There are 60 minutes In a second. This means that 50 minute passed between 3:23 and 4:13.
Answer:
f ( x ) = ( x - 5 ) ² - 20
Step-by-step explanation:
1- Add the same value to both sides
f ( x ) = x ² - 10x + 5
2- Add 25 to the expression
f ( x ) + ? = x ² - 10x + ? + 5
3- Add 25 to the left-hand side
f ( x ) + ? = x ² - 10x + 25 + 5
4- Factor the expression
f ( x ) + 25 = x ² - 10x + 25 + 5
5- Move the constant to the right
f ( x ) + 25 = ( x - 5 ) ² + 5
6- Calculate
f ( x ) = ( x - 5) ² + 5 - 25
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(a) This is the same as computing 4⁵⁵ (mod 11). We have
4² ≡ 16 ≡ 5 (mod 11)
4³ ≡ 4 • 5 ≡ 20 ≡ 9 (mod 11)
4⁴ ≡ 4 • 9 ≡ 36 ≡ 3 (mod 11)
4⁵ ≡ 4 • 3 ≡ 12 ≡ 1 (mod 11)
Then from here,
4⁵⁵ ≡ (4⁵)¹⁰ • 4⁵ ≡ 1¹⁰ • 1⁵ ≡ 1 (mod 11)
(b) Each term in the sum
4ⁿ + 4ⁿ⁺¹ + 4ⁿ⁺² + 4ⁿ⁺³ + 4ⁿ⁺⁴
has a common factor of 4ⁿ, so this sum is the same as
4ⁿ (1 + 4 + 16 + 64 + 256) = 4ⁿ • 341 = 4ⁿ • 11 • 31
So the sum is indeed divisible by 11 for all integers <em>n</em>.
(c) Since 4ⁿ = (2ⁿ)², we know the sum is also divisible by 11 when <em>a</em> = 2.
Answer:
x = 72
Step-by-step explanation:
![\frac{x}{16}=\frac{9}{2} \\\\](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B16%7D%3D%5Cfrac%7B9%7D%7B2%7D%20%20%5C%5C%5C%5C)
Start by multiplying 16 to both sides
![(\frac{16}{1}) * \frac{x}{16} = (\frac{16}{1}) * \frac{9}{2}](https://tex.z-dn.net/?f=%28%5Cfrac%7B16%7D%7B1%7D%29%20%2A%20%5Cfrac%7Bx%7D%7B16%7D%20%20%3D%20%28%5Cfrac%7B16%7D%7B1%7D%29%20%2A%20%5Cfrac%7B9%7D%7B2%7D)
16s on the left-hand cancel
![x =(\frac{16}{1}) * (\frac{9}{2})](https://tex.z-dn.net/?f=x%20%3D%28%5Cfrac%7B16%7D%7B1%7D%29%20%2A%20%28%5Cfrac%7B9%7D%7B2%7D%29)
![x =( \frac{144}{2} )](https://tex.z-dn.net/?f=x%20%3D%28%20%5Cfrac%7B144%7D%7B2%7D%20%29)
we can simplify that expression
![x = 72](https://tex.z-dn.net/?f=x%20%3D%2072)