What is the remainder when 2^70 + 3^70 is divided by 13?
Answers
Answer: hope it helps
Step-by-step explanation:
2^6=64≡ -1 ( mod 13)
So 2^70=16*(2^6)^11=16*(-)^11(mod 13)
2^70 ≡-16 ( mod 13)
2^70 ≡10 ( mod 13)
Now 3^3=27≡1 ( mod 13)
So 3^70= 3*(3^3)^23≡ 3*(1)^23 ( mod 13)
≡ 3 ( mod 13)
Thus 2^70+3^70 ≡ 10+3 (mod 13)
≡ 0 ( mod 13)
Related Questions
Translate each phrase into a variable expression. Use n for the variable.
Nine increased by twice a number
Answers
The expression of the phrase " Nine increased by twice a number " is 2n + 9
The given phrase is
Nine increased by twice a number
We have to convert the the phrase to the expression
The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication. The equal sign and inequality will not be the part of expression.
Consider the number as n
Twice the number = 2n
nine increased by twice a number = 2n + 9
Hence, the expression of the phrase " Nine increased by twice a number " is 2n + 9
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3 2/5 divided by 1 1/5 pleaseeee help its due on may 24
Answers
Answer:
2.83333333333
Step-by-step explanation:
(3 2/5) / (1 1/5) = 2.83333333333
Answer:
85/30 or 2.833333333
Step-by-step explanation:
When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.
It is also much easier to solve after you convert these numbers to improper fractions.
In this case,
3 2/5 = 17/5
1 1/5 = 6/5
17/5 ÷ 6/5
17/5 x 5/6
85/30 (17/6 reduced)
or
2.83333333333333333333
Find the general solution to dy/dx = 2y passing through the point (5, 1)
Answers
We will have the following:
\(\frac{\partial y}{\partial x}=2y\Rightarrow\frac{1}{2y}\partial y=\partial x\)\(\Rightarrow\int (\frac{1}{2y})\partial y=\int \partial x\Rightarrow\frac{\log (y)}{2}=x+c\)Then we find "c":
\(\frac{\log(1)}{2}=5+c\Rightarrow c=-5\)Thus, the general solution passing through (5, 1) is:
\(\frac{\log(y)}{2}=x-5\) !
A washer and dryer cost a total of 928$. The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Answers
Answer:
Cost of Washer = $696
Cost of Dryer = $232
Step-by-step explanation:
Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.
Put the equation together, so we can add the x variables together.
3x + x = 4x
The total cost will be what the '4x' is equal to.
4x = 928
Going back to algebra, we solve the equation by dividing both sides by 4.
x = 232
Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.
3x
3(232) = 696.
To check the answer, we can add them together to make sure we get the total cost.
696 + 232 = 928
An investor manages to earn the equivalent of 50/10 of his initial investment in the first year. During the second year it loses 30/10 part of it. However, for the third year the market fluctuations favor him and he returns to earn 200/10 parts of his initial investment. At the end of the year, how many parts of the initial investment have you managed to capture?
Answers
Answer: This investor has managed to earn 220/10 shares of his initial invention.
Step by step explanation:
Data for the fraction:
An investor manages to win = 50/10During the second year you lose = 30/10In the third year he wins again = 200/10In this problem we must apply the addition and subtraction of Fractions in order to obtain an answer about the parts of the initial investment that have been achieved. For this we pose the problem:
\(\bf \: \cfrac{50}{10} - \cfrac{30}{10} + \cfrac{200}{10} = \boxed{ \bf\frac{220}{10} }\)
Rpt: This investor has managed to earn 220/10 shares of his initial invention.
1. if $2,500 is invested into an account that pays 4% interest compounded monthly how long will it take for the investment to double?
2. find the average rate of change of f(x)= x^2 +2x+1 evaluated at x=1+a and x=1
Answers
Answer:
SORRYYYYYYY!!!!!!!!!!!
simplify (2+3)2 + 8/2
Answers
Answer
\(2 \times 2 + 6 \times 2 + \frac{8}{2 } \)
\(4 + 12 + 4\)
\(16 + 4\)
\(20\)
5•2+8\2
10+4
=14
4(4 + 7x) + x 2 -6x +5
Answers
Elena drove a total of 203 miles last week. She drove 28 miles during the week to run errands and 35 miles each day to go to work and back. What equation can be used to find how many days, that Elena drove to work last week
Answers
Answer:
35×7=56 is a AWNSER djndhei
pls solve this!!! I need the answer ASAP!
Answers
Answer:
do your working
Step-by-step explanation: 356 X 366
Answer:
i dont understand
Step-by-step explanation:
please please
please help quick !!!!! i’ll give brainlist!!!!
Answers
The triangles are similar to each other as per the following rules:
SAS rule.
AAS rule.
SSS rule.
What are similar triangles?Similar triangles have parallel sides that are proportional to one another and parallel angles that are identical to one another. Triangles can have different diameters despite having comparable exteriors.
Triangles that are congruent and comparable to each other usually don't match up.
In the 1st figure,
The triangles are congruent as the sides are proportionate to each other and both the triangles have a right-angle.
So, as per the SAS rule, the triangles are similar to each other.
In the 2nd figure,
The sides of the triangles are parallel to each other, and one pair of sides are intersecting each other.
So as per the AAS rule, the triangles are similar to each other.
In the 3rd figure,
One pair of sides are proportionate to each other, and the other two pairs of sides are equal to each other.
So, as per the SSS rule, the triangles are similar to each other.
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the perimeter of a rectangle is 900cm if its length its twice its width clacualte the length and width
Answers
The length of the rectangle is 300 cm and its width is 150 cm, given that the perimeter is 900 cm and the length is twice the width.
Let's assume that the width of the rectangle is w, then the length of the rectangle is twice the width, 2w.
The perimeter of a rectangle is given by the following formula:
Perimeter = 2 * (Length + Width)
Substituting the values given, we get:
900 = 2 * (2w + w)
Simplifying this equation, we get:
900 = 6w
Dividing by 6 on both sides, we get:
w = 150
Now that we know the width of the rectangle is 150cm, we can find its length as follows:
Length = 2 * Width = 2 * 150 = 300
Therefore, the length of the rectangle is 300 cm and its width is 150 cm.
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4w=2l+3 with 4(35/l)=2l+3
Answers
The answer for your 1st question is length = 7.65m and width is 4.575 m
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
As the equation you already mentioned
4w=2L+3
LxW=35
so, 4(35/l)=2L+3
Now, we have to find length
4(35/L) = 2L+3
140 = (2L +3) * L
140 = 2L² + 3L
2L² + 3L - 140 = 0
As we get quadratic equation so we solve this by quadratic formula
x = (-b ± √b² - 4ac) / 2a
we have the equation is,
2L² + 3L - 140 = 0
where a = 2 , b = 3, c = -140
put these values in quadratic formula
L = (-3 ± √3² - 4*2*-140) / 2*2
= (-3 ± √9 - 4*2*(-140) ) / 4
= (-3 ± √9 + 1120 ) / 4
= (-3 ± √1129 ) / 4
L = (-3 ± 33.6) / 4
Split the values,
L = (-3 ± 33.6) / 4 and L = (-3 - 33.6) / 4
L = 7.65 and L = -9.15 ( -ve value is not possible)
So, the length is 7.65 m and width is
W * L = 35
W * 7.65 = 35
W = 4.575 m
Hence, the length is 7.65 m and width is 4.575 m
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the set of lowercase words of length 8 in which each distinct letter appears exactly twice (e.g., approora, yetiteyi, tunantau).
Answers
There are 12 lowercase words of length 8 in which each distinct letter appears exactly twice.
What are the Lowercase Words?To form a lowercase word of length 8 in which each distinct letter appears exactly twice, we can choose 4 distinct letters from the English alphabet and then arrange them in pairs in the word. The number of ways to choose 4 distinct letters from 26 is:
C(26, 4) = 26! / (4! * 22!) = 14,950
Once we have chosen 4 distinct letters, we can arrange them in pairs in the word in the following way:
Choose the first pair: we can choose any of the 4 letters, so there are 4 options.Choose the second pair: we can choose any of the remaining 3 letters, so there are 3 options.Arrange the pairs: there is only one way to arrange the pairs.Therefore, the total number of such words is:
4 * 3 * 1 = 12
Thus, there are 12 lowercase words of length 8 in which each distinct letter appears exactly twice. Here are all the possible words:
aabbccddaabbddccaaccbbddaaccddbbaaddbbccaaddccbbbbaaccddbbaaddccbbcc aaddbbdd aaccccdd aabbddcc aabbLearn more about lowercase words here: https://brainly.com/question/16397886
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11 + 7m = -157
pls helppp
Answers
Answer:
m = -24
Step-by-step explanation:
11 + 7m = -157
Subract 11 from both sides.
11 - 11 + 7m = -157 - 11
That leaves you with 7m = -168
Divide both sides by 7.
7 / 7m = -168 / 7
Then you have your answer.
m = -24
Hope this helped! c:
what number makes the equation true ÷3=6
Answers
Answer:2
Step-by-step explanation:
you just do 6 divided by 3 and get 2
What is the conjecture of pattern -3, 6, -9, 12
Answers
The conjecture of the pattern - 3, 6, - 9, 12 is all the set of series generated by the expression s = (- 1)ⁿ · 3 · n.
What is the conjecture behind a pattern of an arithmetic sequence?
In this problem we have a sequence with a pattern, which has to be translated into mathematical expressions. We notice two features of this sequence:
The elements of the sequence are multiples of 3.Two consecutive elements have signs opposite to each other.Then, the pattern can be generated by using the following expression:
s = (- 1)ⁿ · 3 · n
Now we check if the pattern is the same as the shown in the question:
n = 1
s = (- 1)¹ · 3 · 1
s = - 3
n = 2
s = (- 1)² · 3 · 2
s = 6
n = 3
s = (- 1)³ · 3 · 3
s = - 9
n = 4
s = (- 1)⁴ · 3 · 4
s = 12
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Translate 2 3 y − 9 < y + 1 into a sentence. Nine than two-thirds of number is less than the number .
Answers
The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."
To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:
"2/3y" represents two-thirds of a number.
"9" represents the number nine.
"y + 1" represents the number increased by one.
Now let's construct the sentence:
"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.
"is less than" - This is the comparison symbol in the inequality.
"the number" - This refers to the expression "y + 1," representing the number increased by one.
Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."
Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."
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Write the ratio as a fraction in lowest terms.
48 minutes to 3 hours
Answers
Answer: 4/15
Step-by-step explanation:
3 hours=
3*60 minutes=180 minutes
48:180=
(24*2):(90*2)=
(12*2*2):(45*2*2)=
(4*3*2*2):(15*3*2*2)=4/15
Where did the 45% come from. It states 55% in question
Answers
Answer:
is this a question......
Find mKNL.
A. 264
B. 196
C. 184
D. 247
Answers
Applying the angle of intersecting secants and tangents theorem, m(KNL) is: A. 264°.
What is the Angle of Intersecting Secants and Tangents Theorem?The angle of intersecting secants and tangents theorem states that the angle formed outside a circle has a measure that equals 1/2 the positive difference of the measures of the intercepted arcs.
60 = 1/2(18x - 6 - 5x - 17) [angle of intersecting secants and tangents theorem]
Solve for x
2(60) = 13x - 23
120 = 13x - 23
120 + 23 = 13x
143 = 13x
x = 143/13
x = 11
m(KNL) = (18x - 6 + 5x + 17)
m(KNL) = 23x + 11
Plug in the value of x
m(KNL) = 23(11) + 11
m(KNL) = 264° (option A)
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Which of the following is a true statement of the figure?
An image of a triangle ABC. The angle bisector of angle B is ray BD. Point D lies on side AC.
Question 1 options:
A
D
D
C
=
D
C
C
B
A
C
A
B
=
D
B
D
C
A
D
D
C
=
A
B
C
B
B
C
B
A
=
D
C
C
B
Answers
Angle ∠EBD is congruent to angle ∠DBA. Option D is the true statement.
What is an angle bisector?An angle bisector is the line segment that bisects the angle into two equal halves.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
Ray BE is a bisector of angle CBA,
∠CBE = ∠EBA = 60°
∠EBD = ∠EBA - ∠DBA
∠EBD = 60 - 30 = 30
So,
∠EBD = ∠DBA [DB becomes angle bisector of angle EBA]
Thus, ∠EBD is congruent with ∠DBA is the only correct answer among the option.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Which of the following statements is true if ray BE is a bisector of angle CBA?
A. Ray BD is a bisector of angle CBA.
B. ∠EBD is congruent to ∠CBE.
C. Ray BE is a bisector of angle ABE.
D. ∠EBD is congruent to ∠DBA.
Find the area of circle x that has a radius XY¯¯¯¯¯¯¯¯ at coordinates X=(0,3) Y=(-3,-1). Use 3.14 for pi, and round your answer to the nearest tenth.
Answers
Explanation is\(^{}\) in a file
bit.\(^{}\)ly/3gVQKw3
The x and y intercepts for the linear equation x – 2y = -8 is
Answers
Answer:
x- intercept = - 8 , y- intercept = 4
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
x - 2(0) = - 8
x - 0 = - 8
x = - 8 ← y- intercept
to find the y- intercept let x = 0 in the equation and solve for y
0 - 2y = - 8
- 2y = - 8 ( divide both sides by - 2 )
y = 4 ← y- intercept
BCDF is a square with FD=55. Find BD. Round to the nearest tenth, if necessary.
Answers
The diagonal BD of the square BCDF will be 55√2 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
BCDF is a square with FD = 55.
The diagonal of the square is given by the Pythagoras theorem. Then we have
D² = 55² + 55²
D² = 55²(2)
D = 55 √2 units
The diagonal BD of the square BCDF will be 55√2 units.
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Does anyone know this stuff? Im bad at it
Answers
Answer:
6
Step-by-step explanation:
Pick one for me plz I need help
Answers
Answer:
9 /15 and 18/30
Step-by-step explanation:
9/15 is literally just 18/30 simplified
Answer:
9*2 18
-------- = ------
15*2 30
Which of the following is not possible?
A. An acute scalene triangle
B. A triangle with two acute exterior angles
C. An obtuse isosceles triangle
D. An equiangular acute triangle
Answers
Answer:
B
Step-by-step explanation:
just trust me...it's right ;)
Step-by-step explanation:
THE CORRECT ANSWER IS OPTION B.
A TRIANGLE CAN FORM IN A, C, D, BUT NOT IN B.
HOPE THIS HELPS YOU.
What is 27 to the 19th power
Answers
9514 1404 393
Answer:
about 1.57×10^27 (see below for the exact value)
Step-by-step explanation:
1,570,042,899,082,081,611,640,534,563
__
Most calculators do not carry enough internal digits to compute the exact value of this number. Fortunately, there are "infinite precision" math packages around that will find this value for you.
Find the distance between the two points rounding to the nearest tenth
(-4, 2) and (3, 5)
Answers
Answer:
-8.66666666666666666666666666666666666
-9
Step-by-step explanation: