To solve the challenge of finding two whole numbers from the digits 1 to 9, while ensuring that one number is double the other, we can approach the problem step-by-step. Let’s denote the smaller number as X. Consequently, the larger number would be 2X. The digits 1 to 9 must be used exactly once in … Read more
Converting Vertex Form to Standard Form To convert the given vertex form of the function f(x) = 2(x – 2)^2 + 32 into standard form, we’ll follow a systematic approach. Step 1: Expand the Squared Term Start by expanding the squared term: (x – 2)^2 = x^2 – 4x + 4 Now substitute this back … Read more
The first ten odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19. To find the sum of these numbers, you can simply add them together: 1 + 3 = 4 4 + 5 = 9 9 + 7 = 16 16 + 9 = 25 25 + 11 = 36 … Read more
The given function is a cubic polynomial expressed as f(x) = x3 + 3×2 + x + 3. To analyze its graph, we should look at several key features of the cubic function: End Behavior: As x approaches infinity (x → ∞), the graph goes to infinity (f(x) → ∞), and as x approaches negative … Read more
Finding Real Solutions by Graphing To find the real solutions of the quadratic equation x² + 2x + 2 = 0 through graphing, we first need to understand the basic characteristics of the parabola represented by this equation. Step 1: Understand the Equation The given equation can be rewritten in standard form, showing the values … Read more
To determine the measure of angle XYZ in circle A, we need to analyze the components involved in the circle diagram. The measure of an angle formed by two points on the circumference and a vertex at the center of the circle can often be calculated using known properties of circles. If XYZ is an … Read more
In geometry, when we refer to two adjacent angles, we are talking about two angles that share a common vertex and a common side, but do not overlap. Now, if the exterior sides of these two angles are described as opposite rays, it indicates a specific relationship between the angles. To understand this better, let’s … Read more
To find the x-intercept of the line given by the equation 2y + 5 = x, we need to determine the point where the line crosses the x-axis. The x-intercept occurs when y is equal to 0. We start by substituting 0 for y in the equation: 2(0) + 5 = x This simplifies to: … Read more
To determine how many 1 cm squares are required to construct a square that is 1 meter on each side, we first need to understand the dimensions involved. A meter is equivalent to 100 centimeters. Therefore, a square that is 1 meter (or 100 cm) on each side will have the following dimensions: Side length: … Read more
To find the equations of the tangent lines to the curve y = x^2 + 1 that are parallel to the line 2y = x + 2, we begin by determining the slope of the given line. The equation 2y = x + 2 can be rewritten in slope-intercept form (y = mx + b) … Read more