Answer:
3(x - 12)(x + 2)
Step-by-step explanation:
Given
3x² - 30x - 72 ← factor out 3 from each term
= 3(x² - 10x - 24) ← factor the quadratic
Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 10)
The factors are - 12 and + 2 , since
- 12 × 2 = - 24 and - 12 + 2 = - 10 , thus
x² - 10x - 24 = (x - 12)(x + 2) and
3x² - 30x - 72 = 3(x - 12)(x + 2)
Answer:
48
Step-by-step explanation:
The ratio of professors to lecturers is ...
P : L = 6 : 11
Then the ratio of professors to total faculty is ...
P : (P+L) = 6 : (6+11) = 6 : 17
That is, professors make up 6/17 of the total faculty. Their number is ...
P = (6/17)·136 = 48
The Community College employs 48 professors.
Answer:
( f h ) (x) = 6 x² - 1
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given<em> f(x) = 3 x - 4</em>
g (x) = −x²+2 x−5
<em> h (x) = 2 x² + 1</em>
j (x) = 6 x + 2 - 8 x
K (x) = 3 x² - x + 7
<u><em>Step(ii)</em></u>:-
<em>( f h ) (x) = f ( h (x)) = f ( 2 x² + 1 )</em>
= 3 (2 x² + 1 ) - 4
= 3 ((2 x² ) + 3 - 4
= <em>6 x² - 1</em>
<u><em> Final answer:</em></u>-
∴ <em> ( f h ) (x) = 6 x² - 1</em>
1. 7 hours and 40 min
2. 1 hour and 24 min
3. 4 hours and 45 min
4. 8 hours and 48 min