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To find the average rate of change of a function over a given interval, you can use the formula: Average Rate of Change = (f(b) – f(a)) / (b – a) In this case, we are looking at the function y = 2e^x over the interval from x = 0 to x = 2. Here, … Read more

To find the quotient of the expression 2x² + 10x + 12 divided by 3, we start by simplifying the expression. The expression can be split into three parts, each divided by 3: The first term: (2x²) / 3 The second term: (10x) / 3 The third term: (12) / 3 Now we simplify each … Read more

To apply the Law of Cosines for finding the length of a side in a triangle, you need to know: The lengths of the other two sides of the triangle. The measure of the angle between those two sides. In mathematical terms, if you wish to find the length of side c in triangle ABC, … Read more

To find an expression that is a factor of the terms 3ab, 6a, 4b, and 8, we need to determine the greatest common factor (GCF) of these terms. Let’s analyze each term: 3ab has factors of 3, a, and b. 6a has factors of 6 and a. 4b has factors of 4 and b. 8 … Read more

To determine which of the given numbers is the largest, we need to calculate the value of each expression. 1. **72 x 106**: – This equals 72,000,000. 2. **309 x 103**: – This equals 309,000. 3. **204 x 104**: – This equals 2,040,000. 4. **5 x 103**: – This equals 5,000. Now let’s compare the … Read more

Solving the Equation: 3x² = 18 To solve the equation 3x² = 18, follow these steps: Isolate x²: First, we need to get x² by itself on one side of the equation. To do this, divide both sides by 3: x² = 18 / 3 This simplifies to: x² = 6 Take the Square Root: … Read more

To find the greatest common factor (GCF) of the polynomial terms 44×6 and 8×5, we need to find the GCF of the numerical coefficients and the GCF of the variable parts. Step 1: Finding the GCF of the Numerical Coefficients The numerical coefficients we have are 44 and 8. To find the GCF of these … Read more

To determine how many solutions the system of equations y = 3.5x and y = 3.5x has, we need to analyze the equations carefully. First, let’s rewrite the equations for clarity: Equation 1: y = 3.5x Equation 2: y = 3.5x Now, you might notice that both equations are exactly the same. This means that … Read more

To find the exact value of tan(7π/8), we can use the half-angle identity for tangent. The half-angle identity states that: tan(θ/2) = ±√((1 – cos(θ)) / (1 + cos(θ))) In our case, we can express 7π/8 as 7π/8 = π – π/8. This allows us to rewrite the tangent function: tan(7π/8) = tan(π – π/8) … Read more

To express the number 30 as a fraction, you can follow a simple approach. A whole number can always be represented as a fraction by placing it over 1. This is because any number divided by 1 is itself. Therefore, you can write: 30 = 30/1 This shows that 30 as a fraction is 30/1. … Read more