How do you find the slope of a line using the coordinates of two points?To find the slope of a line using the coordinates of two points, use the formula: slope (m) = (y2 – y1) / (x2 – x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. This formula calculates the change in the y-coordinates divided by the change in the x-coordinates.
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What is the derivative of the function f(x) = 3x^2 + 2x + 1 with respect to x?
What is the derivative of the function f(x) = 3x^2 + 2x + 1 with respect to x?The derivative of the function f(x) = 3x^2 + 2x + 1 with respect to x is found by applying the power rule. The derivative f'(x) = d/dx (3x^2) + d/dx (2x) + d/dx (1) results in f'(x) = 6x + 2.
What is the value of x if 3(x + 2) = 18?
What is the value of x if 3(x + 2) = 18?To find the value of x, first divide both sides by 3 to get x + 2 = 6. Then, subtract 2 from both sides to obtain x = 4.
How do you solve a system of linear equations using the matrix method (Gauss-Jordan elimination)?
How do you solve a system of linear equations using the matrix method (Gauss-Jordan elimination)?To solve a system of linear equations using the Gauss-Jordan elimination method, first express the system in matrix form as an augmented matrix. Then, perform row operations to transform the matrix into reduced row echelon form (RREF). Once in RREF, the solutions to the system can be read directly from the matrix.
How do you calculate the greatest common factor (GCF) of two numbers?
How do you calculate the greatest common factor (GCF) of two numbers?To calculate the greatest common factor (GCF) of two numbers, list their factors, find the common factors, and select the largest one. Alternatively, use the Euclidean algorithm: divide the larger number by the smaller one, then replace the larger number with the remainder. Repeat until the remainder is zero; the last non-zero remainder is the GCF.
How do you solve the equation $2x + 3 = 7$ and find the value of x?
How do you solve the equation 2x + 3 = 7 and find the value of x?To solve the equation 2x + 3 = 7, first subtract 3 from both sides to get 2x = 4. Then, divide both sides by 2 to find x = 2.
What is the derivative of the function f(x) = x^2 + 3x + 2?
What is the derivative of the function f(x) = x^2 + 3x + 2?The derivative of the function f(x) = x^2 + 3x + 2 is found using basic differentiation rules. The derivative of x^2 is 2x, the derivative of 3x is 3, and the derivative of a constant (2) is 0. Therefore, f'(x) = 2x + 3.
How do you use the method of Lagrange multipliers to find local maxima and minima of a multivariable function subject to a constraint?
How do you use the method of Lagrange multipliers to find local maxima and minima of a multivariable function subject to a constraint?The method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints. This method introduces an auxiliary function called the Lagrangian, which incorporates the original function and the constraint using a new variable called the Lagrange multiplier. By solving the system of equations formed by the partial derivatives of the Lagrangian, one can find the critical points that potentially represent the local maxima or minima of the original function under the given constraint.
How do you solve a system of equations with fractions and decimals in Prealgebra?
How do you solve a system of equations with fractions and decimals in Prealgebra?To solve a system of equations with fractions and decimals in Prealgebra, first convert all fractions to decimals or all decimals to fractions for consistency. Then, use methods like substitution or elimination to solve the system. Simplify your final answers.
What is the difference between a scalar and a vector, and can you provide an example of each?
What is the difference between a scalar and a vector, and can you provide an example of each?A scalar is a quantity with only magnitude, such as temperature (e.g., 25°C). A vector has both magnitude and direction, such as velocity (e.g., 60 km/h north). Scalars are described by a single number, while vectors require multiple components to describe their direction and magnitude.
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