To find the 25th term of the arithmetic sequence 3, 9, 15, 21, 27, we first need to identify the pattern of the sequence. An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. In this case, we can calculate the common difference: 9 – 3 = 6 15 … Read more
Graphing the Inequality x + 2y < 4 Graphing the inequality x + 2y < 4 involves several steps: Rewrite the Inequality: Start by isolating y. You can do this by rearranging the terms: 2y < 4 – x Now, divide by 2 to solve for y: y < 2 – 0.5x Graph the Boundary … Read more
To solve for y in the equation 2x + y = 6, you will need to isolate the variable y. This is done through simple algebraic manipulation. Here’s a step-by-step guide: Start with the original equation: 2x + y = 6 Subtract 2x from both sides: This gives you: y = 6 – 2x You … Read more
To solve the equation p = 2w + 2l for w, follow these steps: Start with the original equation: p = 2w + 2l Isolate the terms involving w on one side of the equation. To do this, you can subtract 2l from both sides: p – 2l = 2w Now, to isolate w, divide … Read more
To determine the probability of both coins landing on heads when two coins are tossed, we can start by identifying the total number of possible outcomes and the number of favorable outcomes. When tossing two coins, each coin has 2 possible outcomes: heads (H) or tails (T). Therefore, the total number of outcomes when tossing … Read more
Factoring the Trinomial: 5x² + 8x + 4 To factor the trinomial 5x² + 8x + 4, we need to find two binomials that, when multiplied together, yield the original trinomial. Let’s break down the process. Step 1: Identify the Coefficients The trinomial consists of three parts: the coefficient of x² (which is 5), the … Read more
To convert the exponential equation 4x = 64 into its logarithmic form in base 10, we first need to understand the relationship between exponential and logarithmic expressions. In general, the exponential equation ab = c can be rewritten in logarithmic form as loga(c) = b. Here, a is the base, b is the exponent, and … Read more
If angles 1 and 2 are complementary, they add up to 90 degrees. If they are also congruent, that means they are equal in measurement. So, we can set both angles to be equal, calling them both x. Thus, we have the equation: x + x = 90 This simplifies to: 2x = 90 Now, … Read more
To find the inverse of the function y = 2x² + 8, we need to follow these steps: Replace y with x: This is the first step in finding the inverse. The equation becomes: x = 2y² + 8 Isolate y: We need to solve this equation for y. Start by moving 8 to the … Read more