To factor the quadratic expression 8x² + 13x + 6, we follow a systematic approach: Identify the coefficients: In the expression ax² + bx + c, we have: a = 8 b = 13 c = 6 Multiply a and c: We calculate: 8 (from a) * 6 (from c) = 48 Find two numbers … Read more
Finding the Maclaurin Series for f(x) = cos(x2) The Maclaurin series is a special case of the Taylor series centered at 0. To find the Maclaurin series for the function f(x) = cos(x2), we first recall the Taylor series expansion for cosine: cos(x) = ∑n=0∞ rac{(-1)nx2n}{(2n)!} Now, by substituting x2 for x, we get: cos(x2) … Read more
Finding the Vertex of a Parabola The vertex of a parabola described by the quadratic equation in the form of y = ax² + bx + c can be found using the vertex formula: x
To solve the system of linear equations: Equation 1: 2x + 3y = 3 Equation 2: 7x + 3y = 24 We can use either the substitution method or the elimination method. Here, we’ll use the elimination method. Step 1: Align the equations We start with the two equations: 2x + 3y = 3 (1) … Read more
To find the standard form of the equation of a line given a point and a slope, we start by using the point-slope form of the equation, which is given by: y – y1 = m(x – x1) Here, (x1, y1) is the point on the line (in this case, (1, 2)), and m is … Read more
Solving the Equation Let’s start by simplifying and solving the equation step by step: Given Equation: 3x + 5 = 2x + 4x + 2 + 5x Combine like terms: On the right side, combine the terms: 2x + 4x + 5x = 11x Now the equation looks like this: 3x + 5 = 11x … Read more
To solve the inequality 5x + 2x < 4, we can start by simplifying the expression on the left-hand side. First, we combine like terms: 5x + 2x = 7x So, the inequality now reads: 7x < 4 Next, we will solve for x by dividing both sides of the inequality by 7: x < … Read more
Factoring the Polynomial To factor the polynomial 27x²y + 43xy², we first look for common factors in the terms. The given polynomial consists of two terms: 27x²y 43xy² In both terms, we can observe that the variable xy is common. Thus, we will factor xy out: 1. Identify the common factor: xy 2. Rewrite each … Read more
To solve the quadratic equation x² + 12x + 11 = 0 by completing the square, follow these steps: Move the constant to the other side: Start by isolating the x² and 12x terms: x² + 12x = -11 Complete the square: To complete the square, take half of the coefficient of x: 12. Half … Read more
To solve the quadratic equation 4x² + 22x + 36 = 0, we can use the quadratic formula: x = \frac{-b \pm \sqrt{b² – 4ac}}{2a} Where a, b, and c are the coefficients from the equation in the form ax² + bx + c = 0. In our equation: a = 4 b = 22 … Read more