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What is the coefficient of the term x7y in the expansion of (x plus y)8?
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∙ 7y ago
It is 8.
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∙ 7y ago
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What is the value of ex in the system of equations x7y 18 xy 6?
Unfortunately, due to the limitations of browsers, most mathematical symbols get removed and it leaves gibberish that is impossible to answer Please edit/re submit your question with a full sentence of what you want solved, replacing mathematical symbols by words: plus for + equals for = power for ^ etc eg "5x² + 2x = 5" should be written as "5 times x power 2 plus 2x equals 5".
What does variables mean in math with sentence?
I'm assuming you mean what is a variable. A variable is a letter that is used to take the place of a number. That letter can be any number. One example is 1+x=2 So x would equal 1. But in most cases the variables are solved for with more complex problems. Also, you may not be solving for the variable at all, it might be a placeholder.______________________________________________________________In elementary mathematics, a variable is an alphabetic character representing a number which is either arbitrary or not fully specified or unknown.Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation.A typical example is the quadratic formula, which allows to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation to the variables that represent them.The concept of variable is also fundamental in calculus. Typically, a function y = f(x) involves two variables, its argument x and its value y. The term "variable" comes from the fact that, when the argument (also called the "variable of the function") varies, then the value varies accordingly.So, variables are (usually) letters or other symbols that represent unknown numbers or values.The following are examples of algebraic expressions and equations containing variables. 2x + 5 = 10, the variable here is x7y + 10 = 24, the variable here is ya2 + b2, the variables here are a and bRefer to link below for more information
How many numbers are there in all from 6000 to 6999 having at least one of their digits repeated?
Note that the numbers from 6000 to 6999 comprise all combinations of three digits, with a 6 stuck on the front. We will consider the combinations of these final three digits.First, let's consider how many three-digit combinations contain one, two or three 7's.There is one occurrence of three 7's: in the combination '777'.Now consider two 7's. This can occur in the pattern '77x', '7x7' or 'x77'. For each of these patterns there are 9 possible values for 'x'. Why not 10? Because if x were '7', then it would be '777' which has three, not two 7's. So there are 9 times 3, or 27 ways for there to be exactly two 7's.Now consider how many occurrences of one 7. The three patterns are '7xy', 'x7y' and 'xy7'. There are 81 combinations of x and y for each of these. (Why not 100? because we are excluding 19 cases where x or y, or both, are 7's.) So there are 81*3, or 243 ways that there can be one 7.So there are 1 + 27, or 28 ways for there to be at least two 7's. And there are 28 ways for there to be a repeated 8, or a repeated 9, and so on. So there are 9 times 28, or 252 ways for a digit other than 6 to be repeated. Why exclude 6? Because we're going to treat it specially.All the numbers from 6000 to 6999 begin with a 6. So it is only necessary for a single 6 to occur in the last three digits for it to repeat. And there are 243 + 27 + 1, or 271 ways that one or more 6's can occur, as we saw above.But wait, we cannot just add 271 to 252, because we would be counting combinations like '6677' or '6767' twice. In fact there are 9 times 3 cases with a repeated 6 and some other repeated digit. (three patterns, and nine possible other digits) So the final count will be 271 + 252 - 27, or 496.So there are 496 numbers between 6000 and 6999 that have at least one repeated digit.
