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To calculate the future value of an investment, we can use the formula: Future Value (FV) = Present Value (PV) x (1 + r) Where: FV = Future Value PV = Present Value (the amount you are investing now) r = interest rate (expressed as a decimal) In this case: PV = $500 r = … Read more

To express the quadratic function y = 2x² + 8x + 1 in vertex form, we will use the technique of completing the square. The vertex form of a quadratic function is given by: y = a(x – h)² + k Here, (h, k) is the vertex of the parabola. Step 1: Factor out the … Read more

To determine the probability of getting exactly 2 tails when flipping a fair coin 7 times, we can make use of the binomial probability formula. This formula is particularly applicable because we have a fixed number of trials (7 flips), two possible outcomes (heads or tails), and each flip of the coin has the same … Read more

An exponent is a fundamental concept in mathematics that indicates how many times a number, known as the base, is multiplied by itself. For example, in the expression 23, the number 2 is the base, and the exponent is 3. This means that you multiply the base (2) by itself three times: 2 × 2 … Read more

To determine what constant should be added to the expression x² + 6x in order to form a perfect square trinomial, we can follow a systematic approach. A perfect square trinomial can be expressed in the form (a + b)², which expands to a² + 2ab + b². In our case, we need to rewrite … Read more

To multiply and simplify the expression involving the numbers 3, 5i, 2, and 4i, you can follow these steps: Group the terms: Start by rearranging the expression for clarity: (3 * 2) * (5i * 4i) Multiply the real numbers: First, multiply the real components: 3 * 2 = 6 Multiply the imaginary numbers: Next, … Read more

To find the nth term of the sequence given (1, 4, 7, 10), we need to identify the pattern or rule that describes the relationship between the terms in the sequence. Looking at the sequence, we see: The first term (n=1) is 1 The second term (n=2) is 4 The third term (n=3) is 7 … Read more

Graphing a Set on the Number Line Graphing a set on a number line is a straightforward process. To illustrate this, let’s assume our set is S = {x | -3 < x < 2}. Here’s how you can effectively graph this set: Draw a Horizontal Line: Begin by drawing a straight horizontal line, which … Read more

In vector mathematics, the component of vector a along the direction of vector b can be determined using the concept of projection. The projection of vector a onto vector b essentially tells us how much of a points in the direction of b. The formula for the projection of vector a onto vector b is … Read more

To solve for t in the equation 32t – 5 = 5t + 25, we will follow these steps: Isolate the variable terms on one side: First, we can move the 5t term from the right side to the left side. To do this, we subtract 5t from both sides: 32t – 5 – 5t … Read more