Answer:
To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;
3·4ⁿ is divisible by 3 and 51 is divisible by 3
Where we have;
= 3·4ⁿ + 51
= 3·4ⁿ⁺¹ + 51
- = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ
- = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ
∴ - is divisible by 9
Given that we have for S₀ = 3×4⁰ + 51 = 63 = 9×7
∴ S₀ is divisible by 9
Since - is divisible by 9, we have;
- 
= 
- is divisible by 9
Therefore is divisible by 9 and is divisible by 9 for all positive integers n
Step-by-step explanation:
Answer:
Step-by-step explanation: 8*2x, 8*-14+13=4x-27
16x-112+13=4x-27
16x-99=4x-27
-4x -4x
12x-99=-27
+99 +99
12x = 72
/12 /12
x=6
Answer:
My net wroth would have changed by $800
Step-by-step explanation:
Because $3,100 - $2,300 = $800
Answer:
y = 30
Step-by-step explanation:
We can use ratio's to solve this
40 20
----- = -----------
100 20 + y
Using cross products
40 * (20+y) = 20*100
Distribute
800 + 40y = 2000
Subtract 800 from each side
40y = 2000-800
40y = 1200
Divide by 40
y = 1200/40
y =30
I) there are 360 degrees in a circle. So subtract all the numbers from 360 to get the angle for econ.
That angle is 65 degrees
ii) If 95 degrees represents 228 books, then 360 degrees represents "x" (total) books. So we have an equation:
<u>95</u> = <u>360</u>
228 x
Solve for x, and we get x = 864
iii) The percentage is 80 degrees out of 360 degrees or 2/9 or roughly 0.222 or 22.2%
