If f(x) = x³, which of the following describes the graph of f(x) = 2?
The graph of f(x) = 2 is a horizontal line that crosses the y-axis at the point (0, 2). This means that no matter what value of x you choose, the output of the function will always be 2. Unlike the original graph of f(x) = x³, which has a distinct curve that rises steeply […]
Find the value of the greater root of x² + 13x + 12 = 0
To find the greater root of the quadratic equation x² + 13x + 12 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a Here, the coefficients are: a = 1 b = 13 c = 12 Now, we need to calculate the discriminant (b² – 4ac): b² […]
If the discriminant of an equation is positive, which of the following is true of the equation?
When the discriminant of a quadratic equation (given in the form ax² + bx + c = 0) is positive, it indicates that the equation has two distinct real roots. This is derived from the quadratic formula: x = (-b ± √(D)) / (2a) where D is the discriminant, calculated as D = b² – […]
Factor 26r3s + 52r5 + 39r2s4: What is the Resulting Expression?
To factor the expression 26r3s + 52r5 + 39r2s4, we first look for the greatest common factor (GCF) of the coefficients and the variables in each term. The coefficients are 26, 52, and 39. The GCF of these numbers is 13. Now let’s identify the variables: The first term has r3s. The second term has […]
Using the Quadratic Formula to Solve x² – 2x – 20: What Are the Values of x?
To find the values of x for the equation x² – 2x – 20 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a) In this equation, a, b, and c are the coefficients from our standard quadratic equation ax² + bx + c = 0. For our […]
What are the odds of rolling two number cubes and getting a sum of seven?
To determine the odds of rolling two number cubes (commonly known as dice) and achieving a sum of seven, we first need to assess the total number of possible outcomes when rolling two dice. Each die has six faces, so when rolling two dice, the total number of potential outcomes is 6 x 6, which […]
A car traveling with constant speed travels 150km in 7200s what is the speed of the car?
To find the speed of the car, we can use the formula for speed, which is defined as the distance traveled divided by the time it takes to travel that distance. In this case, the distance is 150 kilometers and the time is 7200 seconds. Before we proceed, it’s helpful to convert the distance to […]
How many real number solutions are there to the equation 0 = 3x² + x + 4?
To solve the equation 0 = 3x² + x + 4, we can analyze the quadratic equation in the standard form ax² + bx + c. Here, a = 3, b = 1, and c = 4. To determine the number of real solutions, we can use the discriminant, which is given by the formula […]
Find the Arc Length Function for the Curve with Starting Point y=2x^3 and Starting Point P(0,12)
To find the arc length function for the curve defined by the equation y = 2x^3, we use the arc length formula: S = ∫√(1 + (dy/dx)²) dx Firstly, we need to compute the derivative of y with respect to x: dy/dx = d(2x^3)/dx = 6x² Now, we can substitute this expression into the arc […]
What is the prime factorization of 40?
The prime factorization of 40 is 2 × 2 × 2 × 5, or written in exponential form, it is 23 × 5. To arrive at this, we need to break down 40 into its prime factors. We start by dividing 40 by the smallest prime number, which is 2: 40 ÷ 2 = 20 […]