To solve the system of equations y = 3x + 7 and y = x + 9, we will set the two equations equal to each other since both are equal to y. Thus, we can write: 3x + 7 = x + 9 Next, we’ll isolate the variable x. Start by subtracting x from … Read more
When we talk about numbers that have 5 as a factor, we are referring to numbers that are divisible by 5. One important characteristic of such numbers is their ones place digit. A number is divisibly specifically by 5 if its last digit (the ones place) is either 0 or 5. This is due to … Read more
To find the value of x in the equation 8x + 2y = 48 when y = 4, we start by substituting the value of y into the equation. 1. Substitute y in the equation: Original Equation: 8x + 2y = 48 Substituted Equation: 8x + 2(4) = 48 2. Now, simplify the equation: Calculate … Read more
Naming segments and lines might seem similar, but there are important distinctions to consider. When naming a line, you typically focus on a single continuous path or direction. Lines are often referenced in the context of geometry, programming, or art to denote a straight or curved connection between two points. On the other hand, a … Read more
To determine if Isiah is correct that 5a² is the greatest common factor (GCF) of the polynomial a³ + 25a²b⁵ + 35b⁴, we need to examine each term of the polynomial and identify the common factors. The polynomial consists of three terms: a³ 25a²b⁵ 35b⁴ Now, let’s break down each term to find their factors: … Read more
To simplify the complex number 134i into standard form, we need to express it as a + bi, where a is the real part and b is the imaginary part. In this case, the number 134i consists only of an imaginary part, which means: a = 0 (since there is no real component) b = … Read more
In statistical analysis, the z-score is a measure of how far away a data point is from the mean of the data set, expressed in terms of standard deviations. When we say that a data value has a z-score of less than -2 or greater than 2, we are indicating that this data point is … Read more
To find the possible values of r in the quadratic equation r² + 7r + 8 = 0, we can use the quadratic formula, which is given by: r = (-b ± √(b² – 4ac)) / 2a In this equation, a, b, and c are the coefficients from the standard form of the quadratic equation … Read more
To rewrite the equation 4x + 2y = 5 in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, follow these steps: Start with the original equation: 4x + 2y = 5 Isolate the term with y on one side of the equation. To do this, … Read more
To solve the problem of counting how many bit strings of length 10 contain at least three 1s and at least three 0s, we will follow these steps: 1. Calculate Total Bit Strings The total number of bit strings of length 10 can be calculated as: Total bit strings = 210 = 1024 2. Identify … Read more