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To find the rate of change for this running situation, we need to calculate the distance covered per unit of time. Initially, you ran 3 miles in 1 hour. This gives us a rate of: Rate for first segment = Distance / Time = 3 miles / 1 hour = 3 miles per hour Next, … Read more

To simplify the expression 15x² + 24x + 9 + 3x + 3, you need to combine like terms. 1. **Identify like terms**: In the expression, the terms can be categorized as follows: Quadratic term: 15x² Linear terms: 24x and 3x Constant terms: 9 and 3 2. **Combine the linear terms**: Add the coefficients of … Read more

Understanding the Relationship Between the Ladder, Wall, and Angle Imagine a ladder that is 10 feet long leaning against a vertical wall. The angle at which the ladder touches the wall is represented by the Greek letter theta (θ). If we let x denote the horizontal distance from the base of the ladder to the … Read more

To determine how many solutions the given linear system has, we need to analyze the two equations: First Equation: y = 5x + 1 Second Equation: 15x + 3y = 3 Now, let’s substitute the first equation into the second equation to see if we can find any values of x and y: Substituting for … Read more

To find the remainder when a polynomial is divided by a linear expression, we can use the Remainder Theorem. According to this theorem, the remainder of a polynomial f(x) when divided by x – k is simply f(k). In this case, we want to find the remainder of the polynomial f(x) = x^3 + 14x^2 … Read more

To solve for f(12) given that f(log3 x) = 1, we first need to determine the value of x such that log3 x can be related to 12. The equation states that f applied to log3 x yields a result of 1. We need to express log3 x such that we can evaluate it at … Read more

To find the prime factorization of 40, we begin by identifying the smallest prime number that can divide it, which is 2. We can repeatedly divide the number by 2 until it can no longer be divided evenly. First division: 40 ÷ 2 = 20 Second division: 20 ÷ 2 = 10 Third division: 10 … Read more

To solve the equation 6x² – 150 = 0 by factorization, we’ll follow these steps: Step 1: Simplify the equation. Notice that both terms in the equation can be factored by 6, which is a common factor: 6x² – 150 = 0 can be rewritten as 6(x² – 25) = 0. Step 2: Factor the … Read more

When rolling two six-sided number cubes (or dice), each die has six faces showing numbers from 1 to 6. To determine the odds of rolling a total sum of seven, we first need to identify all the possible combinations of the two dice that yield this result. Here are the favorable outcomes that give a … Read more