How can you quickly determine the number of roots a polynomial will have by looking at the equation?
To quickly determine the number of roots of a polynomial, you can use the following methods: Degree of the Polynomial: The degree of a polynomial gives the maximum number of roots it can have. For example, a polynomial of degree 3 can have up to 3 roots. Real Roots vs. Complex Roots: Polynomials may have […]
Find the dimensions of a rectangle with a perimeter of 60m whose area is as large as possible
To find the dimensions of a rectangle with a perimeter of 60 meters that maximizes the area, we start with the formulas for perimeter and area. The perimeter (P) of a rectangle is given by: P = 2(l + w) where l is the length and w is the width. Given that the perimeter is […]
Find the derivative of f(x) = 10x² + 4x at x = 11
To find the derivative of the function f(x) = 10x² + 4x, we will apply the power rule of differentiation. The power rule states that if f(x) = ax^n, then f'(x) = n imes ax^{n-1}. Let’s differentiate each term of f(x): The derivative of 10x² is 2 imes 10x^{2-1} = 20x. The derivative of 4x […]
Solve the system of equations using substitution: y = 2x + 10 and y = 4x + 8
To solve the system of equations using substitution, we start with the two equations: 1. y = 2x + 10 2. y = 4x + 8 Since both equations are equal to y, we can set them equal to each other: 2x + 10 = 4x + 8 Next, we will isolate x. Start by […]
What is the missing term 10x 4×2 7x 3x 6×2?
To find the missing term in the series 10x, 4x², 7x, 3x, and 6x², we first observe the existing terms closely. We can categorize these terms based on their degrees and coefficients. 1. **Identifying the terms**: The given terms consist of: 10x (degree 1) 4x² (degree 2) 7x (degree 1) 3x (degree 1) 6x² (degree […]
Find the slope and the y-intercept of the equation y = 3x + 10
To find the slope and the y-intercept of the equation given, we first need to ensure that the equation is in the slope-intercept form, which is y = mx + b. In this form, m represents the slope and b represents the y-intercept. The equation provided is y = 3x + 10. From this equation, […]
How can we express 02353535 0235 in the form of pq where p and q are integers and q is not equal to zero?
To express the number 02353535 0235 in the form of pq where p and q are integers and q is not equal to zero, we first need to clarify the representation of the number itself. The leading zeros do not affect the numerical value, so we can treat the number as 2353535.235. Now, we can […]
What happens when a race car is traveling on a straight track at a velocity of 80 meters per second?
When a race car is traveling at a velocity of 80 meters per second on a straight track, it is maintaining a constant speed in a forward direction. This velocity indicates how quickly the car is moving, and it reflects the distance the car covers over a unit of time. In practical terms, this means […]
At what points will the line y = x intersect the unit circle x² + y² = 1?
To find the intersection points between the line defined by the equation y = x and the unit circle defined by x² + y² = 1, we can substitute the line’s equation into the circle’s equation. Substituting y = x into x² + y² = 1 gives us: x² + (x)² = 1 This simplifies […]
How do I graph a relation and its inverse using open circles?
To graph a relation and its inverse, you first need to understand what the relation and its inverse represent. A relation typically consists of pairs of input values (x) and output values (y). The inverse of this relation swaps these x and y values. Here’s a step-by-step guide: Plot the original relation: Start by plotting […]