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Volgvan
3 years ago
5

A king company requires 20 hours of labor to produce a standard table, and a chair requires 12 hours of labor. The labor availab

le is 565 hours per week. The company can produce at most 35 chairs per week.
The goal is to find the region that shows the number of tables and chairs that the company can produce in a week, based on the given restrictions. The first step is to represent the situation with a system of inequalities.

Let x be the number of tables and y be the number of chairs.

Which system of inequalities best represents this situation?

please help and thank you!!

Mathematics
1 answer:
Dimas [21]3 years ago
4 0

Since x represents tables, and tables require 20 hours, 20x is the number of hours spent on tables. The total hours must not exceed 565, so must be less than or equal to that value. The first selection is appropriate.

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Answer:

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5 - r / 7 - 1 = 2/3

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3 years ago
Simplify the expression 3/2 (5/3) -1 1/4 + 1/2 Given the answer as a simplified fraction. The simplified expression is a/b.
ella [17]
<h2>Hello!</h2>

The answer is:

The simplified fraction is:

\frac{7}{4}

<h2>Why?</h2>

To solve this problem we must remember the following:

- Addition or subtraction of fractions, we add or subtract fractions by the following way:

\frac{a}{b}(+-)\frac{c}{d}=\frac{ad(+-)bc}{bd}

- Product of fractions, the multiplication of fraction is linear, meaning that we should multiply the numerator by the numerator and denominator by denominator, so:

\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}

- Convert mixed number to fraction,

a\frac{b}{c}=a+\frac{b}{c}=\frac{ac+b}{c}

So, solving we have:

\frac{3}{2}*\frac{5}{3}-1\frac{1}{4}+\frac{1}{2}=\frac{3*5}{2*3} -1\frac{1}{4}+\frac{1}{2}\\\\\frac{3*5}{2*3} -1\frac{1}{4}+\frac{1}{2}=\frac{15}{6} -1\frac{1}{4}+\frac{1}{2}\\\\\frac{15}{6} -1\frac{1}{4}+\frac{1}{2}=\frac{15}{6} -(1+\frac{1}{4})+\frac{1}{2}\\\\\frac{15}{6} -(1+\frac{1}{4})+\frac{1}{2}=\frac{15}{6}-(\frac{4+1}{1*4})+\frac{1}{2}\\\\\frac{15}{6}-(\frac{4+1}{4})+\frac{1}{2}=\frac{15}{6}-\frac{5}{4}+\frac{1}{2}

\frac{15}{6}-\frac{5}{4}+\frac{1}{2}=(\frac{5}{2}-\frac{5}{4})+\frac{1}{2}\\\\(\frac{5}{2}-\frac{5}{4})+\frac{1}{2}=(\frac{(4*5)-(2*5)}{8})+\frac{1}{2}\\\\(\frac{(4*5)-(2*5)}{8})+\frac{1}{2}=(\frac{20-10}{8})+\frac{1}{2}\\\\(\frac{20-10}{8})+\frac{1}{2}=(\frac{10}{8})+\frac{1}{2}\\\\(\frac{10}{8})+\frac{1}{2}=\frac{5}{4}+\frac{1}{2}\\\\\frac{5}{4}+\frac{1}{2}=\frac{(5*2)+(4*1)}{2*4}\\\\\frac{(5*2)+(4*1)}{2*4}=\frac{10+4}{8}=\frac{14}{8}\\\\\frac{14}{8}=\frac{7}{4}

Hence, the simplified fraction is:

\frac{7}{4}

Have a nice day!

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