Find f(g(f(g(fg)))) and fg and their domains f(x) = x + 6 and g(x) = 5x^2
To find the composition of functions f and g, we start by defining the functions based on the given information: f(x) = x + 6 g(x) = 5x² 1. **Finding fg (f composed with g):** To find f(g(x)), we will substitute g(x) into f(x): f(g(x)) = f(5x²) Now, we replace the x in f(x) with […]
Binary numbers are made up of 1s and 0s. What is the base 10 number for the binary number 1000?
To convert the binary number 1000 to its base 10 equivalent, we need to understand how binary counting works. In binary, each digit represents a power of 2, starting from the rightmost digit which represents 20, the next one represents 21, and so on. For the binary number 1000, we can break it down as […]
How do you integrate int cos2x by integration by parts method?
To integrate ∫ cos(2x) dx using the integration by parts method, we start by recalling the formula for integration by parts: ∫ u dv = uv – ∫ v du For our integration, we can choose: u = cos(2x) (which we will differentiate), dv = dx (which we will integrate). Now we compute du and […]
Which binomial is a factor of 9x² + 643x + 8?
To determine if a binomial is a factor of the quadratic expression 9x² + 643x + 8, we can apply factorization techniques or utilize the Rational Root Theorem to find potential factors. First, we can look for factors by considering the roots of the equation 9x² + 643x + 8 = 0. This can be […]
How to Find the Height of a Trapezoid Without the Area
To find the height of a trapezoid without directly using the area, you can use the lengths of the bases and the lengths of the non-parallel sides (legs). Here’s how you can do it: Let’s say you have a trapezoid with bases of lengths a and b, and the lengths of the non-parallel sides are […]
What is 3 to the second power?
3 to the second power, often written as 3², is a mathematical expression that means 3 multiplied by itself. To calculate it, you would perform the multiplication: 3 × 3 = 9 Therefore, 3 to the second power is equal to 9. This concept is part of exponentiation, where the number (the base) is multiplied […]
How to Find the Y Intercept of a Quadratic Function
To find the y-intercept of a quadratic function, you’ll want to evaluate the function when the variable x is equal to zero. A quadratic function is typically in the form of: f(x) = ax² + bx + c Here, a, b, and c are constants. The y-intercept occurs where the graph of the function crosses […]
How many solutions will this system of equations have: 2y = 24 and 3x – 6y = 72?
To determine how many solutions the given system of equations has, we first need to express each equation in a more standard form. 1. From the first equation, we have: 2y = 24 If we solve for y, we divide both sides by 2: y = 12 Now we know that for any value of […]
Which equation shows the quadratic formula used correctly to solve 7x² + 9x for x?
To solve the quadratic equation 7x² + 9x = 0 using the quadratic formula, we first need to identify the coefficients in the standard form of a quadratic equation ax² + bx + c = 0. In this case: a = 7 b = 9 c = 0 The quadratic formula is given by: x […]
How can we simplify 1 – sin(x)?
To simplify the expression 1 – sin(x), we can look for a way to rewrite it in a more manageable form. One common approach in trigonometry is to express the sine function in terms of cosine, or to use Pythagorean identities. The sine function is related to the cosine function through the identity: sin2(x) + […]