s substitute y in the first equation: 2x + 4(3x) = 12 This simplifies to: 2x + … Read more
To find the fifth term of the geometric sequence with the given initial terms of 5, 15, and 45, we start by understanding the nature of a geometric sequence. A geometric sequence is defined by the property that each term after the first is found by multiplying the previous term by a fixed, non-zero number … Read more
To simplify the expression 2 + 1 × 32 ÷ 3, we need to apply the rules of order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here is the step-by-step breakdown: Identify operations: In our expression, we have … Read more
To find the area of a figure, you first need to identify the type of shape you’re dealing with, as different shapes have different formulas to calculate their area. Here are some common shapes and their area formulas: Rectangle: Area = Length × Width Triangle: Area = (Base × Height) / 2 Circle: Area = … Read more
The area under the standard normal distribution curve between two z-scores can be found using statistical tables or a standard normal distribution calculator. In this case, we want to find the area between z = 0 and z = 2.16. Here’s a step-by-step guide on how to calculate this area: Understand the Standard Normal Distribution: … Read more
To solve for the value of x in the equation 400015x = 25000, follow these step-by-step instructions: Isolate x: To begin, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 400015. Perform the division: The equation will now look like this: … Read more
First Partial Derivatives of the Function z = x sin(xy) To find the first partial derivatives of the function z = x sin(xy), we will differentiate with respect to each variable while treating the other variable as a constant. 1. Partial Derivative with respect to x We denote the partial derivative of z with respect … Read more
To solve for y in the equation 2x + 3y = 6, you’ll want to isolate y on one side of the equation. Here’s a step-by-step guide: Start with the original equation: 2x + 3y = 6 Subtract 2x from both sides: 3y = 6 – 2x Now, divide both sides by 3: y = … Read more
The y-intercept of a line is the point where the line intersects the y-axis. This occurs when the value of x is zero. For the line represented by the equation y = x + 3, we can find the y-intercept by substituting 0 for x: y = 0 + 3 Upon solving this, we get: … Read more
Finding the Remainder To find the remainder of the polynomial 4x³ + 2x² + 18x + 38 when divided by x – 3, we can utilize the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial f(x) by x – c is simply f(c). Step 1: Determine f(c) In this … Read more