What is converse inverse and contrapostive?

Answers

Answer 1

Answer:
rhythm of the falling rain answered 6 yearGiven an if-then statement "if p, then q", we can create three related statements:

A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause.

For instance, “If it rains, then they will cancel school.”
“It rains, “is the hypothesis.
“They will cancel school,” is the conclusion.

To form the converse of the conditional statement, interchange the hypothesis and the conclusion.

The converse of “If it rains, then they will cancel school.” is
“If they cancel school, then it rains.”

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

The inverse of “If it rains, then they will cancel school” is “If it does not rain, then they do not cancel school.”

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.

The contrapositive of “If it rains, then they will cancel school” is “If they do not cancel school, then it does not rain.”

Summary:
Statement If p, then q.
Converse If q, then p.
Inverse If not p, then not q.
Contrapositive If not q, then not p.

If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true.

Example:
Statement If a person is 18 years old, then he is a legal adult.
Converse If a person is a legal adult, then he is 18 years old.
Inverse If a person is not 18 years old, then he is not a legal adult.
Contrapositive If a person is not a legal adult, then he is not 18 years old.

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Horatio has taken out a $12,450 unsubsidized Stafford loan to pay for his four-year undergraduate education. The loan has an interest rate of 7.3%, compounded monthly, and a duration of ten years. Horatio will allow interest capitalization. Making monthly payments, how much interest will Horatio have paid in total by the time the loan is paid in full? Round all dollar values to the nearest cent.

Answers

I'll just give you an answer based on my understanding.
I'll use the formula for compounding interest.

A = P(1+r/n)^nt

A = future value of the loan including interest
P = principal of the loan
r = interest rate
n = number of times the interest is compounded per year (monthly=12)
t = number of years the money is loaned for

Given:
P = 12,450
r = 7.3%, compounded monthly
t = 10 years

A = 12,450 (1+0.073/12)^12*10
A = 12,450 (1.006)¹²⁰
A = 12,450 (2.05)
A = 25,522.50

25,522.50 - 12,450 = 13,072.50 total interest paid.

The correct answer will be option A.

A and B start from the same point and travel west and north, respectively. A travels 3 miles per hour faster than B. At the end of two hours, they are 30 miles apart. Find their distances.

Answers

Answer:

Step-by-step explanation:

I believe you're actually looking for their respective rates. If A travels directly west and B travels directly north, and the distance between them is 30 miles, what we have is a right triangle situation. The hypotenuse of the triangle is 30. If the distance an object travels at a certain rate for given time is d = rt, then for B, our formula for distance is d = 2r (since the time each traveled is 2 hours). A traveled 3 miles per hour faster, so the formula for distance for A is d = (r + 3)2. Again, each traveled for 2 hours, so t = 2. Distributing we get that d = 2r + 6. Now that we have each expression for A and B, we use them in Pythagorean's Theorem to find the only unknown we have which is r. That's why I said in the beginning that I believe what you're actually looking for is the rate that each traveled. Our equation is:

$30^2=(2r+6)^2+(2r)^2$ and

$900=4r^2+24r+36+4r^2$ and

$900=8r^2+24r+36$

Putting everything on one side and setting the quadratic equal to 0 to factor, we get

$8r^2+24r-864=0$

You can factor out an 8 to make the numbers a bit smaller:

$8(r^2+3r-108)=0$

Factor to get

8(r - 9)(r + 12)=0

That means, by the Zero Product Property, that 8 = 0, r - 9 = 0, or r + 12 = 0. We all know that 8 doesn't = 0, so forget that one!! If r - 9 = 0, then r = 9. If r + 12 = 0. then r = -12. We all know that rate cannot be negative (velocity can, but we are not using vector math here), so we discount rate as -12. That means that r = 9. B's rate is 9 then and A's rate is 12. There you go!

Given the point (5,6) and the slope of 5, find y when x=21

Answers

If slope is 5, 5.(x-5)=y-6 so 5x-y-19=0. When x=21, y=86.

$\sf{Slope =(y_2-y_1)/(x_2-x_1)}\n\n5 = (y - 6)/(21-5) \n\n5=(y-6)/(16)\n\n16(5) = y-6\n\n80 = y-6\n\ny = 80 + 6\n\n\boxed{\bf{y=86}}$

Which of these nonterminating decimals can be converted into a rational number? Option 1: 00.818118111. Option 2: 0.020304050. Option 3: 00010110111. Option 4: 00.321321321.