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Bond [772]
3 years ago
7

Prove whether or not, the following set of coordinates form a right triangle. Complete your work in the space provided or upload

a file that can display math symbols if your work requires it. A = (2, 1), B = (7, 1), C = (2, 4)
Mathematics
1 answer:
Natasha2012 [34]3 years ago
6 0

This is a right triangle.

AC forms a line parallel with the Y axis.

AB forms a line parallel with the X axis.

The intersection of AC with AB must therefore be perpendicular.

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For each of the following, use logic laws to decide whether the statement is a tautology contradiction, or neither. a (a) (A B)
spayn [35]

Answer:

The statement (A\rightarrow \lnot B)\land (B\rightarrow A) is a contingency.

The statement (P\rightarrow \lnot P)\land P is a contradiction.

Step-by-step explanation:

A tautology is a proposition that is always true.

A contradiction is a proposition that is always false.

A contingency is a proposition that is neither a tautology nor a contradiction.

a) To classify the statement (A\rightarrow \lnot B)\land (B\rightarrow A), you need to use the logic laws as follows:

(A\rightarrow \lnot B)\land (B\rightarrow A) \equiv

\equiv (\lnot A \lor\lnot B)\land(\lnot B \lor A) by the logical equivalence involving conditional statement.

\equiv (\lnot B\lor \lnot A )\land(\lnot B \lor A) by the Commutative law.

\equiv \lnot B \lor (\lnot A \land A) by Distributive law.

\equiv \lnot B \lor (A \land \lnot A) by the Commutative law.

\equiv \lnot B \lor F by the Negation law.

Therefore the statement (A\rightarrow \lnot B)\land (B\rightarrow A) is a contingency.

b) To classify the statement (P\rightarrow \lnot P)\land P, you need to use the logic laws as follows:

(P\rightarrow \lnot P)\land P \equiv

\equiv (\lnot P \lor \lnot P)\land P by the logical equivalence involving conditional statement.

\equiv P \land (\lnot P \lor \lnot P) by the Commutative law.

\equiv (P \land \lnot P) \lor (P \land \lnot P) by Distributive law.

\equiv F \lor F \equiv F by the Negation law.

Therefore the statement (P\rightarrow \lnot P)\land P is a contradiction.

8 0
3 years ago
Two ways to write 600,000+80,000+10
inn [45]
Six hundred thousand ,+ Eighty thousand ,+ ten.
8 0
3 years ago
Read 2 more answers
Solve the equation<br> 15x+2=45x+4
BaLLatris [955]
15x + 2 = 45x + 4

Subtract 2 from both sides, as well as subtracting 45x from both sides.

15x - 45x = 4 - 2

-30x = 2

Divide both sides by -30.

x = 2/-30

x = - 1/15

~Hope I helped!~
5 0
3 years ago
Find the equivalent fraction of 1/3 equals
kolezko [41]

Equivalent Fractions for 1/3:

1/3, 2/6, 3/9, 4/12, 5/15, 6/18, 7/21, 8/24, 9/27, 10/30,

6 0
3 years ago
Read 2 more answers
As a town gets smaller, the population of its high school decreases by 8% each year. The senior class has 320 students now. In h
Semmy [17]

Answer:

in 13.95 years the senior class will have 100 students.

Step-by-step explanation:

P(h) = p(0.92)^t (equation for exponential change)

P(h) - population of highschool (or senior class) = 100

p - staring amount = 320

t = time in years

100 = 320(0.92)^t

1/3.2 = .92^t (divide both sides by 320)

log(1/3.2, .92) = t (log base 0.92 of 1/3.2 equals t)

13.9497 = t

6 0
3 years ago
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