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lord [1]
3 years ago
9

Find the value of 'x'. (2x + 1) (6x - 9)

Mathematics
2 answers:
MakcuM [25]3 years ago
5 0

Answer:

(2x+1)(6x−9)

=12x2−12x−9

Step-by-step explanation:

ipn [44]3 years ago
4 0

Answer:

Step-by-step explanation:

12xx^{2}-12<em>x</em>-9

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A bookstore packs 6 books in a box. The total weight of the books 14 1/4 pounds. If each book has the same weight, what is the w
Aleks04 [339]

Answer:

2.375 or 2 3/8

Step-by-step explanation:

You want to do total weight over total number of items.

14 1/4 / 6 books = 2.375

8 0
3 years ago
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Suppose f(x)=x+2. Find the graph of f(1/3x)
8090 [49]

Answer:

f(x)=x+2.

f(1/3x)=1/3 x+2=(x+6)/3or x/3+2

6 0
2 years ago
The symbol ⊕ is used to denote exclusive or, so p ⊕ q ≡ (p v q) ^ ~ (p ^ q).
Elan Coil [88]

I'll use text forms of the logical symbols because copying/pasting on mobile is annoying.

⊕ = XOR

∨ = OR

∧ = AND

~ = NOT

↔ = IFF (meaning "if and only if")

→ = IMP (short for "implies")

and for logical equivalence I'll use a regular equal sign.

Then

p XOR q = (p OR q) AND NOT (p AND q)

(a) By definition of XOR, we have

p XOR p = (p OR p) AND NOT (p AND p)

= p AND NOT p

and this is tautologically FALSE.

(b) To rewrite XOR, first distribute the NOT over the AND using DeMorgan's law:

NOT (p AND q) = NOT p OR NOT q

Then we can interchange the AND and ORs using their respective distributive properties. That is,

p XOR q = (p OR q) AND (NOT p OR NOT q)

= (p AND (NOT p OR NOT q)) OR (q AND (NOT p OR NOT q))

= ((p AND NOT p) OR (p AND NOT q)) OR ((q AND NOT p) OR (q AND NOT q))

Both (p AND NOT p) and (q AND NOT q) are tautologically FALSE, so the truth value of either OR depends only on the other statements, so we have

p XOR q = (p AND NOT q) OR (q AND NOT p)

Recall the definition of IFF:

p IFF q = (p IMP q) AND (q IMP p)

Also recall that IMP is logically equivalent to

p IMP q = p OR NOT q

Then we have

p IFF q = (p OR NOT q) AND (q OR NOT p)

so that its negation is

NOT (p IFF q) = NOT ((p OR NOT q) AND (q OR NOT p))

= NOT (p OR NOT q) OR NOT (q OR NOT p)

= (NOT p AND q) OR (NOT q AND p)

The statements in bold match, so p XOR q is indeed equivalent to NOT (p IFF q).

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