How does the graph of g(x) = 3x² compare to the graph of f(x) = 3x?
The graphs of g(x) = 3x² and f(x) = 3x represent different types of functions that exhibit distinct behaviors and shapes. Firstly, g(x) = 3x² is a quadratic function. Its graph is a parabola that opens upwards. The vertex of this parabola is at the origin (0, 0), and as x moves away from 0 […]
What is the x value such that y = 15 – 3x and y = 0?
To find the value of x when y is equal to 0, we can start by setting the equation y = 15 – 3x to zero: 0 = 15 – 3x Next, we will solve for x. We can rearrange the equation: 3x = 15 Now, divide both sides by 3: x = 15 / […]
In Quadrilateral PQRS Below, Sides PS and QR are Parallel. For What Value of X?
To determine the value of x in quadrilateral PQRS, where sides PS and QR are parallel, we can apply the properties of transversals and parallel lines. When two lines are parallel, any line that intersects them creates pairs of angles that are either corresponding, alternate interior, or consecutive interior angles. If we assume we have […]
If 10 of x is 20, what is 23 of x?
To figure out what 23 of x is, we first need to find the value of x from the statement that 10 of x is 20. We can set up an equation based on this information: 10x = 20 Now, we need to isolate x. We do this by dividing both sides of the equation […]
What is the first step when rewriting y = 3x^2 + 9x + 18 in the form y = a(x – h)^2 + k?
The first step in rewriting the quadratic equation y = 3×2 + 9x + 18 into the vertex form y = a(x – h)2 + k is to factor out the coefficient of x2 from the quadratic and linear terms. In this case, we start with the equation: y = 3×2 + 9x + 18 […]
How do you divide a fraction by a fraction?
Dividing a fraction by another fraction may seem tricky at first, but it’s quite simple once you understand the process. To divide a fraction by a fraction, you need to follow these steps: Flip the second fraction: Take the fraction you are dividing by and flip it. This means you take the reciprocal of that […]
Determine the points at which the graph of the function has a horizontal tangent line f(x) = x² + x + 8
To find the points where the graph of the function f(x) = x² + x + 8 has a horizontal tangent line, we first need to calculate the derivative of the function. The derivative, f'(x), represents the slope of the tangent line at any point on the graph. 1. Calculate the derivative: Using the power […]
How do you simplify the expression (1/9 – 1/x) / (1/81 – 1/x²)?
To simplify the expression (1/9 – 1/x) / (1/81 – 1/x²), we will first rewrite the fractions with a common denominator. Starting with the numerator: The common denominator between 9 and x is 9x. So we rewrite 1/9 as (x)/(9x) and 1/x as (9)/(9x). This gives us: 1/9 – 1/x = (x – 9)/(9x) Now, […]
What is the slope of a line that passes through the points (20, 30) and (40, 14)?
The slope of a line that passes through two points can be calculated using the formula: slope (m) = (y2 – y1) / (x2 – x1) In this case, we have the points (20, 30) and (40, 14). We can assign these points as follows: (x1, y1) = (20, 30) (x2, y2) = (40, 14) […]
If tanh(x) = 5/13, find the values of the other hyperbolic functions at x
To find the values of the other hyperbolic functions given that tanh(x) = 5/13, we can utilize the definitions of the hyperbolic functions in terms of ex. The hyperbolic functions are defined as follows: sinh(x) = (ex – e-x) / 2 cosh(x) = (ex + e-x) / 2 tanh(x) = sinh(x) / cosh(x) From the […]