Solve the Equation 15 + 4 – 7x = 9
To solve the equation 15 + 4 – 7x = 9, we first need to combine like terms and isolate the variable. Step 1: Combine the numbers on the left side. 15 + 4 equals 19, so the equation now looks like: 19 – 7x = 9 Step 2: Next, we will isolate the term […]
True or False: If f and g are inverse functions, the domain of f is the same as the range of g
This statement is True. When we have two functions, f and g, that are inverses of each other, this means that for every output of function f, there is a corresponding input in function g that will return to the original value. More specifically, if f: A → B, then g: B → A, where […]
How can we factorise the expression 2x³ + 54y³ + 4x + 12y?
To factorise the expression 2x³ + 54y³ + 4x + 12y, we need to look for common factors and group the terms effectively. First, we can group the terms: 2x³ + 4x 54y³ + 12y Now, let’s factor out the common factors from each group: For the first part, 2x³ + 4x: we can factor […]
How to Simplify 17 6 x 10 2 12?
To simplify the expression 17 6 x 10 2 12, we first need to clarify the notation. It seems to represent a series of numbers, but it looks like there might be some multiplication or combination implied between them. Let’s break down the expression assuming that there are multiplication signs between the numbers where appropriate: […]
How to Solve the Equation: 3x + 4 = 4x + 1 + 2?
To solve the equation 3x + 4 = 4x + 1 + 2, we first simplify the right side. Combine the constants: 1 + 2 = 3, so we can rewrite the equation as: 3x + 4 = 4x + 3 Next, we’ll get all the terms involving x on one side and the constant […]
Given the function f(x) = 2x, find the value of f(132)
To find the value of f(132) using the function f(x) = 2x, we need to substitute 132 in place of x in the equation. So, we perform the following calculation: f(132) = 2 * 132 f(132) = 264 Thus, the value of f(132) is 264.
What is the linear factorization of the function f(x) = x^4 – 9x^2?
To factor the function f(x) = x4 – 9×2, we start by observing that we can factor out a common term. Here, we notice that both terms contain x2. First, let’s rewrite the function: f(x) = x2(x2 – 9) Next, we see that the expression in the parentheses, x2 – 9, is a difference of […]
What is the graph of the system y = 2x + 3 and 2x + 4y = 8?
To graph the system of equations given by y = 2x + 3 and 2x + 4y = 8, we will first manipulate both equations so we can easily plot them. Starting with the first equation, y = 2x + 3, this is already in slope-intercept form (y = mx + b), where the slope […]
If Two Events A and B Are Such That P(A) = 0.7, P(B) = 0.4, and P(A ∩ B) = 0.2
To understand the relationship between two events A and B given their probabilities, we can use the basic principles of probability. We know that: P(A) = 0.7 P(B) = 0.4 P(A ∩ B) = 0.2 Now, let’s break down what these probabilities mean: – P(A) is the probability that event A occurs, which is 70%. […]
What is the probability of drawing a king or an ace from a standard deck of cards?
When you draw a card from a standard deck of 52 playing cards, you want to know the probability of drawing either a king or an ace. Let’s break this down. A standard deck contains 4 kings (one for each suit: hearts, diamonds, clubs, and spades) and 4 aces (also one for each suit). This […]