Answer:
The sum of the given series is 1023
Step-by-step explanation:
Geometric series states that a series in which a constant ratio is obtained by multiplying the previous term.
Sum of the geometric series is given by:
where a is the first term and n is the number of term.
Given the series: 
This is a geometric series with common ratio(r) = 2
We have to find the sum of the series for 10th term.
⇒ n = 10 and a = 1
then;
Therefore, the sum of the given series is 1023
3.84 meters because 2% of 48 is 0.96, 0.96*4, which is 3.84
Answer:
(x+1)(2x+5)
Step-by-step explanation:
f(x) = 2x² + 7x + 5
Factor the expression by grouping. First, the expression needs to be rewritten as 2x²+ax+bx+5. To find a and b, set up a system to be solved.
a+b=7
ab=2×5=10
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 10.
1,10
2,5
Calculate the sum for each pair.
1+10=11
2+5=7
The solution is the pair that gives sum 7.
a=2
b=5
2x²+7x+5 as (2x²+2x)+(5x+5).
(2x²+2x)+(5x+5)
Factor out 2x in the first and 5 in the second group.
2x(x+1)+5(x+1)
Factor out common term x+1 by using distributive property.
(x+1)(2x+5)
Answer:
Step-by-step explanation:
Answer:
The answer is below
Step-by-step explanation:
a) Let x represent the time taken to drive to see the relatives and let d be the distance travelled to go, hence:
60 mi/h = d/x
d = 60x
When returning, they still travelled a distance d, since the return trip takes 1 h longer than the trip there, therefore:
40 mi/h = d/(x+1)
d = 40(x + 1) = 40x + 40
Equating both equations:
60x = 40x + 40
60x - 40x = 40
20x = 40
x = 40/20
x = 2 h
The time taken to drive there = x = 2 hours
b) The time taken for return trip = x + 1 = 2 + 1 = 3 hours
c) The distance d = 60x = 60(2) = 120 miles
The total distance to and fro = 2d = 2(120) = 240 miles
The total time to and fro = 2 h + 3 h = 5 h
Average speed = total distance / total time = 240 miles / 5 h = 48 mi/h
