Answer:
1. 15
2. 8
Step-by-step explanation:
The two sequence are geometric progression GP, because they follow a constant multiple (common ratio)
The nth term of a GP is;
Tn = ar^(n-1)
Where;
a = first term
r = common ratio
For the first sequence;
The common ratio r is
r = T3/T2 = 540/90 = 6
r = 6
T2 = ar^(2-1) = ar
T2 = 90 = ar
Substituting the values of r;
90 = a × 6
a = 90/6
a = 15
First term = 15
2. The sam method applies here.
Common ratio r = T3/T2 = 128/32 = 4
r = 4
T2 = ar^(2-1) = ar
T2 = 32 = ar
Substituting the values of r;
32 = a × 4
a = 32/4
a = 8
First term = 8
Answer:
A
Step-by-step explanation:
(because -4 is equal to -4 and meets the condition of the top inequality, you plug in -4 into the top function)
![g(-4)=\sqrt[3]{(-4)+5}\\\\g(-4)=\sqrt[3]{1} =1](https://tex.z-dn.net/?f=g%28-4%29%3D%5Csqrt%5B3%5D%7B%28-4%29%2B5%7D%5C%5C%5C%5Cg%28-4%29%3D%5Csqrt%5B3%5D%7B1%7D%20%3D1)
Since 
represents the number of years passed since 2005, in 2005 we have 
, and in 2015 we have 
. Let 
represent the profits of Jones and Davis, respectively, at year y.
We have
Choosing the best company somehow depends on how much time you can wait: Jones start with a higher value (10 vs 8), but it has a descending trend, because the multiplicative factor 
goes to zero as t grows.
On the other hand, Davis starts with a smaller value, but 
tends to infinity as t grows.
So, if you need an immediate result, the most valuable company is Jones, otherwise you're certain can Davis will eventually become bigger.
More precisely, we have
So, after 11 years, Davis will overcome Jones.
Answer: C
Step-by-step explanation:
The given graph is a straight line graph.
Slope of a straight line graph is expressed as
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
From the graph,
y2 = 4
y1 = 1
x2 = 2
x1 = 1
Slope = (4 - 1)/(2-1) = 3/1 = 3
If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line parallel to the graph is 3
