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
The general form of a parabola that opens upwards can be given as x² = 4py, where p denotes the distance from the vertex of the parabola to the focus. In this equation, if we want to determine the value of p for the equation x² = 12y, we need to align it with the … Read more
To find the composite function fg(x) where f(x) = 9x² and g(x) = x³, we first need to understand what composite functions are. A composite function means that we take the output of one function and use it as the input for another function. In this case, fg(x) means we want to calculate f(g(x)). So, … Read more
To find the exact values of the trigonometric functions for the angle whose terminal side passes through the point P(9, 12), we will use the definitions of sine, cosine, and tangent based on the coordinates of the point. First, we need to calculate the radial distance (r) from the origin to the point P(9, 12). … Read more
The greatest common factor (GCF) is the largest expression that divides two or more expressions without leaving a remainder. To find the GCF of the expressions 4xy² and 20x²y⁴, we can follow these steps: Factor each term: For 4xy²: Start by identifying the coefficients and variables. Coefficient: 4 Variables: x and y (with the exponent … Read more
Converting an improper fraction into a mixed number involves a few straightforward steps. Let’s break it down: Understand Improper Fractions: An improper fraction is one where the numerator (the top number) is greater than or equal to the denominator (the bottom number). For example, the fraction 7/4 is an improper fraction because 7 is greater … Read more
To find the coefficient of the term x9 y in the binomial expansion of (2y + 4x)4, we can first set up the expression as per the binomial theorem, which states that: (a + b)n = ∑_{k=0}^{n} {n \choose k} a^{n-k} b^{k} In our case, a = 2y, b = 4x, and n = 4. … Read more
Parallel lines are defined as lines in a plane that never intersect or meet, no matter how far they are extended in either direction. Here are some key characteristics of parallel lines: Equidistant: Parallel lines remain the same distance apart at any point along their length. This constant distance between them ensures that they will … Read more
To determine the slope of any line that is parallel to the line defined by the equation 9x + 4y = 7, we first need to express this equation in the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. Here’s a step-by-step breakdown: Start … Read more