Solve the equation 5x – 8 = 3x + 10
To solve the equation 5x – 8 = 3x + 10, we’ll start by isolating the variable x. Here are the steps: First, move the terms involving x to one side of the equation. We can do this by subtracting 3x from both sides: 5x – 3x – 8 = 10 This simplifies to: 2x […]
How does Marcus rewrite f(x) = x² + 6x + 4 in vertex form?
To rewrite the quadratic function f(x) = x² + 6x + 4 in vertex form, we need to complete the square. 1. Start with the given function: f(x) = x² + 6x + 4 2. Focus on the quadratic and linear terms, x² + 6x. To complete the square, take half of the coefficient of […]
What is a factor of 6x² x 7?
A factor of the expression 6x² x 7 is any number or variable that divides into the expression without leaving a remainder. To find a factor, we can start by simplifying the expression: 6x² x 7 can be rewritten as (6 x 7) x x², which simplifies to 42x². Now, the factors of 42x² include: […]
What are the largest and smallest 4-digit numbers that can be formed using the digits 4037?
The largest 4-digit number that can be formed using the digits 4, 0, 3, and 7 is 7430. To arrive at this number, we rearrange the digits in descending order, placing the highest digits at the more significant places. Since we cannot start with 0 in a 4-digit number, we position 3 and 0 towards […]
What is one of the factors of 6x³ + 864x?
To find one of the factors of the expression 6x³ + 864x, we can start by factoring out the greatest common factor (GCF) from both terms. First, we notice that both terms have a common factor of 6x
Find the General Solution of the Given Second Order Differential Equation: yy – 12y” = 0
To solve the second order differential equation given by yy – 12y” = 0, we start by rewriting it in a standard form. The equation can be rearranged to: 12y” = yy By dividing both sides by 12, we find: y” = rac{yy}{12} This is a nonlinear second order differential equation. One standard method to […]
What is the inverse of the function f(x) = 2x + 10?
To find the inverse of the function f(x) = 2x + 10, we follow a few straightforward steps. 1. **Replace f(x) with y**: We start by rewriting the function as: y = 2x + 10 2. **Swap x and y**: To find the inverse, we switch x and y, resulting in: x = 2y + […]
How to solve the equation x² = 20 – 4?
To solve the equation x² = 20 – 4, we start by simplifying the right side: x² = 20 – 4 x² = 16 Now, we will take the square root of both sides. Remember that when we take the square root, we need to consider both the positive and the negative roots: x = […]
What is the sum of the measures of the interior angles of an octagon?
The sum of the measures of the interior angles of an octagon is 1,080 degrees. This can be determined using the formula for the sum of the interior angles of a polygon, which is given by: Sum = (n – 2) × 180 Here, n represents the number of sides in the polygon. Since an […]
How do you find the slope of the line whose equation is xy = 6?
To find the slope of the given equation xy = 6, we first need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope. Starting with the equation: xy = 6 We can isolate y by dividing both sides by x (assuming x ≠ 0): y = […]