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Solving the System of Equations We start with the two equations: Equation 1: y = x² – 5x + 4 Equation 2: y = x² – 9x + 18 Since both equations are equal to y, we can set them equal to each other: x² – 5x + 4 = x² – 9x + 18 … Read more

Solving the Equation: 5x² + 4x – 9 = 0 To solve the quadratic equation 5x² + 4x – 9 = 0, we can use the quadratic formula: x = \frac{{-b \pm \sqrt{{b^2 – 4ac}}}}{{2a}}, where a, b, and c are coefficients from the equation in the form ax² + bx + c = 0. … Read more

To solve the equation if 3t = 7, we need to find the value of t first. We can do this by isolating t. Dividing both sides of the equation by 3 gives us: t = 7 / 3 or approximately t = 2.33. Now that we have the value of t, we can find … Read more

If you’re looking for the equation of a graph with its vertex at the point (3, 2), you’re likely referring to a quadratic function, which can be expressed in vertex form. The vertex form of a quadratic equation is given by: y = a(x – h)² + k In this equation, (h, k) represents the … Read more

The function f(x) = 23x is a linear function where the coefficient of x is 23. Domain The domain of a function refers to the set of all possible input values (x-values) that the function can accept. For f(x) = 23x, there are no restrictions on the value of x; you can input any real … Read more

Understanding the Expression To determine which expression is a factor of 3xy + 2x + 18y + 12, we first need to simplify and analyze the terms of the provided expression. The expression can be rearranged to facilitate factoring. Rearranging the Expression The expression can be grouped as follows: 3xy + 18y + 2x + … Read more

The prime factorization of a number involves breaking it down into the simplest factors that are prime numbers. To find the prime factorization of 50, we start by identifying the smallest prime number that divides 50. First, we notice that 50 is an even number, so we can divide it by 2: 50 ÷ 2 … Read more

To find the volume of a right triangular prism, you can use the following formula: Volume = Base Area × Height 1. **Calculate the Base Area**: Since the base of the prism is a right triangle, you need to determine the area of the triangle first. The area of a triangle can be calculated using … Read more

To analyze the expression 3 + 4i + 5 + 6i + 3 + 5 + 4i + 6i, we need to identify which property of addition is being displayed. The property that applies here is the Commutative Property of Addition. The Commutative Property states that the order in which two numbers are added does … Read more