Question

Given P(x): √√x² = |x|; Q(x): x-1 = 3; R(x, y): x + y = 0 T(x, y): x + y = y​

Answer 1

=> The simplest form of

56

:

98

56:98 is

4

:

7.

4:7.

Explanation:

Given ratio -

56

:

98

56:98

We have to reduce it to its simplest form,

For that, we have to find the GCD of the numerator as well as the denominator:

So, the GCD for

56

56 and

98

98 is

14.

14.

Now, divide both the numerator and denominator by the GCD:

=

>

56

÷

14

98

÷

14

=>

98÷14

56÷14

=

>

4

7

=>

7

4

Hence, the simplest form is

4

:

7.

4:7.

Answer 2

Explanation:

P(x) is a statement about the square root of x squared equaling the absolute value of x.

Q(x) is a statement about x minus 1 equaling 3. Solving this equation for x we get x = 4.

R(x, y) is a statement about x plus y equaling 0. This is a linear equation and it has infinitely many solutions for x and y as long as x + y = 0.

T(x, y) is a statement about x + y equaling y. This equation is not possible because it will always result in x = 0, y = 0 and thus no solution.

It is important to note that the statement T(x, y) is not a valid equation, it is a contradiction and therefore it has no solution.