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AURORKA [14]
2 years ago
9

Is there a triangle whose angles have these measures in degrees? A) Yes B) No

Mathematics
1 answer:
EastWind [94]2 years ago
7 0

Answer:

No

Step-by-step explanation:

The sum of all internal angles on a triangle must equal 180°

28 + 64 + 100 = 192

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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
Please help i can not fail this!!
ivann1987 [24]
No solution 
i got u fam
4 0
3 years ago
Read 2 more answers
The ratio of losses to wins for Kyle's team is 3 to 2. If the team had played the same number of games, but had won twice as man
Fiesta28 [93]

Answer: The new ratio will be 1/4

Explanation: The initial ratio of losses to wins is 3 to 2. If we sum the numer of losses and wins 3 + 2 = 5 games, that means they loss 3 out of 5 games , and they win 2 out of 5 games.

So if they had won twice as many of the games, that is 2*2=4. And since the number of games is the same ( 5 ), then they would have won 4 games and loss only 1.

So the new ratio of losses to wins will be 1 to 4, or expressed in a fraction: 1/4

4 0
3 years ago
Read 2 more answers
A rectangular field is to be enclosed by a fence and divided
Phantasy [73]

Answer:

80000 square meters

Step-by-step explanation:

perimeter + dividing fence = 800

let a = length

let b = width

let c = length of dividing fence

perimeter = 2*a + 2*b

let's say...

c is the same as the length

2a + 2b + c = 800

2a + 2b + a = 800

3a + 2b = 800

area = length*width

area = a*b

area / b = a

3*(area/b) + 2b = 800

3*(area/b) = 800 - 2b

area/b = (800 - 2b)

area = (800 - 2b)*b

To make the area large, we make the right hand side large.

800b - 2b^2

If you put in terms of x, y it looks like a downward opening parabola, so the max area is at the vertex. Half way between the roots.

y = -2x^2 + 800x

y = -x^2 + 400x

0 = x*(-x + 400)

roots are x= 0 and x = 400

vertex is at x, aka b = 200

area at b=200 is (800 - 400)*200 = 80000

and a is area/b... 80000/400 = 200

5 0
2 years ago
Nadia compares the weights, in grams, of some apples and oranges she find the median abs interquartile range of the weights.
choli [55]

Answer:

Apple

Orange

Step-by-step explanation:

Apple has the greater median with a median value of 150 which is more than that of orange at 130

The sample with the greater variability is the orange sample as the interquartile range value of 11 is greater Than 8 for Apple.

Yes it is possible, because of the greater variation on weight shown by the sample of oranges, then it could be possible.

3 0
3 years ago
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