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Maurinko [17]
3 years ago
7

How do I solve this ?

Mathematics
1 answer:
timofeeve [1]3 years ago
6 0

Answer:

\large\boxed{\{4,\ 7,\ 10\}}

Step-by-step explanation:

X\ \cup\ Y\\\text{The union of a collection of sets is the set of all elements in the collection.}\\\\X\ \cap\ Y\\\text{The intersection}\ X\cap Y\ \text{of two sets X and Y is the set that contains}\\\text{all elements of X that also belong to Y, but no other elements.}\\\\A'\\\text{When A is a subset of a given set U, the absolute complement A}\\\text{is the set of elements in U, but not in A.}

U=\{3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10\}\\A=\{4,\ 6,\ 8\}\\B=\{3,\ 4,\ 7,\ 10\}\\C=\{3,\ 5,\ 9\}\\\\A\ \cup\ B=\{4,\ 6,\ 8\}\ \cup\ \{3,\ 4,\ 7,\ 10\}=\{3,\ 4,\ 6,\ 7,\ 8,\ 10\}\\C'=\{3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10\}-\{3,\ 5,\ 9\}=\{4,\ 6,\ 7,\ 8,\ 10\}\\B\ \cap\ C'=\{3,\ \b4,\ \b7,\ \b1\b0\}\ \cap\ \{\b4,\ 6,\ \b7,\ 8,\ \b1\b0\}=\{\b4,\ \b7,\ \b1\b0\}\\\\(A\ \cup\ B)\ \cap\ (B\ \cap\ C')=\{3,\ \b4,\ 6,\ \b7,\ 8,\ \b1\b0\}\ \cap\ \{\b4,\ \b7,\ \b1\b0\}=\{\b4,\ \b7,\ \b1\b0\}

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What is the value of x?<br><br><br><br> Enter your answer in the box.<br><br> x =
galina1969 [7]
The answer is:  " 11 " .
____________________________________________________
            →     " x  =  11  "  .
____________________________________________________
Explanation:
____________________________________________________
Set up the ratio/ proportion as a fraction:

6 cm / 48 cm = 5 cm / (3x + 7) ; 

→ The "cm" units cancel out; since:  "cm/cm = 1 " ; 

→ The "6/48" = "(6 ÷ 6) / (48 ÷ 6) =  " 1/8 " ; 

→ Rewrite as:  \frac{1}{8} = \frac{5}{3x + 7} ;

Now, we can "cross-multiply" :
__________________________________________________

<u>Note</u>:  Given: \frac{a}{b} = \frac{c}{d} ;  ad = bc ; 
              {b\neq 0 ;  d \neq 0} .
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As such:      
 
    1 * (3x + 7) = 8 * 5 ;

   →  3x + 7 = 40 ; 

Subtract "7" from each side of the equation:

   →  3x + 7 − 7 = 40 <span>− 7 ; 
</span>
to get:  

   → 3x = 33 ; 

Now, divide each side of the equation by "3" ; 
   to isolate "x" on one side of the equation; & to solve for "x" ; 

   →  3x / 3 = 33 / 3 ; 

to get: 
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   →    " x = 11 " .
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   →   The answer is:  " 11 " .
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