What is the value of x in the equation ln x + 6 ln 2x = 1?
To solve the equation ln x + 6 ln 2x = 1, we can begin by using the properties of logarithms. First, recall the definition of logarithm: if y = ln a, then ey = a. We will utilize this to rearrange our equation. Start by rewriting ln 2x: ln 2x = ln 2 + […]
72 is what percent of 480?
To find what percent 72 is of 480, we can set up the equation: Let x be the percentage we are trying to find. Then we have: 72 = (x / 100) * 480 We can solve for x by rearranging the equation: 1. Multiply both sides by 100: 7200 = x * 480 2. […]
What is 15 of 15?
The phrase “15 of 15” typically refers to the concept of a whole or complete set. In this case, it means that you have the entirety of something, which in this instance is 15 out of 15. This might come up in various contexts, such as completing a task, achieving a score, or fulfilling a […]
What is the factored form of the polynomial x² + 9x – 20?
To factor the polynomial x² + 9x – 20, we need to find two numbers that multiply to give the constant term (-20) and add up to the coefficient of the x term (9). The two numbers that satisfy these conditions are 10 and -2. This is because: 10 * (-2) = -20 10 + […]
What is the positive solution of x² – 36 = 5x?
To solve the equation x² – 36 = 5x, we first rearrange the equation to set it to zero: x² – 5x – 36 = 0 Now, we can apply the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a, where a = 1, b = -5, and c = -36. Calculating the […]
A varies jointly as B and C. Find A when B = 7 and C = 9 if the constant of variation is 3.
To solve this problem, we start with the concept of joint variation. When we say that A varies jointly as B and C, it means that A can be expressed as: A = k * B * C where k is the constant of variation. In this case, we know that k = 3, B […]
Which of the following is the correct factored form of the given equation 4x² – 25 = 0?
To factor the equation 4x² – 25 = 0, we can recognize that this expression is a difference of squares. The difference of squares can be factored using the identity: a² – b² = (a – b)(a + b). In our equation, we can identify: a² = (2x)², so a = 2x b² = 5², […]
How to Solve the Quadratic Equation x² + 5x + 6 = 0?
To solve the quadratic equation x² + 5x + 6 = 0, we can factor the equation or use the quadratic formula. In this case, factoring is straightforward. First, we look for two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of x). The numbers 2 and 3 […]
Write an equation that expresses the following relationship
To express a relationship mathematically, we start by identifying the variables involved and how they interact with each other. An equation typically takes the form of a statement that two expressions are equal to each other. For example, if we have variables x and y, and we know that doubling x is equal to adding […]
Which of the following is the inverse of y3x?
To find the inverse of the function represented by y3x, we need to understand what ‘inverse’ means in this context. The inverse of a function switches the roles of the input and output. This means that if we have a function y = f(x), its inverse is x = f(y). For the expression y3x, we […]