In the XY Plane, the Graph of y = x² and the Circle with Center (0, 1) and Radius 3 Have How Many Points of Intersection?
To find the points of intersection between the graph of the quadratic equation y = x² and the circle centered at (0, 1) with a radius of 3, we need to set up the equations. The equation of the circle can be expressed as: (x – 0)² + (y – 1)² = 3² Which simplifies […]
Find an equation in standard form for the hyperbola with vertices at (0, 2) and foci at (0, 11)
To find the equation of a hyperbola in standard form, we start by identifying key values like the center, vertices, and foci based on the given information. 1. **Identify the Center**: The vertices of the hyperbola are at (0, 2) and since hyperbolas are symmetric, the center is the midpoint between the vertices. The distance […]
What is the length of aj if ab ii jk 8 in 875 in 1025 in 14 in?
To determine the length of aj given the relationships and values stated, we need to clarify the context. However, based on the notation provided, it appears that you are working with segments or lines where certain measurements are provided. If ab is parallel to jk and the lengths of segments are mixed with letters and […]
How do you use the substitution method to solve the system of equations 4x + y = 3 and 7x + 9y = 2?
To solve the system of equations using the substitution method, we’ll first rewrite one of the equations to express one variable in terms of the other. Let’s take the first equation: 4x + y = 3 We can isolate y: y = 3 – 4x Now we have y expressed in terms of x. Next, […]
Two thirds of a number reduced by 11 is equal to 4 more than the number. Find the number.
Let’s denote the unknown number as x. According to the problem, two thirds of the number reduced by 11 is equal to 4 more than the number. We can express this as an equation: \( \frac{2}{3}x – 11 = x + 4 \) Now, we’ll solve this step by step: First, we can isolate the […]
If 23 xy then which of the following must be true?
To determine which statement must be true given that the product of 23 and another variable xy is a valid mathematical expression, we first need to understand what this statement implies. Starting with the equation, if 23 * xy is a valid expression, then it means that xy must also yield a finite and defined […]
What is the correct sum of the polynomials 4x³ + 2x + 9 and 2x³ + 5x + 3?
To find the correct sum of the given polynomials, we need to add them together by combining like terms. The polynomials provided are: 4x³ + 2x + 9 2x³ + 5x + 3 Now, let’s add them step by step: Combine the x³ terms: 4x³ + 2x³ = 6x³ Combine the x terms: 2x + […]
How do we find the Taylor series centered at c for the function f(x) = 1 / (x – c + 1)?
To find the Taylor series centered at c for the function f(x) = 1 / (x – c + 1), we need to start by using the definition of a Taylor series. The Taylor series of a function f(x) centered at c is given by: T(x) = f(c) + f'(c)(x – c) + f”(c)(x – […]
If f(x) = 3x^2 + 1 and g(x) = 1 – x, what is the value of f(g(2))?
To find the value of f(g(2)), we need to evaluate g(2) first and then use that result to find f. First, let’s compute g(2): g(2) = 1 – 2 = -1 Now that we have g(2) = -1, we will substitute this into f: f(-1) = 3(-1)^2 + 1 Calculating this, we have: f(-1) = […]
In a triangle ABC, if 3 angle A, 4 angle B, and 6 angle C, calculate the angles.
To find the angles A, B, and C in triangle ABC, we start with the information given: 3 angle A, 4 angle B, and 6 angle C. We can express these in a mathematical form: Let angle A = 3x, angle B = 4x, and angle C = 6x. According to the triangle angle sum […]