devyy To find g(x) ∘ f(x) or g(f(x)), we start with the definitions of the two parent functions. Given: f(x) = 3×2 g(x) = 5x + 10 Now, we will substitute f(x) into g(x). This means that wherever we have ‘x’ in g(x), we will replace it with f(x). Therefore: g(f(x)) = g(3×2) Substituting into the … Read more
To solve for x in the equation 2x + 3x + 4 + 5 = 0, we first need to combine like terms. 1. Combine the x terms: 2x + 3x = 5x This modifies our equation to: 5x + 4 + 5 = 0 2. Next, add the constant terms: 4 + 5 = … Read more
The graphs of y = 6x² + 4 and y = 6x² represent two parabolas that share a common general shape, but they differ significantly in their vertical positioning and vertex location. 1. Shape and Orientation: Both equations describe parabolas that open upwards since the coefficient of x² is positive (6 in this case). Therefore, … Read more
To calculate the perimeter of a regular octagon, you will want to use the formula for the perimeter of a polygon: Perimeter (P) = Number of sides (n) × Length of one side (s) For a regular octagon: Number of sides (n) = 8 Length of one side (s) = 8 cm Now, plug the … Read more
To prove that in a triangle, if one angle is 90 degrees, then the sum of the other two angles is 90 degrees, we can use the properties of triangles and the concept of supplementary angles. First, let’s recall that a triangle consists of three angles. The sum of all three angles in any triangle … Read more
To find the x-coordinates of the solutions to the given system of equations, we need to solve the equations simultaneously. The equations are: Equation 1: x² + y² = 100 Equation 2: y = x² Substituting Equation 2 into Equation 1, we get: x² + (x²)² = 100 This simplifies to: x² + x^4 = … Read more
To prove that two triangles are congruent, one of the following theorems can be applied: Side-Side-Side (SSS) Congruence Theorem: This theorem states that if three sides of one triangle are equal in length to three sides of another triangle, then the two triangles are congruent. Side-Angle-Side (SAS) Congruence Theorem: According to this theorem, if two … Read more
To find the value of y when x = 3 in the least squares regression equation y = 1202 + 1133x, we can simply substitute 3 for x in the equation. Here’s how it works: 1. Start with the equation: y = 1202 + 1133x 2. Plug in the value of x: y = 1202 … Read more
A point is considered to be on the circumference of a circle if the distance from that point to the center of the circle is exactly equal to the radius of the circle. This is a fundamental concept in geometry that defines the relationship between a point and a circle. To determine this, you can … Read more
To find the first and second derivatives of the functions defined by x = cos²(t) and y = cos(t), we will start by applying differentiation rules known as the chain rule and product rule in calculus. Step 1: Finding the first derivative: For x = cos²(t), we will differentiate using the chain rule: dx/dt = … Read more