To determine the missing number in the sequence: 1, 16, 100, 169, we first need to analyze the numbers provided. The numbers in this sequence are perfect squares: 1 = 12 16 = 42 100 = 102 169 = 132 Next, we should identify the pattern in the sequence of square roots: 1, 4, 10, … Read more
To find the equation of a horizontal line that passes through a specific point, we start by acknowledging the characteristics of horizontal lines. A horizontal line maintains a constant y-coordinate regardless of the x-coordinate. In this case, the point given is (2, 4), where the y-coordinate is 4. The equation of a horizontal line can … Read more
To find the polynomial function of the lowest degree with a leading coefficient of 1 and given roots, we need to consider the roots provided: The root i (which is an imaginary number) The root 2 (with a multiplicity of 2) Since we are working with real polynomials, the presence of the imaginary root i … Read more
To find the equation of a parabola with its vertex at the origin (0,0) and a directrix at y = 15, we start by recalling the definition of a parabola: it is the set of all points that are equidistant from a point called the focus and a line called the directrix. 1. Identifying the … Read more
To determine the value of tan Y
The least common denominator (LCD) is the smallest number that can be divided evenly by each of the denominators in a set of fractions. To find the LCD for the numbers 3, 4, 4, 5, 2, and 3, we need to follow a systematic approach: Identify the numbers: We have the numbers 3, 4, 4, … Read more
To find the x-intercepts of the function f(x) = x² + 5x – 36, we need to determine the points where the graph of the function crosses the x-axis. This occurs when f(x) is equal to zero, so we set the equation to zero: x² + 5x – 36 = 0 Next, we can solve … Read more
Synthetic division is a simplified method of dividing polynomials, particularly useful when dividing by linear factors. However, since we are dividing by a polynomial of higher degree (specifically, x² in this case), we can still use a process similar to synthetic division, though it requires more attention to coefficients. First, let’s express the polynomial properly: … Read more
The prime factorization of a number involves breaking it down into its prime factors, which are the building blocks of all integers. To express these factors in exponential form, we count how many times each prime number appears in the factorization. Prime Factorization of 100 Let’s start with the number 100: First, divide 100 by … Read more
To classify the functions f(x) = 4x^2, g(x) = 1/x, and h(x) = 32^x as linear, quadratic, or exponential, we need to examine the form of each function and its characteristics. 1. Linear Functions A linear function has the general form f(x) = mx + b, where m and b are constants. It produces a … Read more