How do you solve the equation x² + 2x + 1 = 17 for x?
To solve the equation x² + 2x + 1 = 17, we first want to rearrange it into a standard quadratic form, which is ax² + bx + c = 0. 1. Start by subtracting 17 from both sides of the equation: x² + 2x + 1 – 17 = 0 This simplifies to: x² […]
How to find the distance between two points on a coordinate plane
To find the distance between two points on a coordinate plane, you can use the distance formula derived from the Pythagorean theorem. The distance formula is: D = √((x2 – x1)² + (y2 – y1)²) Where: (x1, y1) are the coordinates of the first point. (x2, y2) are the coordinates of the second point. Here’s […]
Which of the following is an example of a proper fraction?
A proper fraction is defined as a fraction where the numerator (the top number) is less than the denominator (the bottom number). For example, if we consider the fractions 1/2, 3/4, and 5/3, the fractions 1/2 and 3/4 are proper fractions because in both cases, the numerators (1 and 3) are less than the denominators […]
If the complex number x = 3 + bi and x² = 13, which is a possible value of b: 2, 4, 9, or 10?
To solve for the possible value of b, we start with the complex number x = 3 + bi. We need to compute x²: x² = (3 + bi)² = 3² + 2(3)(bi) + (bi)² = 9 + 6bi – b² Combining like terms, we have: x² = (9 – b²) + (6b)i Since we […]
Which of the following represents 5 x to the 4 ninths power in radical form?
To express 5 x to the 4 ninths power in radical form, we first need to understand what the exponent of 4/9 means. The fraction 4/9 indicates that we have a base raised to a power and then taking a root. In general, the expression a^(m/n) can be converted into radical form as follows: The […]
How to Find the Linearization L(x) of the Function f(x) at x = 9?
To find the linearization L(x) of a function f(x) at a given point, we follow these steps: Identify the function: You need to know the function f(x). Let’s say f(x) is a function that you have in mind. Calculate the value of f at the point: Compute f(9), where 9 is the point at which […]
If four times a certain number increased by 6 is equal to 94, what is the number?
To solve the equation, let’s denote the certain number as x. According to the problem, we can translate the statement into a mathematical equation: 4x + 6 = 94 Now, we need to isolate x. First, we will subtract 6 from both sides of the equation: 4x + 6 – 6 = 94 – 6 […]
How to Divide 2x² + 17x + 35 by x + 5?
To divide the polynomial 2x² + 17x + 35 by x + 5, we can use polynomial long division. 1. First, set up the division: Write 2x² + 17x + 35 under the long division symbol and x + 5 outside. 2. Next, divide the leading term of the dividend (2x²) by the leading term […]
Based on the graph, what are the approximate solutions to the equation 2x = 8 025x?
To find the approximate solutions to the equation 2x = 8 025x, we first need to understand how to interpret the graph of the function. The equation essentially means we are looking for the points where the line corresponding to 2x intersects the line corresponding to 8 025x. If we were to plot 2x and […]
Explain the Elimination Method of Linear Equations in 2 Variables with an Example
The elimination method is a technique used to solve systems of linear equations. The basic idea is to eliminate one variable at a time, allowing us to solve for the remaining variable. This technique is especially useful when dealing with two variables because it simplifies the calculations. Let’s consider an example to illustrate the elimination […]