The inverse of 7 modulo 11 is 4, which means that 4 multiplied by 7 gives a number congruent to 1 (mod 11). This means that 4 is the number that when multiplied by 7 gives a remainder of 1 when divided by 11.
In modular arithmetic, the inverse of a number is the number that when multiplied by the original number gives a result that is congruent to 1 (modulus). For example, if we take the modulus of 11 as an example, then the inverse of 7 modulo 11 is 4, since 7*4 = 28 ≡ 1 (mod 11). This means that 4 is the number that when multiplied by 7 gives a remainder of 1 when divided by 11. The inverse of a number modulo a given modulus can be calculated using the Extended Euclidean algorithm. This algorithm allows us to find the inverse of a number modulo a given modulus by solving a series of equations and using the result to calculate the inverse. For example, in the case of 7 mod 11, the Extended Euclidean algorithm gives us the result 4, which is the inverse of 7 mod 11.
11 = 7*1 + 4
7 = 4*1 + 3
4 = 3*1 + 1
3 = 1*3 + 0
By reading the equations from right to left, we can see that the inverse of 7 mod 11 is 4, since 4*7 = 28 ≡ 1 (mod 11).
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Find the sum of the series.
[infinity] (−1)nπ2n
n=0
62n(2n)!
As per the Maclaurin series, the value of the function is written as 2.8521
The term Maclaurin series is defined as a function that has expansion series that gives the sum of derivatives of that function.
Here we have given that the function is [tex]\sum\frac{(-1)^n\pi^{2n}}{4^{2n}(2n)!}[/tex]
And we need to find the sum of series by using the Maclaurin series as
Now, the sum of series is calculated as,
=>f(n) = [tex]\sum\frac{(-1)^n\pi^{2n}}{4^{2n}(2n)!}[/tex]
When we put the value on n = 0, then we get,
=> f(0) = [1 x 3.14]/1] = 3.14
Now, we have to put the value of the function, the value of x as 1,
Then we get,
=> f(1) = [-1 x 9.8596] / [16 x 2]
=> f(1) = -0.308
And then we have to put the value of function for the value of x as 2,
Then we get,
=> f(2) = [1 x 30.959] / [64 x 24]
=> f(2) = 0.0201
Then the sum of the series is
=> 3.14 - 0.308 + 0.0201
=> 2.8521
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If ΔABC ~ ΔDEF , find the value of x .
What is the slope-intercept form of 3x 4y 5?
The slope of equation 3x-4y = 5 is 3/4.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
Given equation:
3x-4y = 5
To find the slope:
First, we simplify the equation.
-4y = 5 -3x
Divide by -4.
(-4/-4)y = 5/-4 + (-3/-4)x
y = (3/4)x -5/4
Now, we know the slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
Comparing, both the equation,
we get,
m =3/4.
So, the slope is 3/4.
Therefore, the slope is 5/3.
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What are the 8 parallel lines?
Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.
What is answer parallel line?
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.
Parallel lines are two lines in the same plane that are equal distance apart and never intersect.
Real-world parallel line examples include railroad tracks, sidewalk edges, street markings, zebra crossings, the surface of pineapple and strawberry fruit, staircases and railings, and so on.
Parallel lines are lines in a plane that never meet, no matter how far they are extended. The distance between the parallel lines is constant because they never meet.
Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.
these are 8 parallel lines
2x+3y = 6
2x+3y = 4
2x+3y = 1
2x+3y = 2
2x+3y = 3
2x+3y = 8
2x+3y = 7
2x+3y = 5
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What is the solution to 2x² 8x X² 16?
Since the provided expression [tex]2x^{2} +8x-x^{2} +16[/tex] is quadratic, the solution of x are "-4" and "-4" .
What is a quadratic equation?Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.
What are mathematical expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases.
Expression: [tex]2x^{2} +8x-x^{2} +16[/tex]
This means that you need to add the two x² terms and the two x terms, which gives you [tex]x^{2} +8x+16[/tex].
Next, you can simplify the equation by taking out a common factor of x from the consecutive two terms, which gives you [tex]x(x + 4) +4(x+4).[/tex]
Then the equation becomes [tex](x + 4)(x+4).[/tex] which on solving i.e [tex](x+4)=0[/tex]
you will get x= -4 and -4.
Therefore the solution to this equation is x = -4 or x = -4.
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pls answer need help.
Answer: Angle C
Step-by-step explanation:
The length of C-T and T-B would be longer then C-B and push C-B out making angle C the biggest.
Which is a quadratic equation in FACTORED FORM?
A
f(x)=2x2+5x−12f(x)=2x^2+5x-12f(x)=2x
2
+5x−12
B
f(x)=2x+5f(x)=2x+5f(x)=2x+5
C
f(x)=2(x+5)2−12f(x)=2(x+5)^2-12f(x)=2(x+5)
2
−12
D
f(x)=2(x+5)(x−12)f(x)=2(x+5)(x-12)f(x)=2(x+5)(x−12)
Answer:
D) f(x) = 2(x + 5)(x − 12)----------------------
Given options:
A) f(x) = 2x² + 5x − 12,
this is a standard form of quadratic function.B) f(x) = 2x + 5,
this is a linear function, not quadratic.C) f(x) = 2(x + 5)² − 12,
this is vertex form of a quadratic function.D) f(x) = 2(x + 5)(x − 12),
this is a factored form of a quadratic function.What do you call the point where it touches the x-axis?
Answer: x-intercepts
Step-by-step explanation:
basic math
Answer: X intercept
Step-by-step explanation:
The x-intercept is the point at which a graph crosses the x-axis. The y-intercept is the point at which the graph crosses the y-axis. To find the x-intercept of a line, substitute 0 for y into the equation and solve for x.
f(x, y, z) = xz + yz + xy, g(t) = (et, cos(t), sin(t))
The value of g'(t) is ([tex]e^t[/tex], -sin t, cos(t)).
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x, y, z) = xz + yz + xy,
g(t) = ([tex]e^t[/tex], cos(t), sin(t))
Now, differentiating g(t) w.r.t t
g'(t) = ([tex]e^t[/tex], -sin t, cos(t))
Hence, the g'(t) = ([tex]e^t[/tex], -sin t, cos(t)).
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What is variable in algebra for Class 6?
A symbol (often a letter) used in mathematics to represent an unknowable numerical value in quite an equation or algebraic statement.
What is the definition of variable in algebra?A symbol (often a letter) used in mathematics to represent an unknowable numerical value in such an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.Typically, "x" and "y" are used to express unknowable integers. However, it is not required; any letter will do.Example:
Consider the algebraic statement 2x + 6 as an example. In this case, the variable x is open to interpretation. If x = 1, the algebraic expression's value will be 2(1) + 6, or 8.To know more about the variable in algebra, here
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What is the coefficient of x in the expression 4x+ 3y?
The coefficient of x in the expression 4x+ 3y is 4. This means that for every x there is 4 times as much as for every y. The coefficient of x is the number that is multiplied by x in the expression.
In the expression 4x+ 3y, the coefficient of x is 4. This means that the x is multiplied by 4. The coefficient of a term is the number that is multiplied by the variable. In this expression, the x is multiplied by 4 and the y is multiplied by 3. This means that for every x there is 4 times as much as for every y. In order to find the coefficient of x in the expression, we must look at the number that is multiplied by x. In this case, the number is 4. This means that the coefficient of x is 4. For example, in this expression, the coefficient of x is 4 which means that for every x there is 4 times as much as for every y.
4x + 3y
Coefficient of x = 4
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When $36$ consecutive integers are added, the result is $-18$. What is the greatest product that can be obtained by multiplying two of these $36$ integers?
The greatest product that can be obtained by multiplying two of these 36 integers is; 306
How to solve mathematical sequence?We are told that when 36 consecutive integers are added, the product is -18.
Now, the sequence for these integers would be;
x, (x + 1), (x + 2), (x + 3),......(x + 35)
Now, since the addition of these integers gives a negative number, then it suggests to us that the sequence starts with a negative integer and then ends with a positive integer.
Thus, we have;
x + (x + 1) + (x + 2) +(x + 3) + (x + 35) = -18
The formula for sum of an arithmetic sequence is;
Sₙ = (ⁿ/₂)(2a + (n - 1)d)
where a is first term and d is common difference
Thus;
-18 = (36/2)(2x + (36 - 1)1)
-18 = 18(2x + 35)
-18/18 = 2x + 35
2x + 35 = -1
x = -34/2
x = -17
Thus;
The first term = -17
Last term = -17 + 35 = 18
Thus, the greatest product that can be obtained = 18 * 17 = 306
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Answer:
306
Step-by-step explanation:
What is the greatest common monomial factor of 3x²-6x?
Answer:
The greatest common monomial factor of [tex]3x^2 - 6x[/tex] is 3x.
Step-by-step explanation:
To understand what the problem is asking us, let's define the terms.
⭐What does greatest common factor mean?
as factor means a term (x) that is a factor of a number or another term (y),the greatest common factor means the greatest number (x) that is a factor of a number/another term(y)⭐What does monomial mean?
as "mono" means 1,monomial means an expression or equation that consists of only 1 termThus, we need to find the greatest term that is a factor of [tex]3x^2 -6x[/tex]. This term must be a monomial.
First, divide both terms of the polynomial [tex]3x^2 -6x[/tex] by the largest term that is common between the terms.
[tex]3x[/tex] is the largest term.
[tex]3x[/tex] is also a monomial.
Therefore, [tex]3x[/tex] is the greatest common monomial factor.
⭐if this response helped you, please mark it the brainliest⭐
What is a solution on a graph?
Answer:
The solution on a graph is the point where two lines interesect
Step-by-step explanation:
Write the ratio 28:40 in simplest terms
Answer:
Step-by-step explanation:
28/4 = 7
40/4 = 10
Then:
28:40 in simplest terms is:
7:10
Answer:
[tex] \sf \: 7 : 10 [/tex]
Step-by-step explanation:
Now we have to,
→ simplify ratio into simplest form.
The given ratio,
→ 28 : 40
Let's simplify the given ratio,
→ 28 : 40
→ (28) ÷ 4 : (40) ÷ 4
→ (7) : (10)
→ 7 : 10
Therefore, the ratio is 7 : 10.
Both Andrew and Karleigh recorded the distance they ran in x minutes on treadmills.
Andrew
Karleigh
Time in Distance
Minutes
in Miles
18
24
1.5
2
OA) (4,0)
Time in Distance
in Miles
Minutes
30
40
3
Andrew and Karleigh each run for 1 hour. Which statement explains who ran a
greater distance?
C)
Andrew ran a greater distance.
his table increased at a rate of
10
mile per minute.
4
B) Andrew ran a greater distance. The slope of the line described by the data in
his table increased at a rate of mile per minute compared to Karleigh's
12
The slope of the line described by the data in
mile per minute compared to Karleigh's
D) Karleigh ran a greater distance. The slope of the line described by the data in
her table increased at a rate of mile per minute compared to Andrew's
mile per minute
The correct statement regarding the proportional relationships is given as follows:
B. Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of 1/10, compared to 1/12 for Andrew.
How to obtain who run faster?
To obtain the person who runs faster, we need to look at their rates, as the time and the distance form a proportional relationship.
Andrew ran 1.5 miles in 18 minutes and 2 miles in 24 minutes, hence his rate is given as follows:
k = 1.5/18 = 2/24 = 1/12 = 12 minutes per mile.
Karleigh ran 3 miles in 30 miles and 4 miles in 40 minutes, hence her rate is given as follows:
k = 3/30 = 4/40 = 1/10 = 10 minutes per mile.
Due to the lower number of minutes per mile, Karleigh ran faster, and the correct option is given by option B.
Missing InformationAndrew ran 1.5 miles in 18 minutes and 2 miles in 24 minutes.
Karleigh ran 3 miles in 30 miles and 4 miles in 40 minutes.
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Use the diagram below to find the following measures. GN is the angle bisector of ∠MGO.
Answer:
∠MGN = 24°
∠NGO = 24°
Step-by-step explanation:
⭐What is an angle bisector?
An angle bisector is a line, segment, or ray that splits an angle in halfEach halve of the angle is equal to each otherThus, ∠MGN ≅ ∠NGO.
To solve for ∠MGN and ∠NGO, we need to:
Create an equation about their relationshipSolve for "x"Substitute "x" back into the equations to find the angle measures1. Create an equation about their relationship:
If ∠MGN ≅ ∠NGO, then...
[tex]5x-6 = 11x -42[/tex]
2. Solve for "x":
[tex]5x - 6 = 11x -42[/tex]
[tex]42 - 6 = 11x - 5x[/tex]
[tex]36 = 6x[/tex]
[tex]6 = x[/tex]
3. Substitute "x" back into the equations to find the angle measures:
[tex]< MGN = 5x - 6[/tex]
[tex]< MGN = 5(6) - 6[/tex]
[tex]< MGN = 30 - 6[/tex]
[tex]< MGN = 24[/tex]
❗❗❗At this point, you could write that ∠MGN and ∠NGO = 24°, as they are congruent, but you should still substitute "x" into ∠NGO to make sure "x" is correct.❗❗❗
[tex]< NGO = 11x - 42[/tex]
[tex]< NGO = 11(6) - 42[/tex]
[tex]< NGO = 66 - 42[/tex]
[tex]< NGO = 24[/tex]
∴ ∠MGN = 24°
∴ ∠NGO = 24°
Isaiah is a high school basketball player.
In a particular game, he made some free
throws (worth one point each) and some
two point shots. Isaiah scored a total of 12
points and made 4 times as many free
throws as two point shots. Write a system
of equations that could be used to
determine the number of free throws
Isaiah made and the number of two point
shots he made. Define the variables that
you use to write the system.
x + 2y = 12 and x = 4y represents the given word problem in equations
How to form an equation for a word problem?
Here are some steps to follow:
1. Understand all the words used in stating the problem. Understand what you are asked to find.
2. Translate the problem to an equation.
Assign a variable (or variables) to represent the unknown. Clearly state what the variable represents.
3. Carry out the plan and solve the problem.
Use substitution, elimination or graphing method to solve the problem.
According to the given question:
Isaiah scored a total of 12 points. In this game, he made some free throws (worth one point each) and some two point shots.
Let number of free throws be x and number of two point shots be y.
x(1) + y(2) = 12
x + 2y = 12
This equation defines the total number of points scored with free throws and two point shots.
He made 4 times as many free throws as two point shots.
Using the pre defined variables to form the equation as
x = 4y
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2x+3y=0
x+2y=1
solving systems by substitution
Answer: x=-3, y=2
Step-by-step explanation: to solve using substitution, we need either x or y by itself in one equation. let's use x from the 2nd equation since it doesn't have a constant.
so the first equation stays the same at 2x+3y=0
for the second equation, rearrange to solve for x by moving the 2y to the right -> x=2y-1
then, we can plug in this x value to x in the first equation to get,
2(2y-1)+3y=0
then solve for y,
4y-2+3y=0
4y-3y=2
y=2
then to solve for x, plug in y in either of the initial equations. lets choose the second one.
so you'd have,
x+2(2)=1
x+4=1
x=-3
For what value of k are the roots of the quadratic equation 3x² 2kx 27/0 real and equal * 1 point K 7 K 9 K 11?
The value of k where the roots of the quadratic equation are real and equal is k = 9.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
3x + 6 = 9 is an equation.
We have,
3x² + 2kx + 27 = 0
This is in the form of ax² + bx + c.
a = 3
b = 2k
c = 27
Now,
The roots are real and equal.
D = 0
D = b² - 4ac
Now,
b² - 4ac = 0
(2k)² - 4 x 3 x 27 = 0
4k² - 324 = 0
4k² = 324
k² = 324/4
k² = 81
k = √81
k = ±9
Thus,
The value of k is 9 0r -9
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➡some one please help me please.
Answer:
Step 2
Step-by-step explanation:
3x-24=5x
he did -3x on each side but added 3x to 5x instead of subtracting
A spinner is spun that has 15 equal-sized sections numbered 1 to 15. What is the probability the spinner lands on an odd
number?
Answer:
8/15
Step-by-step explanation:
There are 15 equal-sized sectors:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
The odd ones are:
1, 3, 5, 7, 9, 11, 13, 15
There are 8 odd numbered sectors.
p(event) = (number of desired outcomes)/(total number of possible outcomes)
p(odd) = 8/15
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Answer: 1.5 and 20
Step-by-step explanation:
How do you find potential rational roots?
To find potential rational roots, we make use of the rational root theorem
How to determine potential rational root?From the question, we have the following parameters that can be used in our computation:
Task: How the potential rational root is calculated
To make use of the potential rational root, we use the rational root theorem using the following steps
Get the constant term and its factors (p)Get the leading coefficient and its factors (q)Find each possible value of p/q Remove duplicates from the possible rational zeros aboveRead more about rational root theorem at
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Is √ 3x² 5y is a polynomial?
Yes, 3x²A5y is a polynomial.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
we need to check whether 3x²A5y is a polynomial.
An expression is combination of variables, numbers and operators.
For an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.
3x²A5y is a polynomial.
Hence, 3x²A5y is a polynomial.
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How do you determine the nature of the roots of a quadratic equation example?
The nature of the roots of a quadratic equation is described by the discriminant calculated by seeing the equation and comparing it with the standard equation which is given by -
[tex]ax^{2} + bx+c[/tex] , where a , b , c are real numbers .
The root of the equation is given by -
x= (-b )± [tex]\frac{\sqrt{b^{2} - 4ac}}{2a}[/tex]
Here, the term (b^2 - 4ac) is called the discriminant of the quadratic equation .
This discriminant is the defining factor of the nature of the roots.
Now, here arise three cases-
(i) If (b^2 - 4ac) > 0, the roots are real and distinct .
(ii) If (b^2 - 4ac) = 0 , the roots are real and equal.
(iii) If (b^2 - 4ac) < 0 , the roots are not real and they are imaginary i.e. they are complex in nature and of the form a+ib.
Hence, it is the discriminant which determines the nature of roots.
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What is the median numbers 4 8 10 5 9?
The required median of the given data set is 8.
What do we mean by media?Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).
Example: When the numbers are arranged (1, 4, 7), the number 4 lies in the middle, making it the median of 4, 1, and 7.
So, we have the data:
4, 8, 10, 5, 9
Arrange in ascending order as follows:
4, 5, 8, 9, 10
Since 8 is the number in the middle then it is the median.
Therefore, the required median of the given data set is 8.
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A car moving at a constant speed passed a timing device at t = 0. After 9 seconds, the car has traveled 747 ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
The linear function rule to model the distance d in feet of the car traveled after t seconds is d = 83t.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The distance traveled after 9 seconds = 747 ft.
The function rule to model the distance d after t seconds.
d = 83t
When t = 9,
d = 83 x 9 = 747 ft
Thus,
The linear function is d = 83t.
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What is the GCF of 28?
Prakah core x mark in cience and 90 mark in math what in hi total core in cience and math?
Prakash's total score in math and science is (x+90)marks
This word problem will need as to write what we have been given and analyze and come up with an equation to solve it
We are given that Prakash's score in science is = x marks
and that Prakash's score in mathematics = 90 marks
Therefore to get the total score in both math and science will we have to add the score Prakash scored in math and the score Prakash scored in science:
This will translate to (x) +(90)
We will get the total as x+90
hence the total score will be x+90 marks
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