How do you graph the inequality 2x y 4?
To graph the inequality 2x < y + 4, we first need to rearrange it in a more standard form. Let's express it as: 2x – y < 4 Next, we’ll replace the inequality with an equality to find the boundary line: 2x – y = 4 To graph this line, we’ll find the x […]
What Inequality is Used to Find the Domain of the Function f(x) = 5x + 5?
To determine the domain of the function f(x) = 5x + 5, we need to identify any restrictions on the values of x. This particular function is a linear function, meaning it is defined for all real numbers. There are no values of x that would make the function undefined, such as dividing by zero […]
What is the value of p in the linear equation 24p + 12 = 18p + 10 + 2p + 6?
To find the value of p in the equation 24p + 12 = 18p + 10 + 2p + 6, we first need to simplify the equation. Let’s combine like terms on the right side: Combine 18p and 2p, which gives us 20p. Combine the constants 10 and 6, which gives us 16. This simplifies […]
How do we find the median if the number of observations in a data set is odd?
To find the median in a data set with an odd number of observations, follow these steps: Arrange the Data: First, sort the data set in ascending order. This means you need to list the numbers from the smallest to the largest. Count the Observations: Determine the total number of observations in the data set. […]
How Many Kilometers in a Mile?
A mile is equal to approximately 1.60934 kilometers. This means that if you want to convert miles to kilometers, you can multiply the number of miles by this figure. To give you a better perspective, if you were to run a mile, you’d actually be covering about 1.6 kilometers. This conversion is useful for those […]
What is the value of 7 + 3i + 2 + 6i?
To find the value of the expression 7 + 3i + 2 + 6i, we will first combine the real parts and the imaginary parts separately. 1. Identify the real numbers: 7
What is the common ratio between successive terms in the sequence 2, 4, 8, 16, 32, 64?
The common ratio in a geometric sequence can be found by dividing any term by the previous term. In the sequence provided, we can calculate the common ratio as follows: The second term (4) divided by the first term (2) gives us 4 ÷ 2 = 2. The third term (8) divided by the second […]
What is the domain and range of f(x) = 4x + 8?
The given function is f(x) = 4x + 8, which is a linear function. Domain: The domain of a function consists of all the possible input values (x-values). In the case of linear functions, there are no restrictions on the values that x can take. Therefore, the domain of f(x) = 4x + 8 is […]
Which of the following quadratic equations has the solution set 12, 5?
To determine which quadratic equation has the solution set of 12 and 5, we need to construct the quadratic equation from the given roots. The formula for a quadratic equation based on its roots, r1 and r2, is: y = (x – r1)(x – r2) In our case, the roots are 12 and 5. So […]
Is a data value considered an outlier if its z-score is less than -2 or greater than 2?
Yes, a data value is typically considered an outlier if its z-score falls below -2 or exceeds 2. The z-score is a statistical measurement that describes a value’s relation to the mean of a group of values. Specifically, it indicates how many standard deviations a data point is from the mean. A z-score less than […]