How many license plates can be made consisting of 3 letters followed by 2 digits?
To calculate the total number of possible license plates that can be formed with the pattern of 3 letters followed by 2 digits, we need to consider the choices for each part: 1. **Choosing the Letters**: There are 26 letters in the English alphabet. For the first letter, we have 26 options, for the second […]
Solve x² – 24x + 80 by Completing the Square: What is the Solution Set of the Equation?
To solve the quadratic equation x² – 24x + 80 by completing the square, we follow these steps: Move the constant to the other side: Start with the original equation: x² – 24x = -80 Complete the square: Take the coefficient of x, which is -24, divide by 2 to get -12, and then square […]
Match the Angles Greater Than 90 Degrees with Their Reference Angles
To match angles greater than 90 degrees with their reference angles, we first need to understand what a reference angle is. A reference angle is the acute angle formed by the terminal side of the given angle and the horizontal axis. Let’s go through the angles provided: 135 degrees: This angle is in the second […]
Which equation is y = 3x^2 + 22x + 52 rewritten in vertex form?
To rewrite the quadratic equation y = 3x² + 22x + 52 in vertex form, we need to complete the square. The vertex form of a quadratic equation is given by: y = a(x – h)² + k, where (h, k) is the vertex of the parabola. We start with the given equation: y = […]
x 52 81 which of the following expressions represents the solutions to the given equation
To solve the equation involving x that relates to the numbers 52 and 81, we need to clarify the context of these numbers. If we interpret “x 52 81” as an equation such as “x + 52 = 81” or “x – 52 = 81,” we can find the value of x. For example, if […]
Find the Area of the Shaded Region of a Rectangle
To calculate the area of the shaded region within a rectangle, you first need to determine the total area of the rectangle and then subtract the area of any unshaded regions. The formula for the area of a rectangle is given by: Area = length × width Assuming you know the length and width of […]
What is the next number in the sequence: 15, 14, 13, 12, 11, 10, 9?
The next number in the sequence is 8. This sequence is a simple countdown starting from 15 and decreasing by 1 each time. If we observe the numbers, we can see that each number is just one less than the previous one. So, after 9, the logical next number would be 8.
What is the slope of line AB that contains points A(0, 1) and B(1, 5)?
To find the slope of the line AB, we can use the formula: Slope (m) = (y2 – y1) / (x2 – x1) In this case, we have the points A(0, 1) and B(1, 5). Here, (x1, y1) is (0, 1) and (x2, y2) is (1, 5). Now plug in the coordinates: y2 = 5 […]
How do you write an inequality for the situation: all real numbers at most 95 or at least 55?
To express the situation where all real numbers are at most 95 or at least 55, we can break this down into two parts: The phrase “at most 95” translates to the inequality: x ≤ 95. The phrase “at least 55” translates to the inequality: x ≥ 55. Since these two conditions describe two separate […]
If A Varies Inversely as B and A is 3 When B is 4, What is the Value of B When A is 48?
To solve this problem, we start by understanding the relationship where one variable varies inversely as another. In mathematical terms, this can be expressed as: A × B = k Here, k is a constant. From the problem, we know that when A is 3, B is 4. We can substitute these values into the […]