Answer:
a = 4
b = 11
Step-by-step explanation:
To convert the recurring decimals into fraction we will follow the following process.
Given recurring decimal is 0.36363636....
Let x = 0.363636......... (1)
Multiply this decimal with 100.
100x = 36.36363636...........(2)
Now subtract expression (1) from expression (2)
100x = 36.363636.......
<u> x = 0.363636.......</u>
99x = 36
x = 
x = 
Since, 
a = 4 and b = 11 will be the answer.
Answer:
If p is the smallest of n consecutive integers of the same sign than we have p , p+1 , p+2 , … , p+(n−1) ,
So the sum is
∑k=0n−1(p+k)=∑k=0n−1p+∑k=0n−1k=np+n2−n2
Here n=4
So we have 4p+6
And checking
p+(p+1)+(p+2)+(p+3)=4p+6
Note if p=−v
Than you have the same thing as if p=v−n+1 just negative for example 3 consecutive integers the smallest is −5 so the sum is −5+(−4)+(−3)=3×−5+32−32=−15+3=−12
On the other hand:
−(3+4+5)=−(3×3+32−32)=−(9+3)=−12
If p=−v the sum of next v+1 integers is −(∑k=0vk)=−(v2+v2)
Than needs an other v integers to bring it up to 0 again. From there it is
∑k=0hk=h2+h2
Where h=n−(2v+1) .
So recap if p is the smallest of n consecutive integers their sum is
p+(p+1)+(p+2)+…+(p+(n−1))=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪np+n2+n2−(n|p|+n2+n2)((n−|p|)2+(n−|p|)2)−(|p|p+|p|2+|p|2)((n−|p|)2+(n−|p|)2)n≥0p<0∧n<|p|+1p<0∧|p|<n<2|p|+1p<0∧n>2|p|+1
Step-by-step explanation:
Answer:
Comic Books
a: y=-10x+90
b: He will have 10 books at the end of the seventh day.
Step-by-step explanation:
A: Take two points. The y-intercept is (0,90). The graph decreases by 10 each day.
B: Look at day 8.
Answer:

Step-by-step explanation:
step 1
Find the slope of segment HI
The formula to calculate the slope between two points is equal to

we have
H (-4,2), and I (2,4)
substitute the given points


simplify

step 2
Find the slope of the perpendicular line to segment HI
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

we have

so

step 3
Find the midpoint segment HI
we know that
The formula to calculate the midpoint between two points is equal to
we have
H (-4,2), and I (2,4)
substitute
step 4
we know that
The perpendicular bisector of HI is a line perpendicular to HI that passes though the midpoint of HI
Find the equation of the perpendicular bisector of HI in point slope form

we have

substitute

step 5
Convert to slope intercept form

Isolate the variable y



step 6
Convert to standard form

where
A is a positive integer
B and C are integers

Adds 3x both sides

see the attached figure to better understand the problem