If f(x) = 3x² and g(x) = 2x², what is f(g(x))?
To find f(g(x)), we first need to substitute g(x) into f(x). Given the functions: f(x) = 3x² g(x) = 2x² Now, let’s substitute g(x) into f(x): f(g(x)) = f(2x²) Now, replace x in f(x) with 2x²: f(g(x)) = 3(2x²)² Next, we calculate (2x²)²: (2x²)² = 4x⁴ Now, we substitute this back into the equation: f(g(x)) […]
What is the slope for the line perpendicular to the line shown in the graph?
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. To find the slope of the original line, you first need to identify its slope from the graph. The slope (m) is typically represented as the ratio of the vertical change to the horizontal change […]
If 10x = 2, what is the value of 2x?
To solve for the value of 2x given that 10x = 2, we need to isolate x first. Start with the equation: 10x = 2 Now, divide both sides of the equation by 10: x = 2 / 10 x = 0.2 Now that we have the value of x, we can find 2x by […]
Choose the Correct Simplification of the Expression 5xy² · 5y³
To simplify the expression 5xy² · 5y³, we start by applying the rules of multiplication for like bases. First, multiply the coefficients: 5 (from the first term) and 5 (from the second term): 5 × 5 = 25 Next, combine the variables: For y, we have y² and y³. Using the rule of exponents (which […]
How to Find the 3 Quartiles in a Given Data Set?
To find the quartiles in the data set 55, 55, 59, 60, 62, 65, 64, we first need to arrange the numbers in ascending order. After sorting the data, we have: 55, 55, 59, 60, 62, 64, 65. The quartiles divide the data into four equal parts. To find them, follow these steps: First Quartile […]
What is the first step of the following division problem 8×3 x2 6x 7 2x 1?
To solve the division problem represented as 8x³ ÷ 2 ÷ 6x ÷ 7 ÷ 2x ÷ 1, the first step is to simplify the expression by addressing the first division operation. In this case, we begin by dividing 8x³ by 2. When you divide 8x³ by 2, you proceed as follows: 8 ÷ 2 […]
Which graph can be used to find the solutions to x² + 4x + 4 – 2x – 1 = 0?
To find the solutions to the equation x² + 4x + 4 – 2x – 1 = 0, we first simplify the equation. This can be rewritten as: x² + (4 – 2)x + (4 – 1) = 0 x² + 2x + 3 = 0 This is a quadratic equation of the form ax² […]
Consider Circle T with Radius 24 in and Central Angle 8 5π/6 Radians. What is the Length of Minor Arc SV?
To find the length of the minor arc SV in circle T, we can use the formula for arc length, which is: Arc Length = r * θ Where r is the radius of the circle and θ is the central angle in radians. In this case, the radius r is 24 inches, and the […]
Which statement best describes how to determine whether f(x) = x^4 + x^3 is an even function?
To determine if the function f(x) = x^4 + x^3 is an even function, you need to check the condition for evenness. A function is considered even if: f(-x) = f(x) for all x in the domain of the function. Let’s evaluate f(-x): f(-x) = (-x)^4 + (-x)^3 This simplifies to: f(-x) = x^4 – […]
What is the radius and volume of a cylindrical vessel with a circumference of 132 cm and height of 25 cm?
To find the radius and volume of the cylindrical vessel, we will use the given circumference and height along with the formula for the volume of a cylinder. i. Finding the Radius The formula for the circumference (C) of a cylinder is given by: C = 2 × π × r Where: C = Circumference […]