Answer:
converge
Step-by-step explanation:
The ratio that you multiply by to get the next term is 2/3, which is less than 1, so the geometric series converges by the Geometric Series Test.
Answer:
Step-by-step explanation:
1) First, find the slope of the equation. Use the slope formula 
. Substitute the x and y values of the given points into the formula and solve:
Thus, the slope is 
.
2) Now, use the point-slope formula 
to write the equation in point-slope form (from there we can convert it to slope-intercept). Substitute values for 
, 
, and 
.
Since represents the slope, substitute for it. Since and represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, the end result will be the same) and substitute its x and y values into the formula as well. (I chose (4,1), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the answer.
Answer:
A
Step-by-step explanation:
The constant of proportionality is the ratio between the two proportional variables in a directly proportional relationship. In this case, the variables are 
and 
.
To find the constant of proportionality, all we have to do is divide any value of by its corresponding value of . Let's take the values in the first row of the table. We know that 
and 
, so the constant of proportionality is 
. Hope this helps!
Answer:
a) 91 1/6 gallons
b) 2502 miles
Step-by-step explanation:
You are given a number of miles and a number of gallons for the car. The ratio of these numbers is ...
(261 mi)/(14.5 gal) = 18 mi/gal
We presume this value is constant for this car. Then the questions can be answered by forming and solving a proportion:
a) 1641 miles/(gallons) = 18 mi/(1 gal)
Multiplying by gallons and dividing by 18 mi/gal, we get
1641/18 gal = (gallons) = 91 1/6 gal
It will take 91 1/6 gallons of gasoline for Mary to drive to her friend's house.
___
b) Same deal, but the miles are unknown.
(miles)/(139 gal) = (18 mi)/(1 gal)
Multiplying by 139 gal gives ...
(18 mi)·139 = (miles) = 2502 mi
139 gallons of gasoline will let Mary drive 2502 miles.
Answer:
14
Step-by-step explanation:
6 x 10 = 60
60 - 5 = 55
5 x 10 = 50
50 - 9 = 41
55 - 41 = 14
