Which conditional and its converse are both true?
If x=2,then x^2=4
If x^2=4, then x=2
If x=3, then x^2=6
If x=1, then 2x=2
The conditional and its converse that are both true are:
If x = 2, then x^2 = 4
If x^2 = 4, then x = 2
Name the property of equality that justifies the following statement:
If p=q, then p-r=q-r
Multiplication Property
Symmetric Property
Reflexive Property
Subtraction Property
Subtraction Property
If an elephant weighs more than 2,000 pounds, then it weighs more than Jill’s car. If something weighs more than Jill’s car, then it is too heavy for the bridge. Smiley the Elephant weighs 2,150 pounds.
Based on the given information, we can conclude that Smiley the Elephant weighs more than Jill's car.
Read the following two statements. Then use the Law of Syllogism to draw a conclusion.
If you exercise regularly, you have a healthy body.
If you have a healthy body, you have more energy.
The Law of Syllogism states that if we have two conditional statements, and the hypothesis of the first statement is the same as the conclusion of the second statement, then we can conclude the hypothesis of the first statement implies the conclusion of the second statement.
Using the Law of Syllogism with the given statements:
1. If you exercise regularly, you have a healthy body.
2. If you have a healthy body, you have more energy.
We can conclude:
If you exercise regularly, you have more energy.
Identify the property that justifies the following statement:
Angle ATE is congruent to angles ATE
The property that justifies the statement "Angle ATE is congruent to angle ATE" is the Reflexive Property of Congruence. This property states that any geometric figure or angle is congruent to itself.
To find out which conditional and its converse are both true, we can examine each statement one by one:
1. If x=2, then x^2=4.
- Converse: If x^2=4, then x=2.
Both the original and the converse statements are true because if x is indeed equal to 2, then squaring 2 does result in 4, and vice versa, if x^2 is equal to 4, then the only possible value for x is 2.
2. If x^2=4, then x=2.
- Converse: If x=2, then x^2=4.
Similarly, both the original and the converse statements are true because if x^2 is indeed equal to 4, then taking the square root of 4 results in x being equal to 2, and vice versa, if x is equal to 2, then squaring 2 does result in 4.
3. If x=3, then x^2=6.
- Converse: If x^2=6, then x=3.
In this case, the original statement is false because squaring 3 results in a value of 9, not 6. Therefore, the original statement is false and its converse is also false.
4. If x=1, then 2x=2.
- Converse: If 2x=2, then x=1.
Both the original and the converse statements are true because when x is equal to 1, multiplying 1 by 2 indeed results in 2, and vice versa, if 2x is equal to 2, then dividing 2 by 2 gives the value of x being equal to 1.
In summary, the first statement "If x=2, then x^2=4" and its converse "If x^2=4, then x=2" are both true.