Using the <em>system of equation</em> created, Emily will catch up Lucy after 30 seconds
Given the Parameters :
- Lucy's distance = 2t
- Emily's distance = 5t
<u>We can set up an equation to represent the required scenario thus</u> :
Emily's distance = Lucy's distance + 90
5t = 2t + 90
We solve for t
<em>Collect like terms</em> :
5t - 2t = 90
3t = 90
Divide both sides by 3 to isolate t
t = 90/3
t = 30
Therefore, Emily will catch up with Lucy after 30 seconds
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Answer:
x=-2.5 if the function is
Step-by-step explanation:
has discontinuities when the denominator is 0.
You will either have a hole or a vertical asymptote depending on what happens to the numerator after you find when the bottom is 0.
That is whatever you found that makes the bottom 0, if it makes the top also 0 then you will have a hole at x=the number that made the bottom 0.
If it makes the top anything other than 0, then it is a vertical asymptote at x=the number you found that made the bottom 0.
Let's do this now.
When is -4x-10 equal to 0?
We have to solve the equation:
-4x-10=0
Add 10 on both sides:
-4x=10
Divide both sides by -4:
x=10/-4
Reduce by dividing top and bottom by 2:
x=5/-2
x=-5/2
or
x=-2.5 (if you want decimal form)
Now does it make the top 0? This is the deciding factor on whether you have a hole at x=-2.5 or a vertical asymptote at x=-2.5.
Let's see.
8(-2.5)-3=-23
Since the top is not 0 at x=-2.5 then you have a vertical asymptote at x=-2.5.
If the top were 0, then you would have had a hole at x=-2.5.
Y = - 10x + 2
the slope is -10
rise over run
the line is declining 10 units for every one unit to the right
and the line hits the y-axis at + 2 so 2 = b
Three consecutive integers that have a sum of 45 are 14, 15 and 16. 14+15+16=45
Answer:
for 
Step-by-step explanation:
Given
-- First Term
--- half common difference
Required
Find the recursive rule
First, we calculate the common difference

Multiply through by 2


The second term of the sequence is:

The third term is:

So, we have:


Substitute f(1) for 3

Express 1 as 2 - 1

Substitute n for 2

Similarly:

Substitute f(2) for 11

Express 2 as 3 - 1

Substitute n for 3

Hence, the recursive is:
for 