Answer:
108 th term is zero
Step-by-step explanation:
The nth term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 99 and a₉₉ = 9 then
a₁ + 8d = 99 → (1)
a₁ + 98d = 9 → (2)
Subtract (1) from (2) term by term to eliminate a₁
0 + 90d = - 90
90d = - 90 ( divide both sides by 90 )
d = - 1
Substitute d = - 1 into (1) for value of a₁
a₁ + 8(- 1) = 99
a₁ - 8 = 99 ( add 8 to both sides )
a₁ = 107
Then
107 - (n - 1) = 0
107 - n + 1 = 0
- n + 108 = 0 ( subtract 108 from both sides )
- n = - 108 ( multiply both sides by - 1 )
n = 108
The 108th term is zero
Answer:
slope of M'N' = 1
Explanation:
First, we will need to get the coordinates of points M' and N':
We are given that the dilation factor (k) is 0.8
Therefore:
For point M':
x coordinate of M' = k * x coordinate of M
x coordinate of M' = 0.8 * 2 = 1.6
y coordinate of M' = k * y coordinate of M
y coordinate of M' = 0.8 * 4 = 3.2
Therefore, coordinates of M' are (1.6 , 3.2)
For point N':
x coordinate of N' = k * x coordinate of N
x coordinate of N' = 0.8 * 3 = 2.4
y coordinate of N' = k * y coordinate of N
y coordinate of N' = 0.8 * 5 = 4
Therefore, coordinates of M' are (2.4 , 4)
Then, we can get the slope of M'N':
slope = (y2-y1) / (x2-x1)
For M'N':
slope = (3.2-4) / (1.6-2.4)
slope = 1
Hope this helps :)
4/(1/2) = 8
8 * 1 1/3 = 8 8/3 = 10 2/3 cups of B
Answer:
x = -9, 9.
Step-by-step explanation:
x^2 - 81 = 0
x^2 = 81
x = -9, 9.