How to Simplify the Expression 3a^4 + 2a^2 + 5a + 10 + 2a^4 + 4a^2 + 5a + 2?
To simplify the expression 3a4 + 2a2 + 5a + 10 + 2a4 + 4a2 + 5a + 2, we need to combine like terms. First, let’s group the terms based on their degree: Terms with a4: 3a4 + 2a4 Terms with a2: 2a2 + 4a2 Terms with a: 5a + 5a Constant terms: 10 […]
In how many ways can 4 people sit next to each other in a movie theater row?
To determine the number of ways 4 people can sit next to each other in a movie theater row, we need to consider these 4 people as a single unit or block since they are sitting together. 1. **Treat them as a block**: When we treat the 4 people as a single block, we effectively […]
Consider Triangle GHJ: What is the Length of the Line Segment HJ?
To find the length of the line segment HJ in triangle GHJ, we need to know the coordinates or lengths of the other sides of the triangle. Typically, we would use the distance formula or the Pythagorean theorem if we have the lengths of the other two sides. Assuming we have the coordinates of points […]
Find the area under the standard normal distribution curve between z = 2.16 and z = 0
To find the area under the standard normal distribution curve between z = 2.16 and z = 0, we first need to determine the cumulative distribution function (CDF) values for these z-scores. The area under the curve corresponds to the probability of a standard normal variable falling between these two z-scores. 1. **Cumulative Probability for […]
In the diagram, which angle is part of a linear pair and part of a vertical pair?
To determine which angle is part of both a linear pair and a vertical pair, we need to understand the definitions of these concepts. A linear pair consists of two adjacent angles that sum up to 180 degrees. This means that if two angles are next to each other on a straight line, they form […]
Three of four numbers have a sum of 22 and the average of the four numbers is 8: What is the fourth number?
To find the fourth number, we first need to establish some basic facts based on the information given. The average of the four numbers is 8. The formula for the average is: Average = (Sum of all numbers) / (Total numbers) Since the average is 8 and there are 4 numbers, we can calculate the […]
If f(x) = 8 – 10x and g(x) = 5x + 4, what is the value of f(g(2))?
To find the value of f(g(2)), we first need to evaluate g(2) and then substitute that result into f. Starting with g(x): g(x) = 5x + 4 Now plug in x = 2: g(2) = 5(2) + 4 = 10 + 4 = 14 Now that we have g(2) = 14, we can find f(g(2)), […]
What is the integration of log 1 x x with limit 0 to 1?
To evaluate the integral of the function log(1 – x) from 0 to 1, we can set it up as follows: We need to compute: ∫ from 0 to 1 log(1 – x) dx This integral can be solved by using integration by parts. Let: u = log(1 – x) thus du = -1/(1 – […]
Use the Rational Root Theorem to List All Possible Rational Roots for the Equation 3x³ + 9x + 6 = 0
To find the possible rational roots of the polynomial equation 3x³ + 9x + 6 = 0, we can utilize the Rational Root Theorem. This theorem states that any rational solution, in the form of a fraction p/q, must have the numerator p as a factor of the constant term (the term without x) and […]
Which of the following represents the zeros of f(x) = x³ + 4x² + 5x – 20?
To find the zeros of the polynomial function f(x) = x³ + 4x² + 5x – 20, we need to determine the values of x for which f(x) = 0. This involves either factoring the polynomial or using numerical methods such as synthetic division or the Rational Root Theorem to identify possible rational zeros. By […]