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To solve the equation 2s² + 12s – 132 = 0, we can start by simplifying the equation. 1. **Divide the entire equation by 2** to make the coefficients smaller: s² + 6s – 66 = 0 2. **Now, we can use the quadratic formula** to find the values of s. The quadratic formula is: … Read more

To find out what percent 72 is of 480, we can use the formula for percentage: Percentage (%) = (Part / Whole) x 100 In this case, the Part is 72 and the Whole is 480. Plugging these values into the formula, we get: Percentage = (72 / 480) x 100 Now, let’s do the … Read more

Converting decimals to fractions or mixed numbers is a straightforward process. Let’s break down each of the decimals you provided. a) Converting 0.2 To convert 0.2 into a fraction, we recognize that it can be read as “two tenths.” This translates mathematically as: 0.2 = 2/10 Next, simplify the fraction by dividing both the numerator … Read more

To find the common ratio of the given sequence 125, 25, 5, 1, we first need to understand what a common ratio is. In a geometric sequence, the common ratio (r) is the factor by which we multiply each term to get the next term. Let’s calculate the common ratio step-by-step: Divide the second term … Read more

To determine which constant can be added to the expression x² + 10x to form a perfect square trinomial, we follow a straightforward process. A perfect square trinomial is typically in the form of (a + b)² or (a – b)², which expands to a² + 2ab + b². In our case, we need to … Read more

To solve the equation sin²(2x) sin(x) = 0, we need to consider when either factor of the equation equals zero. The equation consists of two parts, sin²(2x) and sin(x). Let’s break it down. Step 1: Set each factor to zero The equation is satisfied if either of the following holds true: sin²(2x) = 0 sin(x) … Read more

The equation y = x represents a linear relationship between the variables y and x. In the context of linear equations, the general form can be expressed as y = mx + b, where m is the slope of the line and b is the y-intercept. In the equation y = x, we can rewrite … Read more

Completely Factoring the Expression To factor the expression 25x² + 36 + 25x + 6x + 6 + 25x + 6x + 6 + 5x + 65x + 6 + 5x + 65x + 6, we first need to simplify it. Step 1: Combine Like Terms Combining all the like terms, we have: For the … Read more

To find the solutions to the equation 3x + 4x + 5 = 0, we first need to simplify the left side of the equation. The equation can be grouped based on the terms involving x: Step 1: Combine like terms We can combine the x terms: 3x + 4x = 7x. This leads us … Read more