Given that $13^{-1} \equiv 29 \pmod{47}$, find $34^{-1} \pmod{47}$, as a residue modulo 47. (Give a number between 0 and 46, inclusive.)
The value would be [tex]34^{-1} \pmod{47}=30[/tex]
What is the modulus in mathematics?
In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.
Given that 13^-1 ≡ 29 (mod 47), we can use this information to find the inverse of 34 mod 47. The inverse of a number modulo m is a number x such that the product of the number and its inverse is congruent to 1 mod m.
In the case of the given equation, [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex] is saying that 29*13 = 377 is congruent to 1 mod 47.
We can use this congruence to find the inverse of 34 mod 47. The inverse of 34 mod 47 is the number x such that 34*x = 1 mod 47. So we can write this congruence as [tex]$34x \equiv 1 \pmod{47}$[/tex]
We can use the given congruence of 13^-1 ≡ 29 (mod 47) to find the inverse of 34 mod 47.
Since [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex], we can multiply both sides of the congruence by 34 as:
[tex]$13^{-1} * 34 \equiv 29 * 34 \pmod{47}$[/tex]
Now we can substitute the right side of the equation:
[tex]$13^{-1} * 34 \equiv (13*29) \pmod{47}$[/tex]
And now we can substitute the left side of the equation:
[tex]$34^{-1} \equiv (13*29) \pmod{47}$[/tex]
And since [tex]$13*29 = 377$[/tex] this is congruent to 30 (mod 47) the inverse of 34 mod 47 is 30.
Therefore, the value would be [tex]34^{-1} \pmod{47}=30[/tex]
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The value would be 13.
What is the modulus in mathematics?
In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.
We can use the property of modular inverse that
[tex]$(ab)^{-1} \equiv b^{-1}a^{-1} \pmod{m}$[/tex]
So, [tex]$(13*34)^{-1} \equiv 34^{-1} \cdot 13^{-1} \pmod{47}$[/tex]
[tex]$13^{-1} \equiv 29 \pmod{47}$\\$(13*34)^{-1} \equiv 34^{-1} \cdot 29 \pmod{47}$So, $34^{-1} \equiv (13*34)^{-1} \cdot 13 \pmod{47}$$34^{-1} \equiv 1 \cdot 13 \pmod{47}$$34^{-1} \equiv 13 \pmod{47}$[/tex]
Hence, The value would be 13.
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Find four consecutive odd integers such taht 4 times the sum of the first and third is 4 larger than 4 times the fourth
The four consecutive odd integers = 15, 17, 19, 21
What are integers ?Positive, negative, and zero are all examples of integers.
The Latin word "integer" signifies "whole" or "intact."
As a result, fractions and decimals are not included in integers.
All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.
According to our question-
x + x + 6 = -(x + 4) + 55
x + x+6 = (-x - 4) + 55
2x + 6 = -x + 51
Collect like terms
2x + x = 51 - 6
3x = 45
x = 15
Second integer = x + 2 = 15 + 2 = 17
Third integer = x + 4 = 15 + 4 = 19
Fourth integer = x + 6 = 15 + 6 = 21
The four consecutive odd integers = 15, 17, 19, 21
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How do you write no solution?
No solution is when a system of equations has no solution. This means that the equations are inconsistent, and there is no set of values that can make the equations true.
For example, if the system of equations is 2x + 3y = 4 and 2x + 3y = 5, then there is no solution. This is because no matter what values are chosen for x and y, the equations cannot both be true. This means that the system of equations is inconsistent, and there is no solution.
To symbolically represent no solution, you can use the following notation:
2x + 3y = 4, 2x + 3y = 5 No solution
This notation is used to indicate that the equations are inconsistent and that there is no solution.
Complete question: What is the solution to the equation 2x + 3y = 4 and 2x + 3y = 5?
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How do you find f inverse?
Inverse of function is written by using notation f⁻¹
What is inverse of function?The function that can be reversed into another function is termed as inverse function. It is also called anti function. There are different types of inverse function such as inverse trigonometric function, inverse rational function, inverse log function and so on.
We can determine an inverse function by interchanging the elements that present in the given expressions.
How do we find f inverse?Inverse of the function f is denoted by notation f⁻¹
let, we have given a function, f(x) = 8x + 9
now, we need to find the inverse of the above function.
in the first step we write the function using y and set equal to x
x = 8y +9
in the next step, we arrange to make the y subject,
x - 9 = 8y
8y = x - 9
y = (x - 9)/ 8
use the notation f⁻¹ = (x - 9)/ 8
this is the inverse of function f.
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auggie bought 8 books. Some books cost $13 each and the rest of the books cost $24 each. They spent a total of $159. Write a system of linear equations that could represent the given situation
Answer: Let x be the number of $13 books that Auggie bought and y be the number of $24 books. Then we can represent the given information in the following system of linear equations:
x + y = 8 (the total number of books Auggie bought is 8)
13x + 24y = 159 (the total amount of money Auggie spent is $159)
This system of linear equations represents the given situation. We can use this system to find out how many books Auggie bought of each price by solving the system of equations.
The equation (1) represents the number of books that Auggie bought is 8, and equation (2) represents the amount of money he spent $159. This system of equations is a valid representation of the given situation because the values of x and y that satisfy the system of equations will be the number of $13 books and the number of $24 books that Auggie bought.
Step-by-step explanation:
Its pre-algebra. I need it fast
Answer:
Obtuse and isosceles
Step-by-step explanation:
obtuse because an angle is more than 90* and isosceles because two sides are equal.
Hope this helps!
It takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.What is the length (in meters) of the train
After solving, the length of the trains in meters is 60 meters.
In the given question, it takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.
We have to find the length (in meters) of the train.
Let the length of the train is x.
The length of the bridge is 100 meters.
As we know that the formula of the speed is the ratio of distance that he traveled in the certain duration of time.
So Speed = Distance/Time
So according to the question;
(x + 100)/40 = x/15
Now solving the expression using the cross multiplication
15x + 1500 = 40x
Subtract 15x on both side, we get
25x = 1500
Divide by 25 on both side, we get
x = 60 meters
Hence, the length of the trains in meters is 60 meters.
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4. Nicole uses 2.5 meters of ribbon to decorate
door wreaths. There are 20 meters of ribbon on a
spool. Write an equation that could be used to
determine the number of wreaths that Nicole
could decorate using one spool of ribbon. Solve.
Equation:
An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:
W = S / R
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:
W = S / R
where W is the number of wreaths, S is the total length of ribbon on the spool, and R is the length of ribbon used per wreath.
Plugging in the given values, we get:
W = 20 / 2.5
Solving for W, we get:
W = 8
So Nicole could decorate 8 wreaths using one spool of ribbon.
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How do you solve 3 equations with 3 unknowns on a Casio calculator?
The process to solve 3 equations with 3 unknown is explained below.
The term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign.
The process of 3 equation with 3 unknown variable is explained step by step as follows:
First of all we have to write all the equations in standard form cleared of decimals or fractions.
And then we have to choose a variable to eliminate them then we have to choose any two of the three equations and eliminate the chosen variable.
After that we have to select a different set of two equations and eliminate the same variable as in Step 2.
Now, we have to solve the two equations from steps 2 and 3 for the two variables they contain.
And then we have to substitute the answers from Step 4 into any equation involving the remaining variable.
And then finally we have to check the solution with all three original equations.
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store a charges $8 per movie plus a $10 shipping fee for each order (no matter how many movies are in the order). An order of movies from store z always costs the same as ordering the same number of movies from store A. How much does store Z charge per movie
Store Z charges $8 per movie.
What is an expression?
An expression is the mathematical statement that is formed by numerical and variable terms along with operators. It represents the method of a mathematical operation in a symbolic form.
How much does store Z charge per movie?
given, store A charges $8 per movie.
for each order shipping fee = $10
if store A is ordered x movie at a time than the total cost for one order
represented by the expression, $8 x + $10.
As per question, store Z cost always the same as store A for one order.
so, cost for one order in case of store Z = $8x + $10
if x denotes the number of movies that is ordered at a time, then the Z store charges $ 8 per movie.
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In the figure below, side AC of ABC lies on line l.
A. 25
B. 30
C. 22
D. 24
As you can see, 5y is an external angle of triangle ABC
we know that 5y=180-x
since angle B is 40, and angle A=x and C=x, we have
x%2Bx%2B40=180
2x=180-40
x=140%2F2
x=70
so, angle A=70 and C=70
then
5y=180-70
5y=110
y=110%2F5
y=22
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Show youR WORK please send. A photo it could help
Answer:
Step-by-step explanation:
1 ft= 12 inches
So 5ft = 60 Inches
4= 0.3
Thus, Its 60.3
need help quickly
The polygons are similar. x = ___ Write your answer as a decimal
Answer:0.23
Step-by-step explanation:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The circle equations for circles with diameters of 12 units that lie on the y-axis are:
x^2 + (y – 3)^2 = 36x^2 + (y + 8)^2 = 36Which equations represent circles?We want to find the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis, now, remember that the general equation for a circle of radius R and a center (a, b) is:
(x - a)^2 + (y - b)^2 = R^2
If we want a circle that lies on the y-axis, then a = 0, and if the diameter is 12 units, then the radius is R = 6 units.
Then the equation is something like:
x^2 + (y - b)^2 = 6^2 = 36
The two circle equations with this form are:
x^2 + (y – 3)^2 = 36x^2 + (y + 8)^2 = 36Learn more about circle equations:
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Jack invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of his investment after x years: f(x)
Equation = P(1+r)^x, where P is the initial amount invested, r is the fixed interest rate, and x is the number of years.
It is important to note that the equation provided is the formula for compound interest. P is the initial principal, r is the annual interest rate, and x is the number of years the money is invested. The equation gives the total amount of money in the account after x years.
It should be also noted that the interest rate is given as a decimal and not a percentage.
For example, if the interest rate is 5%, then r = 0.05.
In order to use this equation, the value of P, r and x should be known
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Factor expression 12p-28 factored using GCF is?
Answer:
4(3p - 7)
Step-by-step explanation:
First find the factors of 12 and 28:
12: 1, 2, 3, 4, 6, 12
28: 1, 2, 4, 7, 28
Notice any common factors: 1, 2, 4
Now, out of these factors, 4 is the GCF since it is the greatest common factor, so divide 12 and 28 by 4:
12/4 = 3. 28/4 = 7.
Hence, 12p-28 = 4(3p - 7)
1. You have cup of flour in a bin and
7
-
2
8
-
3
cup of flour in a bag. To determine
whether you have enough flour for a
3
recipe that needs 1 cups of flour,
4
should you use an estimate, or is an
exact answer required? Explain.
The exact value is required. In this case, they don't have enough for 1 3/4 cups of flour.
How to express the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
From the information, the person had 2/3 cup of flour in a bin and 7/8 flour was still in the bag. In this case, it should be noted that they also wanted to know of they had enough for 1 3/4 cups of flour.
This will be calculated thus:
= 2/3 + 7 / 8
= 16/24 + 21/24
= 37 / 24.
= 1 13 / 24
This is not enough for 1 3/4 cups of flour.
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Range of 63, 42, 28, 45, 36, 48, 32, 40, 57, 49
There is a line that includes the point (9,–8) and has a slope of –19. What is its equation in point-slope form?
Answer:
y +8 = -1/9(x -9)
Step-by-step explanation:
You want the point-slope form of the equation of the line through point (9, -8) with slope -1/9.
Point-slope formThe equation of the line through point (h, k) with slope m is ...
y -k = m(x -h)
You have (h, k) = (9, -8), and m = -1/9. Using these values, the equation is ...
y +8 = -1/9(x -9)
3. How many groups 1/2 of days are in 1 week?
groups
please help me find the surface area of this triangular prism
The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.
How do you find the area of a prism?The surface area of a triangular prism is defined as the sum of the area of its five faces. To calculate the surface area, we need the values of the base, length, and height of the triangular prism. Its formula equals the sum of two times the base area and three times the product of the base and length of the prism.Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. The formula A = 1 2 b h is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.To find the surface area of a prism, use the formula SA=2B+ph, where SA stands for surface area, B stands for area of the base of the prism, p stands for the perimeter of the base, and h stands for the height of the prism.Two triangles' area: 18×24÷6x3 = 432cm^2
The widest rectangle's area: 30×7 = 210cm^2
The rectangle facing the left's area: 18×7= 126cm^2
The rectangle facing the ground's area: 24×7= 168cm^2
Total Surface Area: 432+210+126+168 = 936cm^2
=936cm^2
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The school surveillance camera was able to capture an image of the suspect. The image
shows the thief standing next to the gym door. In real life the door measures 84 inches but
is 14 cm in the image. If your suspect is 10.83 cm in the photo. How many inches tall are
they in real life? (Round to nearest whole inch.) Report the height in feet and inches. Ex.
"2 feet 5 inches"
Answer:
77.4 inches
6 feet 4 inches
Step-by-step explanation:
what persent of 14 is 10.83 is 77.35
what persent of 84 is 77.3571428571 is 92.08
what is 92.08% of 84 is 77.34
77.34 inches to feet is 6 feet and 4 inches
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Use the image below for Part A, Part B, and Part C.
Two triangles: GHI and JKL
Both have one similar angle but different side lengths
Part A: Sharon says the triangles above are similar using the AA Postulate. Is she correct?
Part B: Explain the answer from Part A.
Part C: If HI=7, find KL. Show your work.
Please Help!
Answer:
see explanation
Step-by-step explanation:
A
for the triangles to be similar by the AA postulate then 2 angles in both triangles must be congruent.
In this case we are only given 1 pair of congruent angles.
Thus not able to say similar by AA postulate, therefore Sharon is incorrect in her assumption.
B
the sides are of different lengths but the ratios of corresponding sides are equal, that is
[tex]\frac{JK}{GH}[/tex] = [tex]\frac{8}{4}[/tex] = 2 and [tex]\frac{JL}{GI}[/tex] = [tex]\frac{10}{5}[/tex] = 2
If the ratios of 2 pairs of corresponding sides of 2 triangles are equal and the included angles are congruent , then the triangles are similar, so
Δ GHI and Δ JKL are similar by the SAS postulate
C
the ratios of corresponding sides are equal , then
[tex]\frac{KL}{HI}[/tex] = [tex]\frac{JL}{GI}[/tex]
[tex]\frac{KL}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )
KL = 14
Charlie runs laps around a track. The table shows how long it takes him to run different numbers of laps. How long would it take Charlie to run 5 laps?
Number of laps 2 4 6 8 10
Time (min) 18 36 54 72 90
It will take Charlie ___
minutes to run 5 laps.
270 mins - 10 laps
xmins -5 laps
(cross multiply)
270*5=10x
10x=1350
x= 1350/10
x=135 mins
Solution for 4x+3y=11 over 2x+y=7
Answer
x=-1/2,=29/4
explanation
2 Dylan needs 2.5 liters of water for an experiment. He has 1.125 liters.
How much more water does Dylan need?
Show your work.
Dylan needs how many
liters of water.
So Dylan needs 1.375 liters of water more for his experiment.
Define percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Define Fraction.Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
To find out how much more water Dylan needs, we can subtract the amount of water he currently has from the amount of water he needs for the experiment.
2.5 - 1.125 = 1.375 liters
So Dylan needs 1.375 liters of water more.
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Of the 50 members of a staff, 40 percent worked the day shift and the remaining 60 percent worked the night shift in a given week. Of the staff members, 80 percent prefer working the day shift and the remaining 20 percent prefer working the night shift. What is the minimum number of staff members who failed to receive his or her preference of shift that week
The minimal number of employees who did not get their preferred shift that week was 20.
Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.
But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.
We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.
But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.
Thus, 20 is the minimum number of staff members who failed to receive her preference of shift that week.
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What is the mole of o2?
The number of mole O₂ is 2. Since the subscript of oxygen denotes the number of moles.
What is a diatomic element?
Diatomic molecules—so named because they only contain two atoms of the same or different chemical elements—are molecules that are made up of two atoms. A diatomic molecule is considered to be homonuclear if it contains two atoms of the same element, such as oxygen (O₂) or hydrogen (H₂).
One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.
The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.
The subscript part of a chemical compound represents the number of moe of the chemical compound. The subscipt of O₂ is 2. Thus the number of mole is 2.
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Luke just accepted a job at a new company where he will make an annual salary of $58000. Luke was told that for each year he stays with the company, he will be given a salary raise of $2000. How much would Luke make as a salary after 9 years working for the company? What would be his salary after tt years?
Answer:
1. $76,000
2. $58,000 + $2,000 * t
Step-by-step explanation:
2. Now, you might be questioning why we are going with the second question first, but this will be useful as it sets up our equation to make the first question easier. So, we will start with Luke's base salary of $58,000. Then, we will add $2,000 for every year he works at the company. If he works for t years and gains $2,000 on his salary per year, our equation will look like this:
$58,000 + $2,000 * t
That is the equation.
1. Now, using our previous equation, $58,000 + $2,000 * t, we will substitute 9 in for t. We get:
$58,000 + $2,000 * 9
Then, we simplify, giving us:
$58,000 + $18,000 = $76,000
The data set represents the total number of tickets each person purchased for a play.
0,0,1,1,1,2,2,2,4,
What is the median of the daya?
Answer:
The median of the data is 1