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riadik2000 [5.3K]
3 years ago
8

What is Y=2x+5 solve for x

Mathematics
1 answer:
Stells [14]3 years ago
4 0

Answer:

X=-5/2

Step-by-step explanation:

First for Y=2x+5 you change the y into 0

Then you replace the 0 with 2x but change the sign so it will be -2x so it will look like -2x=5

then you divide both sides by 2

Finally you get -5/2

Hopefully this helps

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Read 2 more answers
Let A = {a, b, c}, B = {b, c, d}, and C = {b, c, e}. (a) Find A ∪ (B ∩ C), (A ∪ B) ∩ C, and (A ∪ B) ∩ (A ∪ C). (Enter your answe
wariber [46]

Answer:

(a)

A\ u\ (B\ n\ C) = \{a,b,c\}

(A\ u\ B)\ n\ C = \{b,c\}

(A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}

(A\ u\ B)\ n\ C = (A\ u\ B)\ n\ (A\ u\ C)

(b)

A\ n\ (B\ u\ C) = \{b,c\}

(A\ n\ B)\ u\ C = \{b,c,e\}

(A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}

A\ n\ (B\ u\ C) = (A\ n\ B)\ u\ (A\ n\ C)

(c)

(A - B) - C = \{a\}

A - (B - C) = \{a,b,c\}

<em>They are not equal</em>

<em></em>

Step-by-step explanation:

Given

A= \{a,b,c\}

B =\{b,c,d\}

C = \{b,c,e\}

Solving (a):

A\ u\ (B\ n\ C)

(A\ u\ B)\ n\ C

(A\ u\ B)\ n\ (A\ u\ C)

A\ u\ (B\ n\ C)

B n C means common elements between B and C;

So:

B\ n\ C = \{b,c,d\}\ n\ \{b,c,e\}

B\ n\ C = \{b,c\}

So:

A\ u\ (B\ n\ C) = \{a,b,c\}\ u\ \{b,c\}

u means union (without repetition)

So:

A\ u\ (B\ n\ C) = \{a,b,c\}

Using the illustrations of u and n, we have:

(A\ u\ B)\ n\ C

(A\ u\ B)\ n\ C = (\{a,b,c\}\ u\ \{b,c,d\})\ n\ C

Solve the bracket

(A\ u\ B)\ n\ C = (\{a,b,c,d\})\ n\ C

Substitute the value of set C

(A\ u\ B)\ n\ C = \{a,b,c,d\}\ n\ \{b,c,e\}

Apply intersection rule

(A\ u\ B)\ n\ C = \{b,c\}

(A\ u\ B)\ n\ (A\ u\ C)

In above:

A\ u\ B = \{a,b,c,d\}

Solving A u C, we have:

A\ u\ C = \{a,b,c\}\ u\ \{b,c,e\}

Apply union rule

A\ u\ C = \{b,c\}

So:

(A\ u\ B)\ n\ (A\ u\ C) = \{a,b,c,d\}\ n\ \{b,c\}

(A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}

<u>The equal sets</u>

We have:

A\ u\ (B\ n\ C) = \{a,b,c\}

(A\ u\ B)\ n\ C = \{b,c\}

(A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}

So, the equal sets are:

(A\ u\ B)\ n\ C and (A\ u\ B)\ n\ (A\ u\ C)

They both equal to \{b,c\}

So:

(A\ u\ B)\ n\ C = (A\ u\ B)\ n\ (A\ u\ C)

Solving (b):

A\ n\ (B\ u\ C)

(A\ n\ B)\ u\ C

(A\ n\ B)\ u\ (A\ n\ C)

So, we have:

A\ n\ (B\ u\ C) = \{a,b,c\}\ n\ (\{b,c,d\}\ u\ \{b,c,e\})

Solve the bracket

A\ n\ (B\ u\ C) = \{a,b,c\}\ n\ (\{b,c,d,e\})

Apply intersection rule

A\ n\ (B\ u\ C) = \{b,c\}

(A\ n\ B)\ u\ C = (\{a,b,c\}\ n\ \{b,c,d\})\ u\ \{b,c,e\}

Solve the bracket

(A\ n\ B)\ u\ C = \{b,c\}\ u\ \{b,c,e\}

Apply union rule

(A\ n\ B)\ u\ C = \{b,c,e\}

(A\ n\ B)\ u\ (A\ n\ C) = (\{a,b,c\}\ n\ \{b,c,d\})\ u\ (\{a,b,c\}\ n\ \{b,c,e\})

Solve each bracket

(A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}\ u\ \{b,c\}

Apply union rule

(A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}

<u>The equal set</u>

We have:

A\ n\ (B\ u\ C) = \{b,c\}

(A\ n\ B)\ u\ C = \{b,c,e\}

(A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}

So, the equal sets are:

A\ n\ (B\ u\ C) and (A\ n\ B)\ u\ (A\ n\ C)

They both equal to \{b,c\}

So:

A\ n\ (B\ u\ C) = (A\ n\ B)\ u\ (A\ n\ C)

Solving (c):

(A - B) - C

A - (B - C)

This illustrates difference.

A - B returns the elements in A and not B

Using that illustration, we have:

(A - B) - C = (\{a,b,c\} - \{b,c,d\}) - \{b,c,e\}

Solve the bracket

(A - B) - C = \{a\} - \{b,c,e\}

(A - B) - C = \{a\}

Similarly:

A - (B - C) = \{a,b,c\} - (\{b,c,d\} - \{b,c,e\})

A - (B - C) = \{a,b,c\} - \{d\}

A - (B - C) = \{a,b,c\}

<em>They are not equal</em>

4 0
3 years ago
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