If a number is divisible by both 2 and 3 then we can say the number is divisible by
If a number is divisible by both 2 and 3, we can say the number is divisible by 6. This conclusion comes from understanding the rules of divisibility and the concept of the least common multiple (LCM). The number 6 is the smallest number that both 2 and 3 can divide without leaving a remainder. […]
What error did Holly make in her expression: 11m + 13n + 6mn + 10m + 7n + 3mn + m + 20n + 9mn?
Holly’s expression seems to be a mix of terms involving variables m and n, but she made a mistake by not combining like terms properly. Let’s break down the terms: Terms with m: 11m, 10m, m Terms with n: 13n, 7n, 20n Terms with both variables mn: 6mn, 3mn, 9mn Now let’s combine the like […]
What value is missing from Samuel’s solution when finding the difference of the polynomials 15x² + 11y² + 8x – 7x² – 5y² – 2x – x² – 6y² – 6x?
To find the difference of the polynomials, we first need to combine like terms. Let’s organize the polynomials Samuel is working with: 15x² 11y² 8x -7x² -5y² -2x -x² -6y² -6x Now we can group them: For x² terms: 15x² – 7x² – x² = 15x² – 8x² = 7x² For y² terms: 11y² – […]
When is f(x) = 4x^3 + 3x^2 + ax + b divided by x – 1?
When we divide the polynomial f(x) = 4x^3 + 3x^2 + ax + b by x – 1, we want to know if x – 1 is a factor of the polynomial. By the Factor Theorem, x – 1 is a factor of f(x) if f(1) = 0. Let’s substitute x = 1 into the […]
How to Find the Roots of the Function f(x) = x³ + x² – 6x
To find the roots of the function f(x) = x³ + x² – 6x, we need to solve the equation f(x) = 0. This means we set the function equal to zero: x³ + x² – 6x = 0 First, we notice that each term on the left side of the equation has a common […]
Write the Equation in Slope-Intercept Form: What are the Slope and Y-Intercept for 9x + 10y = 9?
To convert the equation 9x + 10y = 9 into slope-intercept form, we need to solve for y. Start by isolating the term with y: 10y = -9x + 9 Next, divide every term by 10 to solve for y: y = -\frac{9}{10}x + \frac{9}{10} This is now in slope-intercept form, which is y = […]
If 2y lies on the graph of y = 4x, then what is y?
To find the value of y, we start with the equation of the graph given as y = 4x. If we say 2y lies on this graph, we can set up the equation: 2y = 4x Next, we can solve for y by dividing both sides of the equation by 2: y = 2x Thus, […]
By Inspection, Find a Particular Solution of y = 2y + 6
To solve the equation y = 2y + 6 by inspection, we begin by isolating y on one side of the equation. First, let’s rearrange the equation: y – 2y = 6 This simplifies to: -y = 6 Now, multiplying both sides by -1 gives us: y = -6 Therefore, by inspection, a particular solution […]
If f is continuous on (-∞, ∞), what can you say about its graph? Select all that apply.
If a function f is continuous on the interval from negative infinity to positive infinity, we can make several key observations about its graph: The graph has no breaks or holes: Since f is continuous, its graph does not have any jumps, asymptotes, or holes. You can draw the graph of f without lifting your […]
Which of the following is a factor of f(x) = 4x³ + 11x² – 75x + 18?
To determine the factors of the polynomial f(x) = 4x³ + 11x² – 75x + 18, we can use several methods, including the Rational Root Theorem or synthetic division. First, we can look for possible rational roots using the factors of the constant term (18) and the leading coefficient (4). The factors of 18 are […]