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weeeeeb [17]
3 years ago
5

Solve for a. Please help!

Mathematics
1 answer:
Marizza181 [45]3 years ago
8 0

Answer:

a = 7

Step-by-step explanation:

This is a special trig triangles. Special trig triangles are identified by their angle measures and their sides have a unique relationship. This is a 30 - 60 - 90 triangle which has sides 1 - √3 - 2 or multiples of this. This means all 30 - 60 - 90 triangles have side lengths with the pattern 1 - √3 - 2. Here the triangle has a - 7√√3 - 14. The value of a is 7 since 7*√3 = 7√3 and 2*7 = 14.

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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
What is m∠DHG? Enter your answer in the box.
LenaWriter [7]

the 2 equations given are vertical angles which mean they would equal the same.

Set the two equations to equal each other to solve for x:

6(x-2) = 3x+30

Simplify the left side:

6x-12 = 3x+30

Add 12 to eac side:

6x = 3x+42

Subtract 3x from each side"

3x = 42

Divide both sides by 3:

X = 42/3

X = 14


Now you know X, replace x with 14 in the equation for DHG:

DHG = 6(x-2)

6(14-2)

Simplify:

6(12)

Multiply:

72

Angle DHG is 72 degrees.

6 0
3 years ago
Read 2 more answers
I need the answer and the work (it’s geometry)
Kisachek [45]

Answer:

D

Step-by-step explanation:

The starting point is B and the ray extends towards A.

So the asnwer is D.

6 0
3 years ago
Ibout lt
Vikki [24]
It is 60 times greater because 60 pennies=6 dimes . 6 dimes=60 pennies
Or
10 times greater because 6×10=60 60=6 dimes
8 0
3 years ago
Read 2 more answers
9 is 25% of what number??
AlexFokin [52]
So because 25%=1/4 we would know to multiply 9*4
Which would get our answer to be 36 :)
6 0
3 years ago
Read 2 more answers
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