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borishaifa [10]
3 years ago
10

What is the solution to 4x+63 ≤ 18?​

Mathematics
2 answers:
dsp733 years ago
8 0
The answer is x ≤ -45/4
galben [10]3 years ago
6 0

Answer:

- \frac{45}{4}

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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
Pls helppp
kicyunya [14]

Answer:

1,080 cm2

Step-by-step explanation:

you need to find the surface area...so

15x12=180

180x4=720

12x12=144

144x2=288

720+288=1008

8 0
3 years ago
Jack is selling wristbands and headbands to earn money for camp. He earns $2 for each wristband and $3 for each headband. He wan
Oksi-84 [34.3K]
Your answer will most likely be a.
5 0
3 years ago
Read 2 more answers
Each time Shelley goes tobthe store she likes to buy gum.She buys one pack for $1.00 and then another pack for $0.50 more.How mu
Umnica [9.8K]

Answer:

$2.50

Step-by-step explanation:

Shelley buys one pack of gum for $1

Price of gum: $1

Total amount of money spent: $1.00

Shelley buys another pack of gum for $0.50 more

1 + 0.50 = 1.5

Price of gum: $1.50

Total amount of money spent: $2.50

3 0
2 years ago
Last term of the arithmetic progression 8,15,22 is 218. Find<br>the number of terms.​
icang [17]

Answer:

31 terms.

Step-by-step explanation:

218 = 8 +  (n-1)7

210 = (n-1)7

30 + n-1

n = 31

There would be 31 terms in the given AP.

7 0
3 years ago
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