How do you solve the system of equations 5x + y = 9 and 3x + 2y = 4?
To solve the system of equations 5x + y = 9 and 3x + 2y = 4, we can use the substitution or elimination method. Here, we’ll use the substitution method. First, we solve the first equation for y
What is the difference between two numbers if their LCM is 495, HCF is 5, and their sum is 100?
To find the difference between two numbers given their LCM, HCF, and sum, we can use the relationship between these values. Let the two numbers be a and b. We know from the problem that: LCM(a, b) = 495 HCF(a, b) = 5 a + b = 100 We also know the relationship between LCM […]
How do you simplify the expression 3x + 62x² + 4x + 5?
To simplify the expression 3x + 62x² + 4x + 5, we first look for like terms. Like terms are terms that have the same variable raised to the same power. In this expression, we can identify like terms among the terms with x: 3x 4x We combine these two terms: 3x + 4x = […]
How do you divide 3x^3 2x^2 * 2 by x^2?
To divide the expression 3x^3 * 2x^2 * 2 by x^2, we first need to multiply the terms in the numerator. Start by combining the coefficients and the like terms: The coefficients: 3 * 2 * 2 = 12 The variable parts: x^3 * x^2 = x^{3+2} = x^5 This gives us 12x^5 in the […]
When constructing an inscribed square, how many lines will be drawn in the circle: 2, 3, 5, or 7?
When constructing an inscribed square within a circle, you will actually draw a total of two lines that connect the vertices of the square to the circle. The inscribed square will have four vertices, and to form the square, two pairs of lines are required to connect these vertices in a way that creates the […]
If cos lies in the quadrant IV what can be the value of cos?
In the fourth quadrant, the cosine function takes positive values. This is due to the fact that in this quadrant, the x-coordinates of points on the unit circle are positive while the y-coordinates are negative. The cosine of an angle in the fourth quadrant can be any value in the range of 0 to 1 […]
A student solved the equation below by graphing: log6(x) = 1, log2(2x) = 2. Which statement about the graph is true?
The graphs of the equations log6(x) = 1 and log2(2x) = 2 intersect at a specific point. To find this point, we need to solve both equations separately. For the equation log6(x) = 1, this means that the value of x must equal 61 = 6. Therefore, the first equation gives us the point (6, […]
What are the zeros of the polynomial function f(x) = x³ – 2x² – 24x?
To find the zeros of the polynomial function f(x) = x³ – 2x² – 24x, we need to set the function equal to zero and solve for x: f(x) = 0 => x³ – 2x² – 24x = 0 First, we can factor out the common term, which is x: x(x² – 2x – 24) […]
Given f(x) = (4x + 1) / 3, solve for f(13)
To solve for f(13), we need to substitute the value of x with 13 in the given function f(x). Fist, we start with the function: f(x) = (4x + 1) / 3 Now we replace x with 13: f(13) = (4(13) + 1) / 3 Next, we calculate the value inside the parentheses: 4(13) = […]
Let f(x) = 3x + 6 and g(x) = x + 2. Find g(f(x)) and its domain.
To find g(f(x)), we first need to determine what f(x) is. We are given that: f(x) = 3x + 6 Next, we will substitute f(x) into g(x). The function g(x) is defined as: g(x) = x + 2 Now, to find g(f(x)), we replace x in g(x) with f(x): g(f(x)) = g(3x + 6) Now […]