Answer:
x = - 4, x = 6
Step-by-step explanation:
Given
f(x) = x² - 2x + 3 and f(x) = 27, then equating the 2 gives
x² - 2x + 3 = 27 ( subtract 27 from both sides )
x² - 2x - 24 = 0 ← in standard form
Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 2)
The factors are - 6 and + 4, since
- 6 × 4 = - 24 and - 6 + 4 = - 2, thus
(x - 6)(x + 4) = 0
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 4 = 0 ⇒ x = - 4
The first partner in the handshake can be any one of 15 people.
The second partner can be any one of 14 people.
So the total number of possible arrangements is (15 x 14) = <u>210</u> .
<em><u>BUT . . . .</u></em>
If Mr. Smith and Mr. Jones are shaking hands, it doesn't matter which one is the first partner and which one is the second partner ... It's the same handshake either way.
That number of ' <u>210</u> ' up above counted both ways separately. The real number of handshakes <em>between different people</em> is half of that 210/2 = <em>105 handshakes</em>.
Answer:A
Step-by-step explanation: