Answers
(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 n.
(c) Since 4ⁿ = (2ⁿ)², we know the sum is also divisible by 11 when a = 2.
Related Questions
how to solve this derivative.
f(x)={ln(3x)}^2x
with steps...
Answers
Rewrite f(x) as a nested exponential-logarithm expression :
[tex]\left(\ln(3x)\right)^{2x} = \exp\left(\ln\left(\ln(3x)\right)^{2x}\right)[/tex]
(where [tex]\exp(x) = e^x[/tex])
One of the properties of logarithms lets us drop the exponent as a coefficient:
[tex]\exp\left(\ln\left(\ln(3x)\right)^{2x}\right) = \exp\left(2x\ln\left(\ln(3x)\right)\right)[/tex]
Now, by the chain rule, we have
[tex]f(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \implies \\\\ f'(x) = \left(\exp\left(2x\ln\left(\ln(3x)\right)\right)\right)' \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2x\ln\left(\ln(3x)\right)\right)'[/tex]
By the product rule,
[tex]f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left( (2x)' \ln\left(\ln(3x)\right) + 2x\left(\ln\left(\ln(3x)\right)\right)' \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left( 2\ln\left(\ln(3x)\right) + 2x\left(\ln\left(\ln(3x)\right)\right)' \right)[/tex]
By the chain rule again,
[tex]f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + 2x \cdot \dfrac1{\ln(3x)} \cdot \left(\ln(3x)\right)' \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + \dfrac{2x}{\ln(3x)} \cdot \dfrac1{3x} \cdot (3x)' \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + \dfrac{2}{3\ln(3x)} \cdot 3 \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + \dfrac{2}{\ln(3x)} \right)[/tex]
Then simplify this to
[tex]f'(x) = \boxed{\left(\ln(3x)\right)^{2x} \left(2\ln\left(\ln(3x)\right) + \dfrac{2}{\ln(3x)} \right)}[/tex]
Question 3 of 10 Classify the following triangle. Check all that apply. 70° 15.8 8 80" 30 15 O A. Equilateral B. Obtuse C. Isosceles D. Right E. Acute F. Scalene
Answers
Answer:
the answer F or D
Step-by-step explanation:
Find the slope of (3,-2) and (4,4)
Answers
Answer:
0
Step-by-step explanation:
What is the rate of change of the function y=x-2
Answers
Answer:
The rate of change is 1.
The equation of a line and y-intercept form is
y = mx + b, where m = the slope of the line.
and our given equation y = x - 2 the slope of the line is 1 in other words y = 1x - 2
lý thuyết mạch ... giúp em với
Answers
...........................
What is the value of n in the proportion below?
n/28 = 4/7
•1
•12
•14
•16
Answers
Answer:
n = 16
Step-by-step explanation:
Given the proportion, n/28 = 4/7:
Cross multiply the two fractions:
7n = 28 × 4
7n = 112
Divide both sides by 7 to solve for n:
7n/7 = 112/7
n = 16
Therefore, the value of n = 16.
Please mark my answers as the Brainliest, if you find this helpful :)
Explanation: 7 goes into 28 four times which would set the denominators as equal. But to finish converting the fraction, you would have to multiply 4 by four just like you did the denominator which gives you 16.
What is the average rate of change of g(x)=4x+5 ?
Answers
9514 1404 393
Answer:
4
Step-by-step explanation:
The equation is in slope-intercept form:
y = mx +b
where m is the slope (average rate of change).
In the given equation, m = 4.
The average rate of change is 4.
Ross sold b boxes of cookies, and gabby sold 35 boxes of cookies. Together they sold a total of 69 boxes of cookies
Answers
the answer is b=34
Write 41 and 4 as a mixed number
Answers
Answer:
10 and 1 fourth
Step-by-step explanation:
41 over 4 = 41/4 so you divide 41 by 4 which is 10 R1 so its 10 wholes, 1 and 4
WATTPAD SUGGESTIONS? :)
Answers
Answer:
Step-by-step explanation: about a boy who fell for a girl that was twice his age and yeah something about that :)
if ryan has $1127 left after spending 1/5 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill, what was his monthly salary
Answers
Answer:
$1715
Step-by-step explanation:
1/5 + 1/ 7 = 12/ 35
So, he is left with 23/35 of his salary
if 23/35 of his salary is 1127
his whole salary is 1715
¿A qué velocidad debe circular un auto de carreras para
recorrer 50km en un cuarto de hora?
Answers
Answer:
creo que la respuesta es 3,333.33 mph
Step-by-stepStep-by-step explanation:
If a 4-pound roast takes 150 minutes to cook, how long should a five-pound roast take
Answers
Answer:
A 5-pound roast would take about 187.5 minutes to cook.
Divide 150 minutes by 4 pounds and you get 37.5 minutes. This would be how long it takes to cook each pound. So, you multiply 5 pounds by 37.5 and you get 187.5 minutes for a 5-pound roast to cook.
451 mi/ 7.3 hr. Round to the appropriate number of significant digits.
Answers
Answer:
5
Step-by-step explanation:
Three
consecutive
inirgers
17
The length of a flat screen TV is 5 inches less than 3 times its width. If the perimeter of the TV is
150 inches, find the dimensions.
Answers
To find dimensions 3x-5 + x + x + 3x-5 = 150
Perimeter = 2l + 2w so that’s why we repeated
So now we simplify
8x - 10 = 150
Add 10 to both sides
160 = 8x
Divide 8 from both sides
X=20
So width is 20 inches. and to find length it is:
3(20)-5 = 60 -5
=55
Length = 55 inches
Can I get brainliest answer.
Find the degree of the monomial -1.57k^2
Answers
Answer:
2
Step-by-step explanation:
Degree of the monomial is the highest power in the monomial.
Highest power in the monomial - 1.57k^2 is 2.
So, the degree of the monomial - 1.57k^2 is 2.
simplify each expression and state the number of terms in the final answer.
Answers
1) 4m+3j, 2 terms.
2) -11x+6y+9, 2 terms
3) [tex]11g^5+6g^4-4gh\\[/tex], 2 terms
ingredients: f(6)-20 = (?)cups of sugar. use f(x) = x² - 2x - 3
Answers
Answer:-18 mm sugar
Step-by-step explanation:
Thanks me later
You and your friends Jose and Sarah all live on the same street. You know that Jose lives 7 blocks away from you. Jose says that Sarah lives 6 blocks from him, but he didn't say whether she lives closer to you than he does or further. Let represent the number of blocks from you that Sarah might live.
Answers
Answer:
farthur
Step-by-step explanation:
f(x) = x² + 2ax + a² - a
g(x) = 4 - x²
Let variable a be a real number. Find the range of values of a such that the equation f(x) = g(x) has two different solutions.
***The answer should be -2 < a < 4, but I don't know why.
Answers
Step-by-step explanation:
f(x) = x² + 2ax + a² - a
g(x) = 4 - x²
f(x) = g(x)
x² + 2ax + a² - a = 4 - x²
2x²+2ax+a²-a -4 =0
the equation has two different solutions
=> (2a)² - 4(2)(a²-a-4) > 0
4a²-8a²+8a +32 >0
-4a²+8a+32 > 0
a²-2a-8 >0
(a-4)(a+2) < 0
the answer should be
-2 < a < 4
13.On many multiple-choice tests, 1 point is given for each correct
answer and 0.25 point is taken away for every wrong answer.
(This is to discourage guessing.) Answers that are left blank
do not affect the score. Gloria scored 62 on a test with 100
questions. Let C be the number of questions Gloria correctly
answered and let W be the number of wrong answers she had.
Give three possible pairs of values of C and W.
b. Write an equation that describes all possible solutions.
c. Graph all possible solutions.
a.
Answers
Hoped it helped
Simplify (5 1/3) exponential 3
Answers
125 /3
hope this helps have a great day
mark brainliest:)
[tex]\rm\purple{\overbrace{\underbrace{\tt\color{black}{\:\:\:\:\:\:\:\:Answer:\:\:\:\:\:\:\:\:\:}}}}[/tex]
125/3
[tex]\large\red{ChaEunWoo2009}[/tex]
#CarryOnLearning
a. is the value of the expression (1/4 ^-3)^-2 greater than 1 equal to 1 or less than 1
b. if the value of the expression is greater than 1 show how you can change one sign to make the value less than 1, show how you can change one sign to make the value greater than 1 if the value is equal to 1 show how you can make one change to make the value not equal to 1
please I need an answer quick ._.
Answers
A.
[tex]((1/4)^{-3})^{-2} = (1/4)^{(-3)*(-2)}=(1/4)^6<1[/tex]So it is less than 1
B.
We can change -3 to 3 or -2 to 2.
This will result in:
[tex](1/4)^{-6}=4^6 >1[/tex](a) The value of given expression "((1/4)⁻³)⁻²" is less than 1, and (b) To make value greater than 1, change second exponent to positive; to make it equal to 1, change first exponent to 0.
Part (a) : Starting from the innermost exponent, (1/4)⁻³ simplifies to 4³, which is 64.
So, ((1/4)⁻³)⁻² becomes (64)⁻², which is 1/4096. Since 1/4096 is less than 1, the value of the expression is less than 1.
Part (b) : To change the value to greater than 1:
Change the second exponent to a positive value, making it ((1/4)⁻³)²,
This simplifies to (4³)², which is 4096.
To change the value to equal 1:
Change the first exponent to 0, making it ((1/4)⁰)⁻². This simplifies to (1)⁻², which is 1.
Learn more about Expression here
https://brainly.com/question/10730206
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When x is a nonzero integer, the sum of −10 + x is sometimes negative and sometimes positive. negaive or positive, explain your answer.
Answers
Answer: if the x is negative the answer will be positive but if -10 is the only negative it would be negative. The way I remember is if their is a even amount of negatives is will be positive if theirs a odd amount it would be negative . Hope this helps :)
Step-by-step explanation:
6g = -86; g= -16
Need help
Answers
Answer:
6g = -86
Divide each term in 6 g = − 86 by 6 and simplify.
Exact Form: g = -43/3
Decimal Form: g = −14.¯3
Mixed Number Form:
g = −14 1/3
—————————————————————
g= -16
Vertical line at x = −16
An isosceles triangle has two sides of equal lenght. The length of the third side is 1 ft less than twice the length of one of the equal sides find the length of each side when the perimeter is 23 ft, answer as a comma separated list
Answers
Answer: An isosceles triangle has two sides of equal length. The length of one of the equal sides is two more than 3 times the length of the third side. If the perimeter is 46m, find the length of each side.
Step-by-step explanation:
Hope this helps!
Answer:
Step-by-step explanation:
The perimeter is equal to the lengths of all the sides.
Let x equal the two sides that are equal to each other.
Then the 3rd side is 2x - 1 which is 2 times the length of the equal side minus 1.
So the perimeter 23 = x + x + (2x-1)
Now solve for x
23 = x + x + 2x - 1
add 1 to both sides
24 = x + x + 2x
24 = 4x
x = 6
The two equal sides would be 6 feet each
The other side would be 2(6) - 1 = 11
The perimeter is 6 + 6 + 11 = 23
explain how to calculate a unit rate such as 300 miles per hour 4 hour
my brain is not working today i need help
Answers
Answer:
75
Step-by-step explanation:
divide 4 by 300 and then you will get the answer of 75. I'm so sorry if this is wrong
can you help me pwease i give brainliest
Answers
Answer:
I believe your answer should be B.) I hope this helps! :D
A copy machine makes 32 copies per minute. How many copies does it make in 4 minutes and 15 seconds?
Answers
9514 1404 393
Answer:
136
Step-by-step explanation:
15 seconds is 1/4 minute. We can find the number of copies by multiplying the rate by time:
(32 copies/min)(4.25 min) = 136 copies
The machine can make 136 copies in 4 minutes 15 seconds.
Rewrite the fraction 1/6 as a division expression with the same numbers.
Answers
9514 1404 393
Answer:
1 ÷ 6
Step-by-step explanation:
1/6 is a division expression. It means "one divided by six."
The slash (/) can be replaced by the "divided by" symbol (÷), if you like.
1/6 = 1 ÷ 6 . . . . means "one divided by six"