Given that $k$ is a positive integer less than 6, how many values can $k$ take on such that $3x \equiv k \pmod{6}$ has no solutions in $x$

Answers

Answer 1

Supposing the value of x to be an integer, the values of k that donot

satisfy the given equation 3x = k mod 6 are 1,2,4,5.

What is an integer?

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

What is the difference between integers and whole numbers?

Integers are a set of numbers that include both positive and negative numbers, as well as zero. Whole numbers, on the other hand, only include the set of non-negative numbers starting from 0 (i.e., 0, 1, 2, 3, 4, ...). In other words, whole numbers are a subset of integers.

If 3x = k mod 6 has no solutions in x, then k must not be divisible by 3. The positive integers less than 6 that are not divisible by 3 are 1, 2, 4, and 5. Therefore, k can take on 4 values: 1, 2, 4, and 5.

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Related Questions

What are the 3 different polynomial equation?

Answers

The 3 different polynomial equations are linear polynomial equations, quadratic polynomial equations, and cubic polynomial equations.

A polynomial equation is one where a polynomial is set equal to zero. i.e., it is an equation created with variables, non-negative integer exponents, and coefficients together with operations and an equal sign.

A polynomial equation is always like "polynomial = 0". Algebraically, it is of the form p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₁ x¹ + a₀x⁰ = 0, where

aₙ, aₙ₋₁, ...., a₁, a₀ are coefficients and all these numbers are real numbers.

'x' is the variable.

p(x) means "polynomial in terms of variable x"

'n' is a non-negative integer, it is the degree of p(x).

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Select the correct answer.A wooden board that is 108 inches long is cut into two equal parts. What is the length of each part in feet

Answers

4.5 is the length of each part in feet. This can be solved by using the concept of feet.

What is feet?

foot, plural feet, any of a wide range of ancient, medieval, and modern linear measurements (often 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.

The foot measured [tex]11^{\frac{1}{42}[/tex] inches in antiquity. The typical man's foot measures 12 inches in length nowadays.

Given that:

The length of the wooden board is given as = 108 inches.

As it is cut in 2 equal parts, it becomes: 108/2 = 54 inches in each

We have to calculate the length of each part in feet, so divide 54 by 12.

As we know,

12 inches = 1 feet

Thus, 54 inches = 54/12 feet = 4.5 feet

So, the length of each part is 4.5 feet.

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Emily invested $810 in an account paying an interest rate of 3 and 5/8% compounded monthly. Jûlian investéd $810 in an account paying an interest rate of 3 and 1/4% compòunded continuoûsly

Answers

Answer:

$1752

Step-by-step explanation:

------------

Added below

I HAVE A F PLEASE HELP ASAP 100 POINTS

Answers

It’s the relationship of X

Answe num 3 and 4 plz and thx

Answers

Answer:

41 1/4 and 15

Step-by-step explanation:

So for the first question, we know that a single inch of thread has 16 1/2 bolts. We know that there are 2 1/2 inches of thread.

To find the total anount of bolts in the thread, we can multiply 2 1/2 by 16 1/2:

2 1/1*16 1/2 = 41 1/4

That is our first answer.

For our next answer, we know that a book is 1 7/8 inches big.

The bookshelf is 28 1/8 inches big.

To find how many of the 1 7/8 inch big books can fit in the 28 1/8 inch big bookshelf, we can divide 28 1/8 by 1 7/8:

28 1/8/1 7/8

=

15

So our 2nd answer is 15.

Hope this helps!

Find three consecutive numbers such that the sum of twice the first, three times the second and four times the third togetherbmakes 191.​

Answers

Answer:

find 3 consecutive numbers such that twice the first , 3 times the second and 4 times the third together make 191 ?

Let n-1,n and n+1 be three consecutive numbers.

Given

2(n-1)+3n+4(n+1)=191

2n-2+3n+4n+4=191

9n+2=191

9n = 189

n = 21

So, n-1=20 and n+1=22

So the answer is 20,21,22

[tex] \huge \bold{\color{red}{ANSWER}}[/tex]

[tex]\pmb { \orange{Given }:} \sf{ Three \: Consecutive \: numbers}[/tex]

[tex]\pmb{\orange{To find}: } \sf{Least \: of \: the \: numbers}[/tex]

[tex]\pmb{\orange{Solution}: }[/tex]

[tex]\sf{Let \: the \: three \: consecutive \: numbers \: be }[/tex]

[tex] \sf\red x, \red {x+1}, \red{x+2}[/tex]

[tex]\sf{Twice \: the \: number = 2\red x}[/tex]

[tex]\sf{3 \: times \: the \: Second \: number = 3(\red{ x+1})}[/tex]

[tex]\sf{4 \: times \: the \: third \: number= 4(\red {x+2})}[/tex]

according to question

[tex] \pmb{2\red x + 3(\red{x+1})+4(\red{x+2})= 191}[/tex]

[tex] \pmb{2\red{x} + 3\red{x}+3+4\red{x}+8= 191}[/tex]

[tex] \pmb{9\red{x}=191-11 = 180}[/tex]

[tex] \pmb{\red{x}=20}[/tex]

[tex] \sf{∴the \: three \: Consecutive \: numbers \: are} [/tex]

[tex] \pmb{\pink{20}, \pink{21}, \pink{22}}[/tex]

_________________......

[tex] \purple{ \pmb{LearningLifeII}}[/tex]

A profit of $28 is more than a profit of $18. True or false

Answers

True
Sorry if it’s wrong

Please help no links explain to

Answers

Answer:

43 degrees i think............

Pls answer asap I’m literally stumped it’s not that hard tho

Answers

Answer:

[tex]d=11.3125[/tex]

Step-by-step explanation:

Given

[tex]\frac{-4(-8.625+2d)}{-8} +3=10[/tex]

Lets solve for [tex]d.[/tex]

Start on the left side with the fraction.

Factor -4 out of -8.

[tex]\frac{-4(-8.625+2d)}{-4(2)} +3=10[/tex]

Cancel the common factor of -4.

[tex]\frac{-8.625+2d}{2} +3=10[/tex]

Subtract 3 from both sides.

[tex]\frac{-8.625+2d}{2} =7[/tex]

Multiply both sides by 2.

[tex]\frac{-8.625+2d}{2} *2=14[/tex]

Cancel the common factor of 2.

[tex]-8.625+2d=14[/tex]

[tex]2d-8.625=14[/tex]

Add 8.625 to both sides.

[tex]2d=22.625[/tex]

Divide both sides by 2.

[tex]d=11.3125[/tex]

How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2

Answers

On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735

what is mean absolute deviation?

The average of the absolute deviations from the center point within a dataset is called the mean absolute deviation. This statistic summarizes the statistical spread or variability. Each data point's average distance from the mean is known as the dataset's mean absolute deviation. This gives a sense of the dataset's variability. To determine the absolute value, take the mean from each integer in the dataset and then subtraction. Take the total of the absolute values next. Subtract the aforementioned sum from the total number of items in the dataset to obtain the mean absolute deviation.

12,12,12,22,23,32,43

Mean Absolute Deviation (MAD): 8.8979591836735

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Answer:

On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735

Step-by-step explanation:

Write an equation in terms of x that represents the given statement.

Four increased by three times a number is 34

Answers

Answer: 3x+4=34

Step-by-step explanation: let the number be x

A.T.Q

the number is 3 times i.e 3x

4 increase=3x+4.

and it says the equation is equal to 34.

3x+4=34


what is the value of x?

Answers

Answer:

x = 20

Step-by-step explanation:

All sides are equal ( as shown by the markings )

An equilateral triangle's angles = 60

Ask self, what can I multiply by 3 to get 60?

Look at the box-and-whisker plot. What is the measure of the first quartile (Q1)?

A: 43.5


B: 50.0


C: 41.5


D: 47.5

PLEASE HELP I AM IN A HURRY !!!!!!!

Answers

Answer:

A

Step-by-step explanation:

2021 EDG

Answer:

A) 43.5

Step-by-step explanation:

Help me what’s for life or death

Answers

Answer:

the answer is 6x but i dont know about no starting point or multiplier sorry

Step-by-step explanation:


Trejo says that if you know the x-intercepts,
y-intercepts, domain, and range of a
function then you automatically know the x-
intercepts, y-intercepts, domain, and range
of its inverse. Hilary disagrees. She says you
know the intercepts but that is all you know
for sure. Who is correct? Justify your
answer.

Answers

Trejo is correct, because if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

Trejo says that if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.

But, Hilary disagrees, She says you know the intercepts but that is all you know for sure.

Now,

We know that;

In a function, If if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.

Thus, The Trejo is correct.

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Find surface area of the prism.
4m, 18m, 5m

Answers

Answer:

hi you answer to your question could be 360m². hope this helps

Answer:

364

Step-by-step explanation:

$4000.00 investment. Over 3 years $1080.00 interest accumulated. What was the interest on the loan? The interest is shown in percent as the answer.

Answers

Answer:

9% interest rate

Step-by-step explanation:

Investment = principal = $4000

Interest amount = $1080

Period, t = 3 years

Simple interest = principal * rate * time

1080 = 4000 * rate * 3

1080 = 12000 * rate

Rate = 1080 / 12000

Rate = 0.09

The rate as a percentage = 0.09 * 100% = 9%

Need help with this, finding the length of the third side

Answers

Answer:

its sqrt (50)

Step-by-step explanation:

The triangle has a right angle, therefore we can use the Pythagorean theorem to find the hypotenuse. According to the theorem the sum of the squares of both other sides is equal to the square of the hypotenuse.

We have 5^2+5^2=c^2

=> 25+25=c^2

=> 50=c^2

Therefore c or the missing side is equal to sqrt(50)

Morgan bought 95 roses from the florist for her wedding. The roses cost $1.75 each, including sales tax. If Morgan gives the florist $200, how much change should she get back?

Answers

Answer:

33.75

Step-by-step explanation:

1.75*95 = 16 6.25

200 - 166.25 = 33.75

One line passes through the points (-4, 2) and (0, 3); another line passes through the points
(-3,-2) and (3, 2). Are these lines parallel, intersecting, perpendicular, or identical?

Answers

Answer:

how are you working on a saturday night?

Step-by-step explanation:

Help with this equation plzz

Answers

Answer:

option C I think

Step-by-step explanation:

I remember learning about this last year

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{3}[/tex] x - 2 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

To find c substitute (4, - 7) into the partial equation

- 7 = - 12 + c ⇒ c = - 7 + 12 = 5

y = - 3x + 5 → D

A triangle has side lengths of 3x, 24, and 5x. The side with 5x is the longest side. What value of x would make a right triangle?​

Answers

Answer:

To form a right triangle, one of the sides of the triangle must be the hypotenuse and the other two sides must be the legs. The hypotenuse is the longest side of a right triangle and the side opposite the right angle. In this case, the side with length 5x is the hypotenuse. Therefore, the sides with lengths 3x and 24 must be the legs.

We can use the Pythagorean Theorem to determine the value of x that will make this a right triangle. The Pythagorean Theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:

5x^2 = 3x^2 + 24^2

Solving for x, we get:

x = sqrt(24^2/(5^2 - 3^2)) = sqrt(576/16) = 6

Therefore, a value of x = 6 will make this a right triangle.

Step-by-step explanation:

I’ll give brainliest

Answers

Answer:

I think is would be 32√

Denise's cell phone plan is $29.95 per month plus $0.10 per minute of call time. Denise's
cell phone bill is $99.95. For how many minutes was she billed?

Answers

Answer:

700 minutes

Step-by-step explanation:

Let y represent the cost and x represent the number of minutes of call time

We have the equation

99.95 = 0.10x + 29.95

Now let's solve

99.95 = 0.10x + 29.95

70 = 0.10x

x = 700 minutes

So, she was billed for 700 minutes

If you can, please give me a Brainliest; thank you!

Kara Paid 24.64$ to ship 11 packages. Each package has the same size and weight. How much did it cost to ship 1 package?

Answers

Answer:

2.24$

Step-by-step explanation:

Charles uses a graphing calculator to find a quadratic regression model f for a given set of data. When he compares model f to an earlier regression model g for the same data, he determines that g more accurately models the data. Which of the following statements are true? Select all that apply.
A. Function f likely had fewer residuals near the x-axis than function g.
B. Function f likely had more residuals equal to 0 than function g.
C. Function g had more residuals near the y-axis than function f.

Answers

Answer:

C

Step-by-step explanation:

a is wrong because residuals are solved using y and not x

b is wrong because a residual closer to 0 would be more accurate, but f is less accurate than g

c is right because residuals are solved using y and a more accurate residual would be closer to the real answer's y value

hope this helped ^_^

If Point B represents an alternate combination of flutternutters & blank books, then how much of each product could be produced?

Answers

From the given graph, at Point B a total of 8000 fluffernutters & 500 blank books could be produced.

The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this context, a graph is made up of vertices connected by edges.

In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.

Straight line graphs called linear graphs are used to show the relationship between two quantities. This graph makes it easier to show a result as a collection of straight lines. The term "linear" simply means a straight line; curves, dots, bars, etc. are not used.

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people wear anklet in one leg or both leg? And which side left or right?

Answers

Most people that I see wearing anklets on one leg and it’s usually their right one but I know some people wear one on their left leg as well

What is the smallest natural number value
for n if the solution for √56n is also a
natural number?

Answers

Answer:

2√14

Step-by-step explanation:

√56 = √4 × √14

which is

2√14

a circular pool has a radius of 7.5 ft the calculate the length of the trim needed to go around the entire edge of the pool​

Answers

Answer:

pretty sure it would be 30 ft.

Step-by-step explanation:

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