devyy A horizontal line is characterized by having the same y-coordinate for all points along the line. In other words, the y-value remains constant regardless of the x-value. In this case, the point given is (3, 8). The y-coordinate is 8. Since the horizontal line must pass through this point, it will have the equation of: … Read more
Identifying the Equation with a Single Solution To determine which of the given equations has only one solution, we need to analyze each equation individually. The main focus will be on the nature of their roots, which can be discerned by examining their discriminants. Equation: x² – 4x + 4 = 0 The discriminant (D) … Read more
The slope-intercept form of a line is expressed as y = mx + b, where m represents the slope of the line and b is the y-intercept. To find this equation for the line that passes through the points (1, 3) and (3, 7), we’ll first need to calculate the slope (m). To calculate the … Read more
The given sequence is: 5, 25, 125, 625. To find the explicit rule for the nth term, let’s first observe the pattern in the sequence. We can see that each term is a power of 5: The first term (n=1) is 5^1 = 5 The second term (n=2) is 5^2 = 25 The third term … Read more
To solve the equation 3x + 2x + 5 = 4x + 2, we will follow these steps: Combine like terms on the left side: The left side of the equation can be simplified by combining the terms with x. So, 3x + 2x becomes 5x. Thus, the equation now looks like this: 5x + … Read more
To simplify the expression √5(10 – 4√2), we can follow these steps: Distribute the square root: Start by distributing √5 across the terms inside the parentheses: √5 * 10 gives us 10√5. √5 * (-4√2) can be simplified as follows: Multiply -4 by √5 * √2, which equals -4√(5 * 2) or -4√10. Now, putting … Read more
The function f(x) = 4x + 8 is a linear function, which can be analyzed to determine its domain and range. Domain: The domain of a function refers to all the possible input values (x-values) that the function can accept. Since linear functions can take any real number as input, the domain of f(x) = … Read more
To find out how many fish can fit in the tank, we can use the relationship between volume, density, and mass. Here, we need to calculate the total number of fish based on the density and volume of the tank. The formula to determine the number of fish is: Number of Fish = Density × … Read more
Understanding Slope and Zeros of Linear Functions A linear function can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope indicates how steep the line is and the direction in which it moves—upward if positive and downward if negative. Relationship Between … Read more
To factor the polynomial x³ + 4x² + 5x + 20 by grouping, follow these steps: Group terms: Divide the polynomial into two groups. For this polynomial, we can group the first two terms and the last two terms: (x³ + 4x²) + (5x + 20) Factor out common factors: From the first group (x³ … Read more