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katen-ka-za [31]
3 years ago
9

Help plz

Mathematics
1 answer:
Tom [10]3 years ago
4 0

Answer:

1680 ways

Step-by-step explanation:

Permutation has to do with arrangement

If a contractor builds homes of 8 different models and presently has 4 lots to build on, the number of ways he can arrange his homes is expressed as;

8P4 = 8!/(8-4)!

8P4 = 8!/4!

8P4 = 8*7*6*5*4!/4!

8P4 = 8*7*6*5

8P4 = 1680

Hence the can arrange his homes 1680 ways

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The value of x in the equation is x=-44.

The given equation is \frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}.

An algebraic expression in mathematics is an expression that's made from variables and constants, together with algebraic operations (addition, subtraction, etc.). Expressions are made of terms.

Firstly, apply the distributive property as a(b+c)=ab+ac and get

\begin{aligned}\frac{3}{4}\times \frac{1}{4}x+\frac{3}{4}\times 8-\frac{1}{2}x-2&=\frac{3}{8}\times 4-\frac{3}{8}\times x-\frac{1}{4}\\ \frac{3x}{16}+6-\frac{x}{2}-2&=\frac{3}{2}-\frac{3x}{8}-\frac{1}{4} \end

Now, rearrange the terms by taking variable terms on the left-hand side and constant terms on the right-hand side as

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Further, simplify the above expression by taking L.C.M as

\begin{aligned}\frac{3x-8x+6x}{16}&=\frac{6-1}{4}-4\\ \frac{x}{16}&=\frac{5-16}{4}\\ \frac{x}{16}&=\frac{-11}{4}\end

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\begin{aligned}4\times \frac{x}{16}&=4\times \frac{-11}{4}\\ \frac{x}{4}&=\frac{-11}{1}\end

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x=-44

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Learn about algebraic expression from here brainly.com/question/8690932

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