devyy

To solve the original inequality 3x + 5 < 10, we first isolate x. 1. Start by subtracting 5 from both sides of the inequality: 3x + 5 – 5 < 10 – 5 3x < 5 2. Next, we divide both sides by 3 to isolate x: x < rac{5}{3} So far, we have … Read more

Finding the Vertex of the Parabola The equation of the parabola is given as: y = x² + 6x + 2 To find the vertex of a parabola represented by a quadratic equation in the standard form y = ax² + bx + c, we can use the formula for the x-coordinate of the vertex: … Read more

To express the functions cos(1/x) and tan(1/y) solely in terms of x and y, we start by breaking each function down to understand their dependencies on the variables. 1. **Understanding the Functions**: The cosine function cos(1/x) involves the variable x. Here, 1/x transforms the input, with x influencing the angle in radians that the cosine … Read more

To find the two numbers based on the conditions provided, we can set up a system of equations: Let x be the first number. Let y be the second number. The two conditions specified can be expressed as: x + y = 30 (the sum of the two numbers is 30) x – y = … Read more

To find the remainder of the polynomial p(x) = x^4 + 9x^3 + 5x^2 + 3x + 4 when it is divided by (x – 3), we can apply the Remainder Theorem. The Remainder Theorem states that for any polynomial f(x), the remainder of the division of f(x) by (x – c) is equal to … Read more

Finding the Function f To find the function f such that f(x) = 5x^3 and the line 5x + y = 0 is tangent to the graph of f, we will go through a series of steps involving calculus and geometric interpretations. Understanding the Tangent Line The equation of the line can be rewritten in … Read more

To solve the equation x × 52 × 81, we start by simplifying the expression. First, let’s consider the product of 52 and 81: 52 × 81 = 4212 This means, we can rewrite the equation as: x × 4212 = 0 To find the values of x that satisfy this equation, we can isolate … Read more

To determine the constant of variation k in the direct variation equation y = kx, you can use the coordinates of the point provided. In this case, the point is (5, 8), where: x = 5 y = 8 Now, substitute these values into the equation: y = kx Replacing y and x with their … Read more

To solve the equation 2 + 3i + x + yi = 6, we will start by isolating the variables. First, we rewrite the equation: Rearranging gives us: x + yi = 6 – (2 + 3i) This simplifies to: x + yi = 4 – 3i Now we can separate the real part and … Read more

To find two consecutive negative integers whose product equals 600, we can start by defining the two integers. Let the first integer be x. Since they are consecutive, the second integer will be x + 1. Given that the product of these integers is 600, we can set up the equation: x * (x + … Read more