To solve this problem, we first need to understand the meaning of a tangent line. A tangent line to the graph of a function at a specific point is a straight line that just ‘touches’ the graph at that point and has the same slope as the function at that point. In this case, we … Read more
To find f(3) for the function f(a) = 2a² + 5a + 4, we need to substitute the value of a with 3 in the function. Here are the steps to do this: Start with the function: f(a) = 2a² + 5a + 4. Substituting a with 3: f(3) = 2(3)² + 5(3) + 4. … Read more
To find the value of tan(θ) when the terminal side of the angle in standard position passes through the point (3, 4), we can use the definitions of the sides in a right triangle formed by the x and y coordinates. In the coordinate point (3, 4): The x-coordinate is 3, which represents the length … Read more
The expression given, 64x + 24x = 30, demonstrates the Commutative Property of Addition. The Commutative Property states that the order in which two numbers are added does not change the sum. In this case, although the terms are organized as ’64x’ and ’24x’, they can be rearranged without affecting the result: For instance, we … Read more
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. To determine if the given sequence 7, 11, 15, 19 is arithmetic, we need to check the differences between its consecutive terms. Let’s break it down: First term: 7 Second term: 11 Third term: 15 Fourth … Read more
Solving the Linear Equations We have the following system of linear equations: Equation 1: 2x + y = 5 Equation 2: 3x + 2y = 4 Step 1: Solve Equation 1 for y From Equation 1, we can express y in terms of x: y = 5 – 2x Step 2: Substitute for y in … Read more
To determine the measure of angle BCD, we first need to understand the context in which angle BCD is situated. Angles can be found in various geometric shapes or configurations, such as triangles, quadrilaterals, or even in the context of intersecting lines. Here’s a detailed explanation of how to find angle BCD: Identify the Key … Read more
To determine the length of a rectangle when the perimeter and the width are known, we can use the formula for the perimeter of a rectangle, which is given by: Perimeter (P) = 2 * (Length (l) + Width (w)) In this case, we already know the perimeter and the width: Perimeter (P) = 34 … Read more
Solving the System of Equations To solve the system of equations 2x + y = 3 and x + 2y = 1, we can use the method of substitution or elimination. Here, we’ll use the elimination method for clarity. Step 1: Align the equations First, we write the equations one under the other: 2x + … Read more