How do you find the inverse of the function f(x) = 3x^2 + 4 when x = 2?
To find the inverse of the function f(x) = 3x² + 4, we start by replacing f(x) with y: y = 3x² + 4 Next, we solve this equation for x in terms of y: Subtract 4 from both sides: y – 4 = 3x² Divide by 3: (y – 4)/3 = x² Take the […]
How to Solve for x in the Equation 32x = 6 + 12?
To solve the equation 32x = 6 + 12, we first need to simplify the right side of the equation. Step 1: Combine the terms on the right side. 6 + 12 = 18 This gives us the simplified equation: 32x = 18 Step 2: Now, we want to isolate the variable x. To do […]
If px = 2x^3 + 3x^2 + 4x, then what is p(1)?
To find p(1), we start by substituting x with 1 in the polynomial px. Let’s plug in the value: px = 2(1)^3 + 3(1)^2 + 4(1) This simplifies to: px = 2(1) + 3(1) + 4(1) Now, calculating each term: px = 2 + 3 + 4 Adding these values together gives: px = 9 […]
What is the smallest 5-digit number exactly divisible by 41?
The smallest 5-digit number is 10000. To find the smallest 5-digit number that is exactly divisible by 41, we need to divide 10000 by 41 and round up to the nearest whole number. First, perform the division: 10000 ÷ 41 ≈ 243.9024 Now, we round this up to the next whole number, which is 244. […]
If A = B and E = F, what is the value of Y?
This question seems to involve algebraic expressions or equations, but it’s not clear how Y connects to A, B, E, and F without more context. In algebra, we often define variables in relation to one another, and equations help us solve for unknowns. To determine the value of Y, we need to understand the relationship […]
Enter the correct value so that each expression is a perfect square trinomial x² + 10x
To make the expression x² + 10x a perfect square trinomial, we need to find a value that can be added to complete the square. A perfect square trinomial takes the form (x + a)², which expands to x² + 2ax + a². In our case, we have: Here, the coefficient of x is 10, […]
What is the solution to the following system of equations: y = x² – 5x + 4 and y = x² – 9x + 18?
To solve the system of equations given by: 1. y = x² – 5x + 4 2. y = x² – 9x + 18 We can set the equations equal to each other since both expressions are equal to y. x² – 5x + 4 = x² – 9x + 18 Next, we can eliminate […]
Find the Equation of the Least Squares Regression Line If x̄ = 20, sₓ = 2, ȳ = 10, sᵧ = 4, r = 0.2
To find the equation of the least squares regression line, we use the formula: y = a + bx where: b is the slope of the regression line a is the y-intercept The slope b is calculated using the formula: b = r * (sᵧ / sₓ) Let’s substitute the values: r = 0.2 sᵧ […]
Point O is the Incenter of Triangle ABC. What is m∠QOB – 30°, 60°, 75°, or 90°?
To determine the measure of angle m∠QOB where O is the incenter of triangle ABC, we first need to understand the properties of the incenter. The incenter is the point where the angle bisectors of a triangle meet, and it is equidistant from all sides of the triangle. Let’s denote the angles of triangle ABC […]
Find the roots of f(x) = x^2 – 62x + 22
To find the roots of the quadratic function f(x) = x² – 62x + 22, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a In this function, the coefficients are: a = 1 b = -62 c = 22 Firstly, we calculate the discriminant: b² – 4ac = (-62)² […]