To evaluate the function f(x) = 2x² + 3x + 5 for the input value of 3, you need to substitute 3 in place of x in the function. Here are the steps to do so: Substitute 3 for x in the function: f(3) = 2(3)² + 3(3) + 5 Now, calculate the value of … Read more
To find the point on the line y = 3x + 4 that is closest to the origin (0,0), we can use a method involving distance minimization. The distance D from any point (x, y) on the line to the origin can be calculated using the distance formula: D = √(x2 + y2) Since y … Read more
To determine the slope of a line given two points, you can use the slope formula: Slope (m) = (y2 – y1) / (x2 – x1) In our case, we have two points: (3, 0) and (2, 7). Here are the coordinates: Point 1 (x1, y1) = (3, 0) Point 2 (x2, y2) = (2, … Read more
To find the value of f(g(144)), we will first need to evaluate g(144) and then use that result to evaluate f. 1. Start with the function g(x) = 2x. We will substitute 144 for x: g(144) = 2 * 144 This gives us: g(144) = 288 2. Next, we’ll plug this result into the function … Read more
To find the remainder when the polynomial x3 + 6×2 + 42x + 79 is divided by x – 5, we can use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) when divided by x – c is equal to f(c). In our case, we will substitute c = 5 … Read more
To find the missing coefficient of the x term of the product of x and 52, we first need to express the product mathematically. The product can be represented as: x * 52 When we perform the multiplication, we distribute x over 52. This results in: 52x Now, in this expression, 52x, the coefficient of … Read more
To verify the equation 54 ÷ 9 = 6, we can use the inverse operation of division, which is multiplication. In this case, to check the validity of the equation, we can multiply the result of the division (which is 6) by the divisor (which is 9). So, we compute: 6 * 9 = 54 … Read more
To find the area of a rectangle when you know its width and the length of its diagonal, you can use the Pythagorean theorem. The formula states that for a right triangle formed by the width, length, and diagonal, the square of the diagonal (hypotenuse) equals the sum of the squares of the other two … Read more
The function you are referring to is f(x) = x² + 1, which is a quadratic function. When we talk about the axis of symmetry for a quadratic function, we are looking for a vertical line that passes through the vertex of the parabola described by the function. To identify the axis of symmetry mathematically, … Read more
To find the equation of a line that passes through a specific point and has an undefined slope, we first need to understand what an undefined slope signifies. In mathematics, an undefined slope occurs when the line is vertical. This means that the x-coordinate of any point on the line remains constant, while the y-coordinate … Read more