Understanding the Distributive Property The distributive property is a fundamental principle in mathematics that describes how to multiply a number by a sum or difference. In simpler terms, it states that you can distribute a multiplication operation over addition or subtraction. This property is typically expressed with the formula: a × (b + c) = … Read more
To find the dimensions of a box with a square base and an open top that has a volume of 32,000 cm³ while minimizing the surface area (and thus the amount of material used), we can follow these steps: Step 1: Define the Variables Let the length of one side of the square base be … Read more
To find the approximate solutions of the quadratic equation 2x² + 7x + 3 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / (2a) In this equation, a = 2, b = 7, and c = 3. Let’s first calculate the discriminant (b² – … Read more
Solution to the System of Equations We are given the two equations: y = 3x + 10 2x + y = 4 To find the solution, we will use the substitution method: Step 1: Substitute y in the second equation We can substitute the expression of y from the first equation into the second equation: … Read more
To find the y-value of the vertex of the quadratic function f(x) = x^2 – 3x + 11, we first need to identify the vertex using the standard formula for a quadratic equation in the form of f(x) = ax^2 + bx + c, where: a = coefficient of x2 b = coefficient of x … Read more
To solve the system of equations: First, we have the two equations: Equation 1: 2x + y = 7 Equation 2: y = 2x + 3 We can substitute Equation 2 into Equation 1. Replace y in Equation 1 with 2x + 3: 2x + (2x + 3) = 7 Simplifying this gives: 2x + … Read more
Solving the System of Equations We have a system of two equations: y = 2×2 y = 3x + 1 To solve for x and y, we can set the two equations equal to each other because they both equal y: 2×2 = 3x + 1 Next, we will rearrange the equation to bring all … Read more
To calculate 3 x 100 using the rules for multiplication by powers of 10, we can first recognize that 100 is a power of 10. In fact, 100 can be expressed as 102, since it represents 10 multiplied by itself. Now, when we multiply a number by a power of 10, we can simply shift … Read more
To find the standard form of the equation of a hyperbola given its foci and vertices, we will first identify the key characteristics of the hyperbola based on the information provided. The foci of the hyperbola are at (0, 8) and (0, -8), while the vertices are at (0, 6) and (0, -6). This indicates … Read more
To find all the roots of the function f(x) = 5×3 + 5×2 + 170x + 280 given that x – 7 is a factor, we will use the Remainder Theorem and polynomial division. According to the Remainder Theorem, if (x – c) is a factor of f(x), then f(c) = 0. Since we know … Read more