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To determine whether the function f(x) = x^5 + x^3 + x is even, odd, or neither, we first need to understand the definitions of even and odd functions: A function is considered even if for every x in the domain, f(-x) = f(x). A function is considered odd if for every x in the … Read more

The polynomial f(x) = 6x^4 + 21x^3 + 4x^2 + 24x + 35 can be factored by following a systematic approach. To determine its factors, we can use techniques such as factoring by grouping, synthetic division, or the Rational Root Theorem. 1. **Finding Rational Roots:** Using the Rational Root Theorem, we can test potential rational … Read more

The scientific notation for the number 3,134,000,000 is written as 3.134 x 109. This means that the decimal point in 3.134 is moved nine places to the right to convert it back to the original number. The coefficient, in this case, is 3.134, which must be greater than or equal to 1 and less than … Read more

A system of linear equations consists of two or more equations that share the same set of variables. The solution to such a system is a set of values for the variables that makes all the equations true simultaneously. In simpler terms, it is the point (or points) at which the graphs of these equations … Read more

To determine the value of c that makes the expression x² + 7x + c + 49 – 4 – 7 – 2 – 7 – 2 – 49 – 4 into a perfect square trinomial, we first need to understand the basis of a perfect square trinomial. A perfect square trinomial takes the form … Read more

To find the new equation of the graph, we start with the original function, which is given by: y = x² 1. **Shifting Horizontally**: To shift the graph horizontally, we adjust the x-value of the function. A shift to the left by 5 units means we replace x with (x + 5). This transforms our … Read more

To simplify the expression √5(8 + 3√6), we will follow a systematic approach that involves distributing the square root of 5 across the terms inside the parentheses. 1. **Distributing √5**: Start by distributing √5 to both terms in the parentheses: √5 * 8 + √5 * 3√6 2. **Calculating Each Term**: The first term: √5 … Read more

To find the area of the triangular region ABC, we start by analyzing the given information. We have a circle with a center O and a radius of 1. This means that any point on the circumference of the circle is 1 unit away from the center O. The segment BC is also given to … Read more

In the Indian numbering system, numbers are grouped differently compared to the Western decimal system. Here’s a breakdown of how to express the provided numerals in words: 1: The number 1 is written as One. 7,532,105: This large number can be broken down into groups of two and three starting from the right: 7532105 = … Read more

To calculate the speed of a car that travels a distance of 150 kilometers in 7200 seconds, we can use the formula for speed: Speed = Distance / Time In this case: Distance = 150 kilometers Time = 7200 seconds Now, plugging in the values into the formula: Speed = 150 km / 7200 s … Read more