To determine the probability of both coins landing on heads when two coins are tossed, we can start by identifying the total number of possible outcomes and the number of favorable outcomes. When tossing two coins, each coin has 2 possible outcomes: heads (H) or tails (T). Therefore, the total number of outcomes when tossing … Read more
Factoring the Trinomial: 5x² + 8x + 4 To factor the trinomial 5x² + 8x + 4, we need to find two binomials that, when multiplied together, yield the original trinomial. Let’s break down the process. Step 1: Identify the Coefficients The trinomial consists of three parts: the coefficient of x² (which is 5), the … Read more
To convert the exponential equation 4x = 64 into its logarithmic form in base 10, we first need to understand the relationship between exponential and logarithmic expressions. In general, the exponential equation ab = c can be rewritten in logarithmic form as loga(c) = b. Here, a is the base, b is the exponent, and … Read more
If angles 1 and 2 are complementary, they add up to 90 degrees. If they are also congruent, that means they are equal in measurement. So, we can set both angles to be equal, calling them both x. Thus, we have the equation: x + x = 90 This simplifies to: 2x = 90 Now, … Read more
To find the inverse of the function y = 2x² + 8, we need to follow these steps: Replace y with x: This is the first step in finding the inverse. The equation becomes: x = 2y² + 8 Isolate y: We need to solve this equation for y. Start by moving 8 to the … Read more
When a car is described as moving in a straight line at a constant speed of 20 meters per second, it means that the vehicle travels in a linear path without changing direction. This speed of 20 meters per second indicates that for every second that passes, the car covers a distance of 20 meters. … Read more
To solve the equation where the quantity of x plus 20 over 2 equals 3x, we can start by expressing this mathematically: We have: (x + 20) / 2 = 3x To eliminate the fraction, we can multiply both sides of the equation by 2: x + 20 = 6x Next, we want to isolate … Read more
To find the value of x in the equation 35x + 7 = 0, we need to isolate x. Here’s a step-by-step breakdown: Start with the original equation: 35x + 7 = 0. Subtract 7 from both sides to begin isolating x: 35x + 7 – 7 = 0 – 7 Which simplifies to: 35x … Read more
To solve the equation x² – 14x + 17 = 96, we first need to rearrange it into standard form. We can do this by moving 96 to the left side of the equation: x² – 14x + 17 – 96 = 0 This simplifies to: x² – 14x – 79 = 0 Now we … Read more