Find the value of c that makes the expression a perfect square trinomial. x2 − 19x + c A) 361 B) 38 C) 361 2 D) 361 4

A (361)

Step-by-step explanation:

A "perfect square trinomial" has the form

ax^2 + 2ab + b^2.  If a happens to be 1, which it is in the given x^2 − 19x + c, then 2(1)(b) = - 19.  Solving for b, we get b = -19/2.

Then b^2 in the general "perfect square trinomial" is the same as c:  (-19/2)^2, or 90.25, or 90 1/4, or 361/4/

Choosing A (361) makes the given expression a perfect square trinomial.

6

step-by-step explanation:

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