Solve each of the following congruences. Make sure that the number you enter is in the range [0,M−1] where M is the modulus of the congruence. If there is more than one solution, enter the answer as a list separated by commas. If there is no answer, enter N.
(a) 148x=1(mod399)
x=
(b) 204x=330(mod399)
x=
Answers
The general solution to the congruence is x ≡ -903/3 ≡ -301 ≡ 97 (mod 133).
What is congruency?
The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.
(a) To solve for x in the congruence 148x ≡ 1 (mod 399), we can use the extended Euclidean algorithm. We want to find integers s and t such that 148s + 399t = gcd(148, 399) = 1. We can use the Euclidean algorithm to find that gcd(148, 399) = gcd(148, 55) = gcd(33, 55) = gcd(22, 33) = gcd(11, 22) = gcd(11, 11) = 11.
Then we can use the extended Euclidean algorithm to find s and t:
11 = 33 - 22
= 33 - (55 - 33)
= 2 * 33 - 55
= 2 * (148 - 2 * 55) - 55
= 2 * 148 - 5 * 55
So s = 2 and t = -5. Since t can be negative, we can add multiples of 399 to t to get a positive t that is congruent to -5 (mod 399). For example, t = 394 is such a positive t.
Therefore, the general solution to the congruence is x ≡ 2 * 394 ≡ 788 (mod 399).
(b) To solve for x in the congruence 204x ≡ 330 (mod 399), we can simplify the congruence by dividing both sides by the gcd(204, 399). We have gcd(204, 399) = gcd(3 * 68, 3 * 133) = 3 * gcd(68, 133) = 3.
Dividing both sides of the congruence by 3, we get 68x ≡ 110 (mod 133). We can use the extended Euclidean algorithm to find integers s and t such that 68s + 133t = gcd(68, 133) = 1. Then we can multiply both sides of the congruence by s to solve for x.
1 = 133 - 2 * 68
= 133 - 2 * (201 - 133)
= 3 * 133 - 2 * 201
= 3 * 133 - 2 * (399 - 2 * 133)
= 7 * 133 - 2 * 399
So s = 7 and t = -2. We can multiply both sides of the congruence 68x ≡ 110 (mod 133) by 7 to get 476x ≡ 770 (mod 133).
Since 476 ≡ -3 (mod 133), we can simplify this congruence further to -3x ≡ 770 (mod 133).
We can add multiples of 133 to 770 to get a positive number that is congruent to 770 (mod 133). For example, we can add 133 to get 903.
Therefore, the general solution to the congruence is x ≡ -903/3 ≡ -301 ≡ 97 (mod 133).
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Related Questions
2+2=
a. 3
b. 5
c. 4
d. 7
Answers
Answer:
C
Step-by-step explanation:
2
+2
-----
4
Please break down how to do these pls
Answers
The value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.
Given expression 1. -4\(x^{-2}\) + 3\(y^{0}\) 2. 2\(x^{0}\)\(y^{-2}\)
Expression for x =2 and y=5
-4x-2 + 3y0
= -4(2)-2 + 3(5)0
= 16+3
=19
Now
2x0y-2
= 2(2)0x(5)-2
= 2 x (1/25)
= 2 x 0.04
= 0.08
Therefore the value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
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In recent years, Sheffield Transportation purchased three used buses. Because of the frequent turnover in the accounting department, a different accountant was in charge of selecting the depreciation method for each bus, and various methods have been used. Information concerning the buses is summarized in the table below. Bus 1, Bus 2, Bus 3, For the declining-balance method, the company uses the declining method rate. For units-of-activity method, total miles are expected to be 125,000. Actual miles of use in the first 3 years were 2021, 27,000; 2022, 35,000; and 2023, 33,000.
(a1) For Bus #3, calculate depreciation expense per mile under units-of-activity method.
Answers
Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.
How is the depreciation expense per mile determined?The units-of-activity method is one of the depreciation methods in use.
Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.
The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.
Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)
Expected total miles for Bus #3 = 125,000
Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)
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Question Completion:Bus Acquired Cost Salvage Useful Life Depreciation
Value in Years Method
1 1/1/12 $99,100 $7,900 4 Straight-line
2 1/1/12 128,000 11,000 4 Declining- balance
3 1/1/13 66,350 8,800 5 Unit-of-activity
Please please please help. I'm in honor's geometry and if I don't get my grade at least to a C, I'm going to fail
In the diagram below, m is the perpendicular bisector of BC.
If BK = 5x, AC = 6x + 7, CP = 4x, AB = 9x – 14. Find BC
Answers
Answer:
BC = 56 units
Step-by-step explanation:
since the main diagonal AK bisects the diagonal BC , then the figure is a kite.
• the disjoint pairs of consecutive sides are congruent in a kite, that is
AB = AC and BK = CK
using the pair AB = AC to solve for x
9x - 14 = 6x + 7 ( subtract 6x from both sides )
3x - 14 = 7 ( add 14 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
Since m bisects BC , then
CP = PB and
BC = CP + PB = 4x + 4x = 8x
then
BC = 8x = 8 × 7 = 56
Reuben made a shirt using 7/8yards of red fabric and 1/4yards of yellow fabric. How many more yards of red fabric did Reuben use?
Answers
Answer and Step-by-step explanation:
To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:
7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8
So, Reuben used 5/8 yards more red fabric than yellow fabric.
Una sala de cine de New York vende las entradas para niños a 3 dólares y las de los adultos a 5 dólares. Si para ver una película pueden ingresar tanto niños como adultos y en un día
ingresan 345 espectadores, recaudando por concepto de venta de boletas 1365 dólares. Se
puede afirmar que el número de niños y adultos que ingresaron fue:
Answers
A la sala de cine ingresaron 180 niños y 165 adultos.
¿Cuántos niños y adultos ingresaron a una sala de cine?
De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:
3 · x + 5 · (345 - x) = 1365
Donde x es el número de niños que asistieron a la sala de cine.
Ahora despejamos la variable correspondiente mediante propiedades algebraicas:
3 · x + 1725 - 5 · x = 1365
1725 - 2 · x = 1365
2 · x = 1725 - 1365
2 · x = 360
x = 180
Ahora, el número de adultos es:
y = 345 - 180
y = 165
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Which relationships would most likely be causal? Select two options.
a positive correlation between the number of homework assignments completed and the grade on the exam
a positive correlation between the temperature in a canyon in the early spring and the number of snakes seen by
hikers
a positive correlation between a child's shoe size and reading speed
a negative correlation between the time a glass of ice water sits on the counter and its temperature
a positive correlation between the number of students attending football games and the number of games that are
won
Answers
Answer:
A and B
Step-by-step explanation:
The relationships that are most likely to be causal are:
A positive correlation between the number of homework assignments completed and the grade on the examA positive correlation between the temperature in a canyon in the early spring and the number of snakes seen by hikers.When are relationships causal?A relationship is causal when one variable has a direct effect on another variable. For example, the number of assignments completed would have an effect on the grade on an exam because as a students compeletes his assingment he becomes more familiar with the course.
Positive correlation means that the two variables have a positive relationship with each other. If one of the variable increases, the other vairable increases.
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Which of the following is the smallest element in the set of natural numbers?
-1
O 1
There is no smallest element; the set is infinite.
0
Answers
Answer:
your answer would be 0 mark as brainliest
The three sides of a triangular fence have lengths 4x + 5, y − 7, and 3x − 2. What is the total perimeter?
A) 7x + y + 10 feet
B) 7x + y − 4 feet
C) 7x + y feet
D) 4x + y − 4 feet
Answers
The correct option is (b) i.e. the total perimeter of the fence is 7x + y − 4 feet.
What is Perimeter?
Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a polygon, circle, or ellipse. It is the sum of the lengths of all the sides or arcs that make up the shape. For example, the perimeter of a square is the sum of the lengths of all its sides, while the perimeter of a circle is the circumference, which is the distance around the circle. The perimeter is often measured in units such as centimeters, meters, or feet, depending on the context of the problem.
Given : sides of the fence
s₁ = 4x + 5
s₂ = y − 7
s₃ = 3x − 2
We know that, perimeter of a triangle is sum of all three sides.
So, Perimeter of the fence = s₁+ s₂+ s₃
= 4x + 5 + y − 7 + 3x − 2
= 7x + y - 4 ft.
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Suppose 15% of $x$ equals 20% of $y$. What percentage of $x$ is $y$ ?
Answers
Answer:
Step-by-step explanation:
A 78.0 kg sprinter starts a race with an acceleration of 1.64 m/s2. If the sprinter accelerates at that rate for 25 m, and then maintains that velocity for the remainder of the 100 m dash, what will be his time (in s) for the race?
Answers
The sprinter will complete the race in approximately 17.07 seconds.
To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.
Acceleration Phase:
The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:
v = u + at
Here:
v = final velocity (which is the velocity at the end of the acceleration phase)
u = initial velocity (which is 0 since the sprinter starts from rest)
a = acceleration
t = time
Rearranging the equation, we have:
t = (v - u) / a
Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:
t = v / a
Plugging in the values, we get:
t = 25 m / 1.64 m/s²
Constant Velocity Phase:
Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:
t = d / v
Here:
d = distance
v = velocity
Plugging in the values, we get:
t = 75 m / (v)
Since the velocity remains constant, we can use the final velocity from the acceleration phase.
Now, let's calculate the time for each phase and sum them up to get the total race time:
Acceleration Phase:
t1 = 25 m / 1.64 m/s²
Constant Velocity Phase:
t2 = 75 m / v
Total race time:
Total time = t1 + t2
Let's calculate the values:
t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)
Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:
v = u + at
Here:
u = initial velocity (0 m/s)
a = acceleration (1.64 m/s²)
t = time (25 m)
Plugging in the values, we get:
v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s
Now, let's calculate the time for the constant velocity phase:
t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)
Finally, let's calculate the total race time:
Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)
Therefore, the sprinter will complete the race in approximately 17.07 seconds.
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The total age of a cat, dog, and a monkey is 4 years 2 months. The dog is twice as old as the cat. The monkey is twice as old as the dog. How old is the monkey?
Answers
Answer:
qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
Step-by-step explanation:
Find the value of (x⋅y). ( Hint solve for x and y first )
Answers
Answer:
x = 0 and y = 0
Step-by-step explanation:
it's a nonsense question.
What is the inverse of the function
f(x) = 121x2 when x > 0?
Answers
Answer:
Step-by-step explanation:the answer is 12x
So far this semester, Franco is averaging a score of 70.7 points on math tests, which is 1% higher than his average last semester. What was the average of his scores last semester?
help me pleasee
Answers
write the equation of the line with the given slope and y-intercept
1. slope is -3 and y intercept of 7
2. slope is 1/4 and y- intercept is -5
Answers
Answer:
See below
Step-by-step explanation:
Remember that y=mx+b:
1) y = -3x+7
2) y = 1/4x-5
Use the table below to answer the following question,
2:
хо 1 2 3 4 5 6
y 100 200 400 800 1,600 3,200 6,400
Which equation BEST fits the data given in the table?
se 3:
Of(x) = { (200)*
Of(x) = 100(2)*
uge 4
f(x) = 200)
age 5
Of(x) = 200(2)*
5
Previous Page
Next Page
Page 2 of 11
Answers
Answer:
I don't know answer what is
does anyone have the keys for edmentum guided notes!!! please help
Answers
It is important to note that sharing or requesting specific keys or answers to educational materials, including guided notes, would be considered unethical and potentially a violation of academic integrity.
Guided notes are intended to assist students in actively engaging with course material and enhancing their learning experience. It is recommended that you approach your teacher or instructor for any clarification or additional resources you may need to fully understand the content.
They are in the best position to provide you with the necessary guidance and support.
Instead of seeking shortcuts or unauthorized access to answers, it is more beneficial to invest time and effort in studying, asking questions, and actively participating in your educational journey.
This approach will not only help you grasp the subject matter more effectively but also promote personal growth and knowledge development.
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Three ways to solve systems of equations ?
Answers
The surface area, S, of a right rectangular prism with length l, width w, and height h 29 can be found using the formula below.
S = 2(lw + wh + hl)
What is the surface area, in square inches, of a prism with a length of 12 inches, a width of 9 inches, and a height of 2 inches?
Answers
The surface area of the rectangle prism with length, width and height is 462 square inches.
Surface area of rectangle prism:
Surface area of prism is defined as the sum of the area of the 2 polygonal bases and the area of the lateral faces. The surface area of a prism is measured using square units.
Given,
Here we have the rectangle prism with length of 12 inches, a width of 9 inches, and a height of 2 inches.
Now, we need to find the surface area of the rectangle prism.
Here we have given that the surface area, S, of a right rectangular prism with length l, width w, and height h can be found using the formula below.
S = 2(lw + wh + hl)
Based on this, in the given question we have the value of
length l = 12 inches
width w = 9 inches
height h = 2 inches.
Now, we have to apply the values on the formula in order to solve it,
S = 2 ((12 x 9) + (9 x 2) + (2 x 12)
When we simplify it, then we get,
S = 2 (189 + 18 + 24)
S = 2 (231)
s = 462
Therefore, the surface area of the rectangle prism is 462 square inches.
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The major characteristic of the data that affects the selection of appropriate statistics is:
Group of answer choices
the level of measurement
the size of the population.
the representativeness of the sample
the number of cases
Answers
The major characteristic of the data that affects the selection of appropriate statistics is the level of measurement.
What is statistics?
Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical methods to gather, summarize, and interpret data, which can be used to make decisions or draw conclusions about a population based on a sample of that population.
The level of measurement determines the type of statistical analysis that can be used to analyze the data. Different types of statistical methods are used depending on the level of measurement of the data.
For example, if the data is nominal (categorical data with no inherent order), then we might use frequency distributions or chi-square tests to analyze it. If the data is interval or ratio (continuous data with an inherent order and equal intervals between values), then we might use measures of central tendency and dispersion, correlation, or regression analysis to analyze it.
Therefore, the major characteristic of the data that affects the selection of appropriate statistics is the level of measurement.
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A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answers
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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Find the sales tax and cost of a PS5 that costs $499. The tax rate is 7.25%. Round your answer to
the nearest cent.
a. What is the sales tax?
b. What is the total cost?
Answers
Step-by-step explanation:
First make an equation.
y=0.0725(499)
This equation would solve for the sales tax.
y=36.1775 or 36.18 because you have to round it l.
To find the total cost, you would do 499+36.18= $537.18
-3n+.5(6+10n)=.25(8n+12)
Answers
Answer:
the correct answer is: n ∈ R
What is 180 in./sec in m/min?
Answers
274.32 is the answer. Tell me if I need to be more precise.
Question 10 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
2y-4x=6
y-2x=7
OA. More than 1 solution
B. x = 4, y = -2
C. x = -1, y = 1
D. No solution
Answers
First isolate y on both then graph
2y-4x=62y=4x+6y=2x+3--(1)And
y-2x=7y=2x+7Update:-
In both equations slope is equal so lines are parallel hence no solutions
Answer:
D. no solution
Step-by-step explanation:
Given system of equations:
\(\begin{cases}2y-4x=6\\y-2x=7\end{cases}\)
The solution to a graphed system of equations is the point(s) of intersection.
From inspection of the graphs (attached), there is no point of intersection so there is no solution.
Proof
Rearrange the given equations to make y the subject:
Equation 1
\(\implies 2y-4x=6\)
\(\implies 2y=4x+6\)
\(\implies y=2x+3\)
Equation 2
\(\implies y-2x=7\)
\(\implies y=2x+7\)
Slope-intercept form of a linear equation: \(y=mx+b\)
(where m is the slope and b is the y-intercept)
Therefore, the slope of both equations is 2. When the slopes of two lines are the same, the lines are parallel ("inconsistent") and therefore never intersect. Hence proving that there is no solution to the given system of equations.
i need helppp please geometryy
Answers
Step-by-step explanation:
2x-15=x5
2x-x=15+5
x=20
stay safe healthy and happy.Answer:
x = 20
Step-by-step explanation:
Because of the angle bisector, we know that the m∠ACE and the m∠ECB are equivalent. Therfore, we can set the equations as equal to eachother and solve for x.
simplify 3(x-y)+3x+2
Answers
Answer:
6x-3y+2
Step-by-step explanation:
I AM BIG BRAIN
What is the area of
the segment? Express
the answer in terms
of pi.
Answers
The area of the segment is 9( π-2) units²
What is area of segment?The area of a figure is the number of unit squares that cover the surface of a closed figure.
A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.
Area of segment = area of sector - area of triangle
area of sector = 90/360 × πr²
= 1/4 × π × 36
= 9π
area of triangle = 1/2bh
= 1/2 × 6²
= 18
area of segment = 9π -18
= 9( π -2) units²
therefore the area of the segment is 9(π-2) units²
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Find the values of a, b and c
Answers
Answer:
3rd option
Step-by-step explanation:
use hypotenuse method