Given:
There are given that the parent functions as a cosine function:
Where,
The amplitude of the function is 9.
The vertical shift is 11 units down.
Explanation:
To find the cosine function, we need to see the standard form of the cosine function:
Where,
a is the amplitude of the function,
Now,
According to the question:
The amplitude of the function is 9, which means:
The vertical shift is 11 units down, which means:
For period:
Final answer:
Hence, the cosine function is shown below;
11)
3x = 180
x = 60
12)
6x + 18 = 180
6x = 162
x = 27
Use the rule of divisibility :
60 is composite because it is even so it can be divided by 2
67 is prime because none if the divisiblility rules work on it
65 is composite because it has a 5 by the end which means it can be divided by 5
<span>63 is composite because the sum of the digits equal to 9 which can be divided by 3 and 9</span>
Answer:
(3x+4)(5x+7)
Step-by-step explanation:
15x^2
+41x+28
Factor the expression by grouping. First, the expression needs to be rewritten as 15x^2
+ax+bx+28. To find a and b, set up a system to be solved.
a+b=41
ab=15×28=420
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 420.
1,420
2,210
3,140
4,105
5,84
6,70
7,60
10,42
12,35
14,30
15,28
20,21
Calculate the sum for each pair.
1+420=421
2+210=212
3+140=143
4+105=109
5+84=89
6+70=76
7+60=67
10+42=52
12+35=47
14+30=44
15+28=43
20+21=41
The solution is the pair that gives sum 41.
a=20
b=21
Rewrite 15x^2
+41x+28 as (15x^2
+20x)+(21x+28).
(15x^2
+20x)+(21x+28)
Factor out 5x in the first and 7 in the second group.
5x(3x+4)+7(3x+4)
Factor out common term 3x+4 by using distributive property.
(3x+4)(5x+7)
