Understanding the Function with Given X-Intercepts To find a function that has x-intercepts at the points (0, 0) and (4, 0), we need to consider how x-intercepts are defined. X-intercepts occur where the function crosses the x-axis, which means at these points, the function’s value is equal to zero. Constructing the Function Since the function … Read more
To solve the equation 2x + 5 = 65 for the variable x, we can follow these straightforward steps: Isolate the term containing x: To do this, we need to eliminate the constant term (which is 5) from the left side of the equation. We can achieve this by subtracting 5 from both sides: 2x … Read more
To find the distance between the tops of the two poles, we can use the distance formula derived from the Pythagorean theorem. The two poles can be visualized as forming a right triangle with the ground. Let’s break down the problem: **Height of the first pole**: 6 meters **Height of the second pole**: 11 meters … Read more
To solve the system of equations y = 5x + 4 and y = 4, we can start by setting the two equations equal to each other since both are equal to y: 5x + 4 = 4 Now, let’s solve for x: Subtract 4 from both sides: 5x = 0 Now divide both sides … Read more
To find the dimensions of the rectangle with the greatest possible area that can be inscribed under the parabola defined by the equation y = 12 – x², with its base on the x-axis, we can follow these steps: 1. Understand the Geometry: We need to inscribe a rectangle in such a way that the … Read more
A regular hexagon, characterized by its six equal sides and angles, exhibits reflectional symmetry through various folds. To demonstrate this property, follow these steps: Gather your materials: You’ll need a regular hexagon cut out from paper. Ensure all sides and angles are equal for the best results. Identify the symmetrical axes: A regular hexagon has … Read more
To find the value of the function f(x) = log₃(5x) minus g(x) = log₃(x), we first need to understand the properties of logarithms. Using the properties of logarithms, we can rewrite the function f(x): f(x) = log₃(5x) This can be broken down using the property of logarithms that states logb(mn) = logb(m) + logb(n). Applying … Read more
The additive inverse of a complex number is obtained by negating both the real and imaginary parts of that number. A complex number is typically expressed in the form a + bi, where a represents the real part and b represents the imaginary part. In this case, the complex number given is 8 + 3i. … Read more
Solution to Find the Measures of Angles PQR and PSR In a quadrilateral, the sum of all interior angles is always 360 degrees. This means we can use this property to find the unknown angles in quadrilateral PQRS. Given: Angle PQR = 7x + 2 Angle PSR = 5x + 14 Find the sum of … Read more
To solve the equation given by f(x) = (x – 5)/3 for f(13), you need to substitute x with 13 in the equation. Here’s the step-by-step process: Start with the function: f(x) = (x – 5) / 3 Substitute x with 13: f(13) = (13 – 5) / 3 Now, perform the calculation in the … Read more