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To eliminate the parameter from the equations involving variables such as x, y, and t, we first start by understanding how these expressions relate to each other. In this specific case, the expression x = 5t and y = t + 8 defines a relationship where y depends on t and x is also defined … Read more

To solve for ‘a’ in the expression 9x + 49x + 4ax2 + b, we first need to simplify the equation. 1. Combine like terms for the coefficients of x: 9x + 49x = 58x So, the expression can be rewritten as: 58x + 4ax2 + b 2. The value of ‘a’ depends on additional … Read more

To determine the probability of rolling two six-sided dice and obtaining a pair of sixes, we can follow a straightforward approach. Each die has six faces, numbered from 1 to 6. When rolling two dice, each die operates independently of the other, meaning the outcome of one die does not affect the other. The total … Read more

To find the slope of a line that is perpendicular to the line represented by the equation 2y + 3x = 1, we first need to rewrite this equation in the slope-intercept form, which is y = mx + b, where m stands for the slope. Starting with the equation: 2y + 3x = 1 … Read more

Converting a fraction to a decimal is a straightforward process. Here are the steps you can follow: Identify the Fraction: Start with the fraction you want to convert. For instance, if you have the fraction 3/4, identify the numerator (3) and the denominator (4). Perform the Division: To convert the fraction to a decimal, divide … Read more

To determine if a triangle with side lengths of 3 cm, 4 cm, and 6 cm is a right triangle, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the … Read more

To find f(2) for the function f(x) = 3x² + 2x + 7, we need to substitute the value of x with 2 into the function. Here’s how to do it step by step: Substitute x with 2: f(2) = 3(2)² + 2(2) + 7 Calculate (2)²: f(2) = 3(4) + 2(2) + 7 Now … Read more

To find the sum of the numbers 6.68 and 0.8, we simply need to add them together mathematically. Here’s how it’s done: First, let’s align the numbers properly, taking care to position the decimal points: 6.68 + 0.80 —— Now, we can proceed to add the numbers column by column, starting from the right: In … Read more

Finding the Standard Form Equation of a Hyperbola To find the equation of the hyperbola with given vertices and foci, we follow a systematic approach. First, we need to understand what we have: Vertices: The vertices of the hyperbola are at (0, 9). Foci: The foci of the hyperbola are at (0, 10). The standard … Read more

To determine which pair of numbers is not a solution to the equation y = 2x, we will start by understanding what this equation represents. The equation indicates that for any value of x, y should be double that value. In other words, if you take a specific number for x, you can calculate y … Read more