Understanding the Sequence Let’s break down the sequence: 4, 8, 12, 20, 52. At first glance, the pattern isn’t immediately obvious, so we need to investigate the relationships between the numbers. Identifying the Pattern We can look at the differences between consecutive numbers: 8 – 4 = 4 12 – 8 = 4 20 – … Read more
The discriminant is an important concept in the context of quadratic equations, as it provides valuable information about the nature of the roots of the equation. For a standard quadratic equation in the form: ax2 + bx + c = 0 the discriminant (denoted as D) is given by the formula: D = b2 – … Read more
To calculate the expression 1 i 1 i, first, it’s important to clarify what this expression means. It seems as though there is a misunderstanding or a typographical error. Typically, in mathematics, we deal with numbers and operators (like addition or multiplication). However, the presence of “i” suggests that we might be looking at imaginary … Read more
The sequence you’ve provided is: 2, 9, 28, 65, 126. To find the explicit formula for this sequence, let’s first examine the terms more closely and look for patterns. The first few terms can be expressed as follows where n starts from 1: 1st term: 2 2nd term: 9 3rd term: 28 4th term: 65 … Read more
To find the solution to the system of equations, we need to set the two equations equal to each other since both equal y: 1. The first equation is: y = 4x + 10 2. The second equation is: y = 2x + 6 Setting them equal: 4x + 10 = 2x + 6 Now, … Read more
To find the value of x in the equation 2x + 3y = 36 when y = 6, we can follow these steps: Start by substituting the value of y into the equation. Since y = 6, we replace y in the equation: 2x + 3(6) = 36 Now, calculate 3(6): 3 * 6 = … Read more
To find the probability of getting one head and one tail when tossing two coins, we will start by determining the possible outcomes. When tossing two coins, each coin has two possible outcomes: heads (H) or tails (T). The combinations of outcomes when tossing both coins can be listed as follows: HH (both coins show … Read more
To determine the value of x in an equation, you need to isolate x on one side of the equation. Let’s go through a step-by-step approach using a simple example equation: Suppose you have the equation: 2x + 5 = 15 Here’s how you can solve for x: Step 1: Subtract 5 from both sides. … Read more
The axis of symmetry for a quadratic function can be determined using the formula: x = -b / (2a) In the function f(x) = x² + 9x + 21, the coefficients are: a = 1 b = 9 c = 21 Plugging the values of a and b into the axis of symmetry formula: x … Read more
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem. The lengths of the sides of the rectangle are the two legs of a right triangle, and the diagonal is the hypotenuse. In our case, the lengths of the sides are: Side 1 (length) = 5 cm Side 2 … Read more