How to Solve for n in the Equation 11n + 1 = 35 – 3n
To solve for n in the equation 11n + 1 = 35 – 3n, we need to isolate n. Here’s how we can do it step by step: Move all terms involving n to one side: Start by adding 3n to both sides of the equation to eliminate n from the right side. The equation […]
What is the approximate area of a circle with a radius of 8 ft using 314?
The formula to calculate the area of a circle is given by: Area = π × r² In this case, the radius (r) of the circle is 8 feet, and we are using the approximation of π as 3.14. Plugging in the values, we get: Area = 3.14 × (8)² Calculating (8)² gives us 64, […]
In a Leap Year, a Day is Added to What Month?
In a leap year, an extra day is added to the month of February. Normally, February has 28 days, but during a leap year, it increases to 29 days. The reason for this adjustment is related to the Earth’s orbit around the Sun. It takes approximately 365.25 days for the Earth to complete one full […]
Which expression is a factor of 2xy, 6x, 3y, 9?
To determine which expression is a factor of 2xy, 6x, 3y, and 9, we first need to identify a common factor among these expressions. Let’s break down each expression: 2xy: This expression is made up of the factors 2, x, and y. 6x: This expression has the factors 2, 3, and x. 3y: This expression […]
Factorize the following: 3x² + 10x + 8
To factor the quadratic expression 3x² + 10x + 8, we need to find two binomials that multiply together to give us this expression. We start with the standard form of a quadratic, ax² + bx + c, where: a = 3 b = 10 c = 8 Next, we need to find two numbers […]
Which Represents the Inverse of the Function f(x) = 4x ?
To find the inverse of the function f(x) = 4x, we start by replacing f(x) with y. So, we have: y = 4x Next, we need to solve for x in terms of y. We can do this by dividing both sides of the equation by 4: x = y / 4 Now, to express […]
If You Flip Three Fair Coins, What Is the Probability That You’ll Get All Three Tails?
To find the probability of getting all three tails when flipping three fair coins, we can start by examining the total number of possible outcomes. Each coin has two possible results: heads (H) or tails (T). When flipping three coins, the total number of possible outcomes can be calculated as follows: Total Outcomes = 2^n, […]
What is the simplified expression for 3 power 3 multiplied by 3 power 3 over 3 power 4?
To simplify the expression (3³ * 3³) / 3⁴, we can use the laws of exponents. First, let’s simplify the numerator: 3³ * 3³ can be combined because of the product of powers rule, which states that when multiplying like bases, we add the exponents. So: 3³ * 3³ = 33+3 = 3⁶ Now, our […]
A Coin is Tossed 5 Times: What is the Probability that All 5 Tosses are Tails?
To find the probability of getting all tails when a coin is tossed 5 times, we can use the basic principles of probability. When a fair coin is tossed, there are two possible outcomes: heads (H) or tails (T). The probability of getting tails on a single toss is: P(T) = 1/2 Since each toss […]
What are the zeroes of f(x) = x² + 2x + 3?
To find the zeroes of the function f(x) = x² + 2x + 3, we need to solve the equation f(x) = 0. So we set up the equation: x² + 2x + 3 = 0 This is a quadratic equation, and we can solve it using the quadratic formula, which is given by: x […]