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To determine the length of a rectangle when the perimeter and the width are known, we can use the formula for the perimeter of a rectangle, which is given by: Perimeter (P) = 2 * (Length (l) + Width (w)) In this case, we already know the perimeter and the width: Perimeter (P) = 34 … Read more

Solving the System of Equations To solve the system of equations 2x + y = 3 and x + 2y = 1, we can use the method of substitution or elimination. Here, we’ll use the elimination method for clarity. Step 1: Align the equations First, we write the equations one under the other: 2x + … Read more

To solve the quadratic equation x² + 8x + 3 = 0 using the completing the square method, follow these steps: Start with the original equation: x² + 8x + 3 = 0 Isolate the constant: x² + 8x = -3 Complete the square: To complete the square, we need to add and subtract the … Read more

The domain of a function refers to the set of all possible input values (x-values) that the function can accept. In the case of the function f(x) = 5x + 7, we are dealing with a linear function, which is one of the simplest forms of function in mathematics. For linear functions, there are no … Read more

To determine the type of polygon with an interior angle measuring 108 degrees, we can use the formula for calculating the interior angle of a regular polygon. The formula for the interior angle of a regular polygon with n sides is: Interior Angle = (n – 2) * 180° / n To solve for n, … Read more

False. While it’s true that all whole numbers are rational numbers, not every rational number can be classified as a whole number. To understand this better, let’s clarify the definitions: Rational Numbers: These are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. For example, &frac{1}{2}, 0, … Read more

When rolling a pair of fair dice, each die has 6 faces, resulting in a total of 36 possible outcomes (6 faces on the first die multiplied by 6 faces on the second die). The probabilities of rolling specific sums can be calculated based on these outcomes. Here’s a breakdown of the probabilities for sums … Read more

Factoring the Expression: 9x² + 12x + 4 To express the quadratic expression 9x² + 12x + 4 in factored form, we will follow these steps: Step 1: Identify the Coefficients In the expression ax² + bx + c, the coefficients are: a = 9 b = 12 c = 4 Step 2: Multiply a … Read more

To convert the decimal 0.375 into a fraction, follow these steps: Identify the place value: The decimal 0.375 has three decimal places. This means it is in the thousandths place. Write it as a fraction: You can express 0.375 as 375/1000, since 375 is in the thousandths. Simplify the fraction: To simplify 375/1000, find the … Read more

To determine what needs to be added to the expression 3x + 7 to equal the expression x2 + 4x + 1, we can set up the equation: 3x + 7 + ? = x2 + 4x + 1 To isolate the unknown (let’s call it k), we rearrange the equation: k = (x2 + … Read more