Write down the converse and contrapositive. if 2 divides x, then x is an even number. hint call this (p? q)

The converse and contrapositive of the given conditional statement are :

Converse : "If x is an even number, then 2 divides x".

Contrapositive : "If x is not an even number, then 2 does not divide x."

Step-by-step explanation:  We are given to write the converse and contrapositive of the following conditional statement :

"If 2 divides x, then x is an even number."

Let us consider that

p : 2 divides x

and

q : x is an even number.

We know that

the CONVERSE of a conditional statement p ⇒ q is written as q ⇒ p.

So, the converse of the given statement is

"If x is an even number, then 2 divides x".

The CONTRAPOSITIVE of the conditional statement  p ⇒ q is written as ~q ⇒ ~p (where ~p stands for the negation of p).

So, the contrapositive of the given statement is

"If x is not an even number, then 2 does not divide x."

Thus, the converse and contrapositive of the given statement are :

Converse : "If x is an even number, then 2 divides x".

Contrapositive : "If x is not an even number, then 2 does not divide x."

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal

choice b

step-by-step explanation:

f(x) = 88x^2 -264x + 300

the line of symmetry of a parabola is defined by

h = -b/2a

where ax^2 +bx+c=0

so

h = - -264/ (2*88)

h = 3/2

so x = 1.5