Which equation is the equation of a line that passes through (10, 3) and is perpendicular to y = 5x + 7?
To find the equation of a line that passes through the point (10, 3) and is perpendicular to the line given by the equation y = 5x + 7, we first need to determine the slope of the given line. The equation of the line y = 5x + 7 can be expressed in slope-intercept […]
What is the ratio of the sum of m terms of two arithmetic progressions if the ratio of their sums for n terms is 7n, 14n, 27?
To find the ratio of the sum of m terms for two arithmetic progressions (APs) given that the ratio of their sums for n terms is 7n, 14n, and 27, we can use the properties of arithmetic progressions. The sum of the first n terms of an AP can be expressed as: Sn = n/2 […]
How do you write the equation that models the relationship where y varies jointly with w and x and inversely with z?
To model the relationship where y varies jointly with w and x and inversely with z, we can start with the concept of joint and inverse variation. Since y varies jointly with w and x, we can express this part of the relationship as: y = k * w * x where k is the […]
How do you simplify the expression 7x + 5x^4 + 5 + 7x^4 + 5 + 9x?
To simplify the expression 7x + 5×4 + 5 + 7×4 + 5 + 9x, we first combine like terms. 1. Identify the like terms: The linear terms are 7x and 9x. The constant terms are 5 and another 5. The x4 terms are 5×4 and 7×4. 2. Combine each type of like term: For […]
Which of the following describes the zeroes of the graph of f(x) = 3x^6 – 30x^5 + 75x^4?
The zeroes of the function f(x) = 3x^6 – 30x^5 + 75x^4 can be found by factoring the equation. First, we factor out the greatest common factor, which in this case is 3x^4. This gives us: f(x) = 3x^4(x^2 – 10x + 25) Next, we simplify the quadratic expression. The expression x^2 – 10x + […]
How do you calculate the percentage difference between two numbers?
To calculate the percentage difference between two numbers, you can follow these steps: First, find the absolute difference between the two numbers. This is done by subtracting the smaller number from the larger number. Next, take that absolute difference and divide it by the average of the two numbers. The average can be found by […]
What is an angle between 0 and 360 that is coterminal with 86?
To find an angle that is coterminal with 86 degrees, we need to add or subtract a full rotation, which is 360 degrees. Coterminal angles share the same terminal side when drawn in standard position. In this case, since 86 is already between 0 and 360, it is coterminal with itself. However, we can also […]
What is the value of sin(8) if the terminal side of an angle in standard position passes through the point (15, 8)?
To find the value of sin(θ) where θ is the angle in standard position that has its terminal side passing through the point (15, 8), we first need to recognize that we can use the coordinates of this point to determine the sine of the angle. The sine of an angle in a right triangle […]
Which shows the first step in the solution to the equation log2(x) + log2(x) = 6 + 4?
To solve the equation log2(x) + log2(x) = 6 + 4, we can start by simplifying both sides of the equation. The left side, log2(x) + log2(x), can be combined because they are like terms. Adding them together gives us 2 * log2(x). For the right side, 6 + 4 simply equals 10. Thus, the […]
What is the sum of 3x² + 5x + 8 + 5x² + 13x + 5?
To find the sum of the expression 3x² + 5x + 8 + 5x² + 13x + 5, we first need to combine like terms. 1. **Identify Like Terms:** – The like terms for x² are 3x² and 5x². – The like terms for x are 5x and 13x. – The constant terms are 8 […]