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Chapter 9: Problem 34
Find the union of the sets. $$\\{1,3,7,8\\} \cup\\{2,3,8\\}$$
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What does it mean if a system of linear inequalities has no solution?
In more U.S. marriages, spouses have different faiths. The bar graph shows the percentage of households with an interfaith marriage in 1988 and \(2008 .\) Also shown is the percentage of households in which a person of faith is married to someone with no religion. (GRAPH CANT COPY) The formula $$1-\frac{1}{2} x+2=$$ models the percentage of U.S. households with an interfaith marriage, \(I, x\) years after \(1988 .\) The formula $$N=\frac{1}{4} x+6$$ models the percentage of U.S. households in which a person of faith is married to someone with no religion, \(N, x\) years after I988. Use these models to solve. a. In which years will more than \(33 \%\) of U.S. households have an interfaith marriage? b. In which years will more than \(14 \%\) of U.S. households have a person of faith married to someone with no religion? c. Based on your answers to parts (a) and (b), in which years will more than \(33 \%\) of households have an interfaith marriage and more than \(14 \%\) have a faith/no religion marriage? d. Based on your answers to parts (a) and (b), in which years will more than \(33 \%\) of households have an interfaith marriage or more than \(14 \%\) have a faith/no religion marriage?
Graph the solution set of each system of inequalities or indicate that the system has no solution..\ \left\\{\begin{array}{l}2 x+y \leq 6 \\\x+y \geq 2 \\\1 \leq x \leq 2 \\\y \leq 3\end{array}\right.
If \(f(x)=x^{2}-3 x+4\) and \(g(x)=2 x-5,\) find \((g-f)(x)\) and \((g-f)(-1) .\) (Section 8.3, Example 4)
Write the given sentences as a system of linear inequalities in no variables. Then graph the system. The sum of the \(x\) -variable and the \(y\) -variable is at most 4 The \(y\) -variable added to the product of 3 and the \(x\) -variable does not exceed 6
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