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
So first number is -10
second number is -6
make 7 1/2 a improper fraction, and divide 15 by the improper fraction to see how long he walks in one minute.
The formula is (x-h)^2+(y-k)^2=r^2
so, using this, and knowing that h is -3 and k is -5 and r is 4, we get
(x--3)^2+(y--5)^2=(4)^2, which equals
(X+3)^2+(y+5)^2=16
:)
Answer:
10 inches
Step-by-step explanation:
The length of the playground in its actual size is 120 feet.
The scale drawing uses a scale of 1 inch to 12 feet.
This means that 1 inch in the drawing equals 12 feet in actual size.
Therefore, the length of the playground on the scale drawing is:
1 inch = 12 feet
x = 120 feet
Cross-multiply:
120 * 1 = 12 * x
=> x = 120 / 12 = 10 inches
The length of a side of the playground on the scale drawing is 10 inches.