How do you solve the system of equations 5x + 2y = 10 and 3x + 2y = 6 algebraically?
To solve the system of equations algebraically, we start by writing down the equations: Equation 1: 5x + 2y = 10 Equation 2: 3x + 2y = 6 Next, we can eliminate one of the variables by subtracting one equation from the other. Let’s subtract Equation 2 from Equation 1: (5x + 2y) – (3x […]
What is the equation in the standard form of a parabola that contains the following points: (2, 18), (0, 2), (4, 42)?
To find the equation of a parabola in standard form, which is typically expressed as y = ax^2 + bx + c, we can use the given points to create a system of equations. We have three points: (2, 18), (0, 2), and (4, 42). We can substitute these points into the standard form equation […]
Based on the graph, what are the approximate solutions to the equation 3x + 8 = 025x?
To find the approximate solutions to the equation 3x + 8 = 025x, we first need to simplify the equation. However, it looks like there might be a typo in the equation since ‘025x’ is unusual. Typically, it should be something like ’25x’ or a similar term. Assuming it was intended to be ’25x’, we […]
How to Find an Equation for the Line Perpendicular to the Tangent Line to the Curve y = x³ + 4x + 1 at the Point (2, 1)
To find an equation for the line perpendicular to the tangent line to the given curve at the specified point, we can follow these steps: Find the derivative of the curve: The first step is to calculate the derivative of the curve, which will give us the slope of the tangent line at any point […]
The jogging track is a mile long. If Ashley jogged around it 4 times, how far did she run?
To determine how far Ashley ran, we need to multiply the distance of the jogging track by the number of times she jogged around it. Since the track is 1 mile long and Ashley jogged around it 4 times, we can do the math as follows: Distance = Length of track × Number of laps […]
What is the equation of the line in slope intercept form that passes through (3, 1) and (1, 5)?
To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b) of the line that passes through the two given points. The two points are (3, 1) and (1, 5). We can calculate the slope using the formula: m […]
Find the Value of x and Measure the Exterior Angle of the Given Triangle
To find the value of x in a triangle, we typically rely on the properties of angles and the relationships in different types of triangles. Let’s consider a triangle where we have two known angles, and we’re trying to find the value of an unknown angle, denoted as x. In any triangle, the sum of […]
How do you simplify the expression 2x + 63x² + 3x + 6?
To simplify the expression 2x + 63x² + 3x + 6, we need to combine like terms. First, let’s identify the like terms in the expression: 2x
Rewrite fx = 2x^2 + 12x + 3 from Vertex Form to Standard Form
To rewrite the quadratic function from vertex form to standard form, we first need to understand what vertex form looks like. Vertex form of a quadratic function is generally expressed as: f(x) = a(x – h)² + k where (h, k) is the vertex of the parabola. In this case, your function is f(x) = […]
How many zeros does the function f(x) = 7x^13 + 12x^9 + 16x^5 + 23x + 42 have?
To determine how many zeros the function f(x) = 7×13 + 12×9 + 16×5 + 23x + 42 has, we need to analyze the behavior of the polynomial. This function is a polynomial of degree 13, which tells us that it can have a maximum of 13 real roots (or zeros) according to the Fundamental […]