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To solve the quadratic equation x² + 12x + 11 = 0 by completing the square, follow these steps: Move the constant to the other side: Start by isolating the x² and 12x terms: x² + 12x = -11 Complete the square: To complete the square, take half of the coefficient of x: 12. Half … Read more

To solve the quadratic equation 4x² + 22x + 36 = 0, we can use the quadratic formula: x = \frac{-b \pm \sqrt{b² – 4ac}}{2a} Where a, b, and c are the coefficients from the equation in the form ax² + bx + c = 0. In our equation: a = 4 b = 22 … Read more

The terms predecessor and successor refer to the relationships between numbers or elements in a sequence or set. A predecessor is defined as the element that comes before another element in a sequence. For instance, in the context of whole numbers, the predecessor of the number 10 is 9, as 9 is the number that … Read more

To express 3 ln(3 ln(9)) as a single natural logarithm, we’ll start by simplifying the argument of the logarithm using properties of logarithms. 1. **Rewrite the inner logarithm:** First, let’s deal with ln(9). We can express 9 as a power of 3: 9 = 32 Therefore, we can rewrite this as: ln(9) = ln(32) = … Read more

To calculate the angle between the hour and minute hands of a clock at 3 PM, we can follow a straightforward formula. The clock is divided into 12 hours, with each hour marking a 30-degree segment on the clock face (360 degrees divided by 12 hours equals 30 degrees per hour). 1. **Position of the … Read more

To determine the inverse of the function f(x) = 4x + h(x) – x + 4h(x) – x – 4h(x) + 34x + h(x) + 14x, we first need to simplify the function itself. 1. **Combine Similar Terms**: Start by grouping the terms involving x and the function h(x): f(x) = (4 – 1 – … Read more

The polynomial you provided is 2x² + 3x + 5. To find its factors, we need to analyze its structure and determine if it can be factored into simpler expressions. Firstly, we look for two numbers that multiply to the product of the coefficient of x² (which is 2) and the constant term (which is … Read more

To find the slope of the line given by the equation 5y – x = 3, we first need to rewrite the equation in slope-intercept form, which is y = mx + b. In this format, m represents the slope and b represents the y-intercept. Let’s start by isolating the term with y: 1. Add … Read more

The fraction 325790 can be interpreted as 325790/1, as it is a whole number. To convert it to a decimal, we perform the division: When we divide 325790 by 1, we get 325790.00. Since we are interested in rounding to the nearest hundredths place, we need to ensure that we observe two decimal places. In … Read more

A quadrilateral with only one pair of opposite sides parallel is known as a trapezoid in American English, while in British English, it is often referred to as a trapezium. This unique shape has distinct characteristics that set it apart from other quadrilaterals. A trapezoid is defined by its two parallel sides, called the bases, … Read more