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To find the coordinates of the image of vertex F after a reflection across the line y = x, we need to understand how reflections work in coordinate geometry. When we reflect a point across the line y = x, the x-coordinate and y-coordinate of that point swap places. Let’s say we have the coordinates … Read more

The complex number you mentioned, 6 + 2i, consists of two distinct components: the real part and the imaginary part. The real part of any complex number is the component that does not contain the imaginary unit i. In the case of 6 + 2i, the real part is simply 6. On the other hand, … Read more

Solving the Equation 2x² + 8 = 0 by Graphing To solve the equation 2x² + 8 = 0 by graphing, you first want to rewrite the equation in a form that represents a function. To do this, we can express the equation as: y = 2x² + 8 Next, we need to plot the … Read more

When discussing measurements, it is vital to understand that 1 millimeter (mm) is a unit of length in the metric system, precisely equal to one-thousandth of a meter. It is important to differentiate between millimeters and other units of measurement to ensure clarity and accuracy. To identify which of the following options does not equal … Read more

To solve the expression -1/8 * 35 * 7, it’s important to follow the correct sequence of operations known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). However, since this expression only involves multiplication, we can directly proceed with the calculations in a left-to-right manner. … Read more

To find the value of a in the equation 8z + 9 = 8z + 9 + a^2 + b, we need to first simplify the equation and isolate a. Let’s start by simplifying both sides: The left-hand side (LHS): 8z + 9 The right-hand side (RHS): 8z + 9 + a^2 + b Notice … Read more

To solve for the values of c and d that satisfy the equation 162x^c y^5 = 3x^2 y^{6d}, we can start by comparing the coefficients, the powers of x, and the powers of y on both sides of the equation. Step 1: Compare the coefficients The coefficient on the left side is 162 and on … Read more

To solve this problem, we first need to calculate the sum of 7 and 9: 7 + 9 = 16 Now, we compare this sum to 12. Since 16 is greater than 12, we will add 3 to the sum: 16 + 3 = 19 Thus, the correct answer is 19.

To find the component form and magnitude of the vector PQ, which goes from point P to point Q, we can follow these steps: Determine the coordinates: Point P has the coordinates (2, 9) and point Q has the coordinates (4, 14). Calculate the components of the vector: The components of the vector PQ can … Read more

The function given is f(x) = x4 + 2x. To find the range of this function, we’ll analyze its behavior. First, let’s evaluate the nature of the function. The term x4 is a polynomial with the highest degree of 4, which means that as x approaches positive or negative infinity, the function value f(x) will … Read more