To convert the equation e3x = 3247 into logarithmic form, we start by understanding the relationship between exponential and logarithmic functions. The general form of an exponential equation is by = x, which can be rewritten in logarithmic form as y = logb(x). In this case, e serves as the base of the exponent. Following … Read more
To find the sale price of the dress, we need to calculate the discount amount first and then subtract that from the original price. Here’s how to do it: The original price of the dress is $6950. The discount percentage is 45%. 1. **Calculate the discount amount:** A discount of 45% means you will pay … Read more
To determine the number of x-intercepts for the graph of the equation y = x2 – 12, we need to find the values of x where y equals zero. This means we set the equation as follows: 0 = x2 – 12 Next, we can rearrange the equation to solve for x: x2 = 12 … Read more
To determine the value of t for a 95% confidence interval with 10 pieces of data, we first need to consider the concept of confidence intervals and how the t-distribution applies in this scenario. When calculating confidence intervals, the t-distribution is used instead of the normal distribution when the sample size is small (typically n … Read more
The equation of the parabola you provided is x² = 28y. This is a standard form for a parabola that opens upwards, which can be rewritten in the more familiar form of: (x – h)² = 4p(y – k) Here, the vertex of the parabola is given by the point (h, k), and 4p is … Read more
To determine which parabola intersects the line y = x + 5 at exactly one point, we need to consider the mathematical condition under which a parabola and a straight line share a single coordinate point. This situation occurs when the quadratic equation representing the parabola has a discriminant of zero. The general form of … Read more
To solve for x in the equation (x + 4) / 3 = 2, we can follow these steps: Isolate the term with x: Start by eliminating the fraction on the left side of the equation. You can do this by multiplying both sides of the equation by 3: (x + 4) / 3 * … Read more
To find the equation of a line that passes through two points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope of the line and b represents the y-intercept. Here are the steps to determine the equation: Determine the coordinates of the … Read more
Understanding the Equation of the Hyperbola To find the equation of a hyperbola with the specified foci and vertices, we start by identifying the characteristics of hyperbolas. A hyperbola is defined by two sets of points that are equidistant from two points called foci. In this case, the foci are located at (5, 0) and … Read more
To solve the inequality 2x > 11 – 5x, we need to isolate the variable x on one side of the inequality. Here are the steps: Add 5x to both sides: 2x + 5x > 11 which simplifies to: 7x > 11 Now, divide both sides by 7: x > 11/7 Convert 11/7 to a … Read more