<span>rhythm of the falling rain answered 6 year<span>Given 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.</span></span>
Answer:
Step-by-step explanation:
1. Subtract 10 from both sides. Then:
2. Divide both sides by -2. Notice that the direction of the symbol of the inequality will change. Then:
3. Add 22 to both sides. Then:
4. Divide both sides by -7. Notice that the direction of the symbol of the inequality will change. Then:
5. Subtract 30 from both sides. Then:
6. Divide both sides by -5. Notice that the direction of the symbol of the inequality will change. Then:
7. Subtract 13 from both sides. Then:
8. Add 12 to both sides. Then:
Answer:
I'm assuming we're solving for the hypotenuse, which is 21.5
Step-by-step explanation:
If a^2+b^2=c^2
Then 19^2+10^2 =461
This is c^2 so we must find the square root of 461
the square root of 461 is 21.47, or 21.5 rounded to the nearest tenth
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
The extreme value of y = (x - h)² - c is the vertex of the equation.
<h3>What are extreme values of a function?</h3>
The extreme values of a function are either the maximum or minimum values of the function.
<h3>The equation of a parabola in vertex form</h3>
The equation of a parabola in vertex form with vertex (h', k) is given by
y = a(x - h')² + k and its extreme values are
- if a > 0 (h', k) is a minimum point and
- if a < 0 (h', k) is a maximum point.
Since y = (x - h)² - c is the equation of a parabola in vertex form, comparing with y = a(x - h')² + k,
So, the cooordinates of the vertex of y = (x - h)² - c is (h, -c).
Now, since a = 1 > 0, (h, -c) is a minimum point.
So, the extreme value of y = (x - h)² - c is the vertex of the equation.
Learn more about extreme value of a function here:
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