Answers
Observe that
7¹ ≡ 7 (mod 100)
7² ≡ 49 (mod 100)
7³ ≡ 343 ≡ 43 (mod 100)
and (using Euclid's algorithm)
7 ⁻¹ ≡ 43 (mod 100)
so that
7⁴ ≡ 7³ × 7¹ ≡ 43 × 7¹ ≡ 1 (mod 100)
This means
7⁷ ≡ 7⁴ × 7³ ≡ 1 × 43 ≡ 43 (mod 100)
Next,
(7⁷)⁷ ≡ 43⁷ ≡ (7 ⁻¹)⁷ ≡ (7⁷) ⁻¹ ≡ 43⁻¹ ≡ 7 (mod 100)
(3 7's)
Next,
((7⁷)⁷)⁷ ≡ 7⁷ ≡ 43 (mod 100)
(4 7's)
A pattern emerges: a power tower involving an even number of 7's will reduce to 43 (mod 100), so the last two digits of ((7⁷)⁷ ... )⁷ with 2020 7's will have 43 as its last two digits.
Related Questions
Write parametric equations of the line [tex]-4x+y=-2[/tex]
a. [tex]x=t, y=4t-2[/tex]
b. [tex]x=t, y=-4t-2[/tex]
c. [tex]x=t, y=4t+2[/tex]
d. [tex]x=t, y=-4t+2[/tex]
Answers
Answer:
Option a
Step-by-step explanation:
Assign a value to variable x =t
Eq becomes
-4t+y=-2
y=4t-2
Help pleaseee, I’ll give brainly!
Answers
Answer:
1) 6r+7=13+7r —> 7r–6r=7–13 —> r = – 6
2) 13–4x=1–x —> 4x–x=13–1 —> 3x=12 —> x=12/3 —> x=4
3)–7x–3x+2=–8x–8 —> –8x+7x+3x=2+8 —> 2x=10 –> x= 10/2 –> x= 5
4)–8–x=x–4x —> –x–x+4x=8 —> 2X=8 —> x= 8/2 —> x= 4
5) –14+6b+7-2b=1+5b —> 5b +2b –6b = –14+7–1 —> b=–8
6) n+2=–14–n —> n+n=–14–2 —> 2n = –16 —> n = – 16/ 2 —> n = – 8
7) n – 3n = 14 –4n —> n –3n + 4n = 14 —> 2n = 14 —> n = 14/ 2 —> n = 7
8) 7a – 3 = 3 + 6a —> 7a – 6a = 3 + 3 —> a = 6
9) 3(1–3x ) =2(–4x+7) —> 3 –9x = –8x+14 —> 9x–8x = 3–14 —> x = –11
10) –10 +x+4–5 =7x –5 —> 7x–x = –10+4–5 +5 —> 6x = –6 —> x= –6/6 —> x = –1
11) –8n +4(1+5n)=–6n–14 —> –8n +4 + 20n = – 6n– 14
20n –8n +6n= –14 –4 —> 18n = – 18 —> n = –18/18 —> n = –1
12) –6n–20=–2n +4(1–3n) —> –6n –20 = – 2n +4 –12n —> 12n +2n –6n = 4 +20 —> 8n =24 —> n = 24/8 —> n =3
I hope I helped you^_^
Answer:
1.
6r + 7 = 13 +7r
6r - 7r = 13-7
-r = 6
r = 6
2.
13 - 4x = 1-x
-4x +x = 1 -13
-3x = -12
x = -12 / -3
x = 4
3.
-7x - 3x + 2 = -8x -8
-10x +2 = -8x -8
-10x +8x = -8 -2
-2x = -6
x = -6 / -2
x = 3
4.
-8 - x = x- 4x
-8 - x = -3x
-x + 3x = -8
2x = -8
x = -8 / 2
x = -4
5.
-14 + 6b + 7 -2b = 1 + 5b
-7 + 4b = 1 + 5b
4b - 5b = 1 + 7
-b = 8
b = -8
6.
n + 2 = -14 -n
n + n = -14 -2
2n = - 16
n = -16 / 2
n = -8
7.
n - 3n = 14 -4n
-2n = 14 - 4n
-2n +4n = 14
2n = 14
n = 14 /2
n = 7
8.
7a - 3 = 3 + 6a
7a - 6a = 3 +3
a = 6
9.
3 ( 1 - 3x ) = 2 (-4x + 7)
3 - 9x = -8x +14
-9x +8x = 14 - 3
-x = 11
x = -11
10.
-10 + x + 4 - 5 = 7x - 5
-10 +x -1 = 7x - 5
-11 + x = 7x - 5
-11 + 5 = 7x -x
-6 = 6x
x = -6/6
x = -1
11.
-8n + 4 ( 1 + 5n ) = -6n -14
-8n + 4 + 20n = -6n -14
12n +4 = -6n -14
12n + 6n = -14 -4
18n = -18
n = -18/18
n = -1
12.
-6n - 20 = -2n + 4 ( 1 - 3n)
-6n - 20 = -2n + 4 - 12n
-6n - 20 = -14n +4
-20 -4 = -14n +6n
-24 = 8n
n = -24/8
n = -3
in 16 years, Marissa will be five times older than she is today. How old is she?
Answers
Answer:
4
Step-by-step explanation:
1 5
2 10
3 15
4 20
i wrote it out
x+16=5x
16=4x
4=x
Marissa is currently four years old.
What is algebra?Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use.
Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.
Let's represent Marissa's current age "x".
According to the given question, in 16 years she will be five times older than she is today, which we can express as:
x + 16 = 5x
Solving for x, we can subtract x from both sides:
16 = 4x
Dividing both sides by 4, we get:
x = 4
Therefore, Marissa is currently 4 years old.
To learn more about the Algebra link is given below.
brainly.com/question/953809
#SPJ6
In a group of 60 numbers, average of
the first 35 numbers is 18, that of next
15 numbers is 10 and that of the
remaining is 30. What is the average
of the entire group of numbers?
a)
16
b)
17
c)
18
d)
19
Answers
Answer:
c. 18
Step-by-step explanation:
First, you would find the total sum of the 60 numbers. The average is always the sum of the numbers divided by the number of numbers.
35*18=630
15*10=150
Now we do not know how many numbers the last group has. However, we can find it out doing 60-35-15 to see how many numbers are left. There would be 10 numbers left
10*30=300
630+150+300=1080
1080/60=18
Hence, the answer is C(18)
Please do a explanation:’)
Answers
Answer:
3x-3xy-2xy-5x+6. ( multiply the number that were outside the bracket)
By BODMAS rule...
= 3x-5x-3xy-2xy+6
= -2x-5xy+6
hope you understood...
Answer and Step-by-step explanation:
We are given an expression to simplify. According to PEMDAS
(Parenthesis, Exponents, Multiplication, Division, Addition, and Subtract [in that order]), we need to start with the parentheses first.
With what we are given, we need to multiply the value outside of the parenthesis to the values inside the parenthesis.
Start with the first set of terms in the expression.
3(x - xy)
We need to multiply 3 to the x and negative xy.
3x - 3xy
Now we go to the next set of terms in the expression.
-x(2y + 5)
Distribute the x (multiply) to the 2y and 5.
-2xy - 5x
Now, we combine like terms within the entire expression.
Combining like terms is essentially saying to combine the terms that have similar properties/values. We have values that have an x with it, and xy with it, and no variables with it. We can combine only the values with the x variable together, and the values with the xy variable can only be combined together. The values without the variables (if you have more than one), will combine only with each other.
3x - 3xy - 2xy - 5x + 6
____________________________________________
-5xy - 2x + 6 <- This is the final answer; the simplified version of the expression.
#teamtrees #PAW (Plant And Water)
Find the value of x in the parallelogram.
Answers
Answer:
75
Step-by-step explanation:
Since the two angles are on the same side of the parallelogram, they're supplementary.
x + (2x - 45) = 180
3x - 45 = 180
3x = 225
x = 75
What is | −34 | ?
-------
l l
-------
l l
--------
Answers
Step-by-step explanation:
Here,
| −34 |
= 34
As,
| | are absolute symbols so it's denote only the neutral number such as, | - 1 | = 1
Answer:
34
Step-by-step explanation:
|-34|
The absolute value bars means taking the non-negative value
|-34| = 34
Helpppppppppp I need help
Answers
Answer:
she is 4 years old just divide 39 by 9
helpppppppppppppppppppppp..... .......
Answers
Answer:
[tex]{ \sf{( \sec \theta - \csc \theta)(1 + \tan \theta + \cot \theta) }} \\ = { \sf{( \sec \theta + \tan \theta \sec \theta + \cot \theta \sec \theta) - ( \csc \theta - \csc \theta \tan \theta - \csc \theta \cot \theta)}} \\ = { \sf{( \sec \theta + \sec \theta \tan \theta + \csc \theta) - ( \csc \theta - \sec \theta - \csc \theta \cot \theta)}} \\ = { \sf{ \sec \theta \tan \theta + \csc \theta \cot \theta }} \\ { \bf{hence \: proved}}[/tex]
find the missing side lengths answers are in simplest radical form with the denominator rationalized.
Answers
Answer:
Option B is the answer
Step-by-step explanation:
x= 8, y=4√2
We know from pythagorean's law
(Hypotenuse) ^2 = (base)^2 + (height) ^2
i need serious helpplease its confusing....
Answers
area: 40p² + 24p
wide: 8p
(40p² + 24p)/ 8p
5p + 3
so, length: 5p + 3 -> (a)
perimeter = wide x 2 + length x 2
16p + (10p + 6)
26p + 6 -> (b)
Thank you so much thank y’all for your help
Answers
Answer:
2(4) + 2(l) >14 (second option is the answer).
Hope this is correct!
69 POINTS !!!!!!!
Which of the following describes the matrix?
[8 9 4]
[5 2 6]
[3 1 7 ]
3×3
3×9
9×3
2x3
Answers
Answer: Choice A) 3x3
The 3x3 refers to the number of rows and the number of columns in that order.
As another example, this matrix
[tex]\begin{bmatrix}1 & 7 & 9\\13 & 41 & 2\\5 & 8 & 7\\92 & 3 & 5\end{bmatrix}[/tex]
is a 4x3 matrix because it has 4 rows and 3 columns.
Violet is playing a board game with her friends. She earns 78 points during the game, and she receives a game-end bonus for achieving her secret objective. With her bonus, Violet came in second place with 91 points. Let b be the number of points Violet earned for the game-end bonus. Write and solve an equation for b.
Answers
Answer:
13
Step-by-step explanation:
78 + b = 91 Equation: Subtract 78 from both sides.
b = 91 - 78
b = 13
You don't need her position in the game or the fact that 91 placed her second.
I need help ASAP!!!Please explain the answer
Answers
Answer:
The formula for area is length times width.
it's 8m long, and 6m wide. When we multiply it, we get 48m that is for one side of the cube, so we count how many sides there is. There's 6, so we multiply 6 times 48 and the complete surface area for the whole cube is 288m
Andrew believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request. He asked 500 students at his school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?” The results are shown in the table below:
(attached)
Help Andrew determine if all students at his school have an equal opportunity to get the math class they requested. Show your work and explain your process for determining the fairness of the class assignment process.
Answers
Answer:
Honor students have a probability of 43% to non-honor students 25%.
Step-by-step explanation:
Prob of honor student getting math class choice = 215/500 = 43%
Prob of non-honor student getting math class choice = 125/500 = 25%
PLEASE ANSWER FAST
The solution set x s2 or x> 4 is consistent with an equation of the form
Answers
Answer:
yes
Step-by-step explanation:
it is not correct I think
To join the tennis club, there is a $10.20
initial fee and a $3.90 yearly fee. What
would be the value of the slope in this
situation?
Use this space to write down notes or work through problems
Your teacher will see what you wrate.
Answers
Answer:
10.20
Step-by-step explanation:
Let
y = Total fee
Initial fee = $10.20
Yearly fee = $3.90
Number of years = x
The equation:
y = 3.90x + 10.20
Recall,
y = mx + c
Where,
x = slope
c = y - intercept
Therefore,
The y - intercept from y = 3.90x + 10.20 is 10.20
the length and breadth of a hall is two times its breadth and the breadth is two times its height if the cost of papering its wall at rs 25 per sq metre is rs 10800 find the cost of paving marbles on its floor at rs 250 per sq .metre
.•♫•♬•plzz helpp•♬•♫•.•♬•♫•.
Answers
Answer:
Answer
Let height of the room be 'h' m.
∴ length of the room=2hm
breadth of the room=
2
3
hm.
area of 4 walls=
1.60
179.20
=112m
2
2(l+b)×h=112
2(2h+
2
3
h)×h=112
2×
2
7
×h
2
=112
h
2
=
14
112×2
=16
h=
16
=4m
length=4×2=8m, breadth=
2
3
×4=6m
for, tiling the floor area=l×b=8×6=48m
cost of tiling=48×6.75=Rs.324
PLZ Help! I'm crying over this....
Answers
Answer:
D
Step-by-step explanation:
The correct option is the Car stops at a distance away from the starting point because the portion shows a constant function away from the starting point.
From the graph we can tell that the distance of the car is a function and it's a line
Answered by G a u t h m a t h
Explain why they substituted cos(60) with 1/2 ?
(Look at image)
Answers
9514 1404 393
Answer:
equals can be substituted anytime anywhere
Step-by-step explanation:
cos(60°) = 1/2, so wherever one appears, the other can be substituted. This is allowed by the substitution property of equality.
__
If you don't substitute at some point, you find the answer to be ...
x = 10/cos(60°)
Most of us are interested in a numerical value for x, so we prefer that cos(60°) be replaced by a numerical value.
Write an expression in simplified form for the area of each rectangle. Width: 7 Length: 5n-9
Answers
Answer:
35n - 63
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
A = 7(5n-9)
Distribute
A = 35n - 63
Area of rectangle = Length * Width
Length is 5n-9
Width is 7
⇛Area = 5n-9(7)
⇛Area = 33n - 63
indices-find The value of 6*7^3
Answers
Answer:
[tex]6 * 7^3 = 2058[/tex]
Step-by-step explanation:
Given
[tex]6 * 7^3[/tex]
Required
Solve
App;y law of indices:
[tex]6 * 7^3 = 6 * 7*7*7[/tex]
Multiply
[tex]6 * 7^3 = 2058[/tex]
In the town of Rockville, 35 of the students in middle school participate in organized sports after school. If 14 of them play basketball, what fraction of the students play basketball?
Answers
Answer:
2/5
Step-by-step explanation:
The fraction that play basketball is the number that play basketball over the total
14/35
Divide the top and bottom by 7
2/5
Solve for p.
–
19p–2p+16p+12=
–
18
p=
Answers
Answer:
6
BRAINLIEST, PLEASE!
Step-by-step explanation:
-19p - 2p + 16p + 12 = -18
-5p + 12 = -18
-5p = -30
p = 6
Answer:
p = 6
Step-by-step explanation:
Given
- 19p - 2p + 16p + 12 = - 18 ( simplify left side )
- 5p + 12 = - 18 ( subtract 12 from both sides )
- 5p = - 30 ( divide both sides by - 5 )
p = 6
Can someone help with number 4 please? Due in 15 mins!!
Answers
Answer:
A. AG = 2 × GD
F. GE = (1/2) × BG
Step-by-step explanation:
The given point G on triangle ΔABC, which is the point of intersection of the medians of the triangle, is the centroid of the triangle
The centroid divides each median line in the ratio 2:1, therefore, we have;
The length of AG = 2 × GD, CG = 2 × GF, and BG = 2 × GE
∴ GE = (1/2) × BG
Therefore, the correct options are;
A. AG = 2 × GD, and F. GE = (1/2) × BG
find the following ratios right triangle. PLS HURRY and disregard my answers.
Answers
Answer:
sinA= 5/13; cosB= 5/13
Step-by-step explanation:
sine is opposite over hypotenuse so 5/13. cosine is adjacent over hypotenuse so 5/13
Find the length of the segment indicated. Round to the nearest tenth if necessary.
Answers
Answer:
x=5
Step-by-step explanation:
x is the length of the line segment from the center to the boderline of circle. So x=5
if the ordered pairs (x-2,3y+1) and (y+1,x+3) are equal,find x and y
plz help me
Answers
x=y+3
3y+1=x+3
x=3y-2
3y-2=y+3
3y-y=5
2y=5
y=2.5
x=(2.5)+3
x=5.5
Daniel buys a new car.
In the first year, the value of the car decreases by 12% of its original value.
The value of the car at the end of the first year is £9680.
(a) Work out the original value of the car.
The value of the car at the end of the first year is £9680.
In each of the second year, the third year, fourth year and the fifth year, the value of the car decreases by
x% of its value at the beginning of each year.
The value of the car at the end of the fifth year is £5000.
(b) Work out the value of x.
Give your answer correct to 3 significant figures.
Answers
Answer:
Step-by-step explanation:
Value of the car at the end of the first year = £9680
Depreciation = 12 %
Original price = £ x
If we reduce 12% of original price from x, we will get £9680
x - 12% of x = £ 9680
[tex]x-\frac{12}{100}x=9680\\\\\\\frac{88}{100}x=9680\\\\x=9680*\frac{100}{88}\\\\x = 11000[/tex]
Original price = £ 11000
