Answer:
This is a convergent geometric series. The sum is 30.
Step-by-step explanation:
In your series, the ratio of terms is 3/5, a value whose magnitude is less than 1. That means the series is convergent. The sum is given by the formula ...
S = a1/(1 -r)
where a1 is the first term (12) and r is the common ratio (3/5). This gives ...
S = 12/(1 -3/5) = 12·5/2 = 30
The series is convergent and has a sum of 30.
Answer:
3 1/2 houses
Step-by-step explanation:
To find the unit rate we must divide 4 by 10
4 hours divided by 10 house = 1/4
1/4 houses per hour
8 hours times 0.4= 3.2 houses
Answer:
b=36-d
Step-by-step explanation:
b=balloons after being popped
d=balloons popped
Answer:
Step-by-step explanation:
Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,
Firstly convert it into <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em><em>c</em><em>e</em><em>p</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line which is <u>y</u><u> </u><u>=</u><u> </u><u>m</u><u>x</u><u> </u><u>+</u><u> </u><u>x</u><u> </u>, as ;
On comparing it to <em>y</em><em> </em><em>=</em><em> </em><em>m</em><em>x</em><em> </em><em>+</em><em> </em><em>c</em><em> </em>, we have ,
Now as we know that the <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>w</em><em>o</em><em> </em><em>p</em><em>a</em><em>r</em><em>a</em><em>l</em><em>l</em><em>e</em><em>l</em><em> </em><em>l</em><em>i</em><em>n</em><em>e</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>s</em><em>a</em><em>m</em><em>e</em><em> </em>. Therefore the slope of the parallel line will be ,
Now we may use <em>p</em><em>o</em><em>i</em><em>n</em><em>t</em><em> </em><em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line as ,
On substituting the respective values ,
Again the equation can be rewritten as ,

Answer: M(2) = $1500*(1 - 0.026)^2 = $1423.01
Step-by-step explanation:
Initially in the acount there is $1500
You lose a 2.6% (or 0.026 in decimal form) per year, so after the first year you have:
M = $1500 - 0.026*$1500 = $1461
After other year, you lose oter 2.6%
M = $1461 - 0.026*$1461 = $1423.01
The equation can be writen as:
M(t) = $1500*(1 - 0.026)^t
Where t is the number of years, you can use t = 2 and get:
M(2) = $1500*(1 - 0.026)^2 = $1423.01