Question

Choose the statement that is true and has a converse that is also true. A. If the equation of a line is y=3x+2, then the slope of the line is 3. B. If x2=100, then x=10. C. If x−1=8, then x=9. D. If an angle measures 45 degrees, then the angle is acute.

Answer 1

No such statement out if the given options.

Explanation:

Statements given are:

A. If the equation of a line is y=3x+2, then the slope of the line is 3.

Here, the statement is true, but converse is NOT true because the equation of line does not depends only on the slope.

B. If x 2=100, then x=10.

Statement is false because if
`x^(2)  = 100,` then x = 10 or x = -10

but converse is true as when x = 10,
`x^(2)  = 100,`

C. If x−1=8, then x=9.

The statement is true, but the converse is FALSE because is x = 9, the equation of x can be any arbitrary equation and not necessarily x − 1 = 8.

D. If an angle measures 45 degrees, then the angle is acute.

Here, the statement is true, but the converse is FALSE as if the angle is acute it can have any measure which is less than 90° and not specifically 45°.

Hence, there does not exists the statement that is true and has a converse that is also true.