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Marat540 [252]
3 years ago
9

What should you do first when simplifying an expression that involved

Mathematics
1 answer:
7nadin3 [17]3 years ago
8 0
The first thing that you do when simplifying an expression with the variable’s values known is to distribute the values. EXAMPLE:
3(7x+9)+6(-16x-40); distribute:
21x+27-96x-240; combine like terms:
(21x+(-96x))+(27+(-240))——-> -75x-213; now plug in the values and solve: -75(6)-213=-663
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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).

3 0
3 years ago
(15 points)Please help out if you can!
Levart [38]

Answer:

The maximum is -3

Step-by-step explanation:

A parabola that opens down (- in front), the vertex represents the highest point on the graph, or the maximum value.

The vertex of the equation is (-7,-3)

So, the maximum y value is -3

8 0
2 years ago
Use table of square to evaluate 6250²÷0.1750²
Hunter-Best [27]

Answer:

1275510204.08

Step-by-step explanation:

please first take square and then division

3 0
3 years ago
HELP WITH MATH!! RLLY COULD USE IT
san4es73 [151]

Answer:

120 square units

Step-by-step explanation:To find the area you do length times hight or l x h. If you want you can also make the triangle and move it to the other side to create a square if thats helps :) but you always do LxH for area :)

7 0
3 years ago
Read 2 more answers
Aurora earns a salary of $25,000 per year. Her benefits are equal in value to 30 percent of her salary. What is the value of Aur
artcher [175]
Her benefits are $7,500
6 0
3 years ago
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