Compute $17^{-1}\pmod{83}$. Express your answer as a residue from $0$ to $82$, inclusive.(You may find it helpful to consider the fact that $17\cdot 5

Answer:

b:  5x-4y+31=0

Step-by-step explanation:

Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are given the slope, m, as (5/4), so we can write:  y = (5/4)x+b.

To find b, just enter the given point, (-3,4), into the above equation and solve for b:

 y=(5/4)x + b

 4=(5/4)(-3) + b   for (-3,4)

 4 = -(15/4)+b

 4 + (15/4) = b

 4 + (3 3/4) = b

b = 7 3/4

The equation becomes y = (5/4)x + 7 3/4

Also written as:  y = (5/4)x + (31/4)

To match this with one of the options, let's multiply by 4 to remove the two fractions:

   y = (5/4)x + (31/4)

   4y = (5)x + (31)

Rearrange so that the expression is = 0:

4y-5x-31 = 0

Now multiply by -1:   -4y+5x+31=0

Rearrange and this will match option b:  5x-4y+31=0

First we can find value of x and. When x=0 then y=-1  and x=1 then y= 3

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term where m is the slope and b is the y-intercept.So the above given equation is called a "linear equation of two variables," where y and x are the variables.

Finding the y value is easy if you know the slope of the line and the x coordinate. Review the equation for the slope of a line. The equation for finding the slope is: m = [y1 - y2] / [x1 - x2]. If you know x, you can solve for y to find the y value for the slope of the line.

Now we have y= 4x-1

lets x=0   then y= -1

     x=1      then y=3

     x=2     then y=7

To find slope

y=mx+c

y= 4x-1

so by comparing we can find m=4

Then we can evaluate given equation y=4x-1

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The ratio for cos (cosine) of angle θ is: cos(θ) =  adjacent side of θ / hypotenuse

We know that in right triangle the cosine of an angle is nothing but the ratio of the side adjacent of  given angle to the hypotenuse.

In right tirnagle for an angle θ, the ratio for cosine of angle θ would be:

cos(θ) =  adjacent side of θ / hypotenuse

Consider following right triangle PQR with angle PQR = 90 degrees

Here, PR is the hypotenuse.

Assume that angle QPR measure α degrees and angle PRQ measures θ degrees.

By definition of cosine of angle θ,

cos(θ) =  adjacent side of θ / hypotenuse

cos(θ) =  QR / PR

And by definition of cosine of angle α,

cos(α) =  adjacent side of α / hypotenuse

cos(α) = PQ / PR

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Answer:

Step-by-step explanation:

A. 2x = -6

    x = -3

 3 + y = 5

   y = 2

(-3, 2)

-9 - 2 = -11

 -11 = -11

3 + 2 = 5

5 = 5

B. 4x + 2y = 1

    6x + 4y = 1

-8x - 4y = -2

 6x + 4y = 1

-2x = -1

x = 1/2

4(1/2) + 2y = 1

2 + 2y = 1

2y = -1

y = -1/2

-2(-1/2) + 3 = 4(1/2) + 2

1 + 3 = 2 + 2

4 = 4

6(1/2) + 4(-1/2) = 1

3 - 2 = 1

1 = 1

C.

-x + 32y = -25

4x + 8y = 100

-4x + 128y = -100

136y = 0

y = 0

-x = -25

x = 25

(25, 0)

32(0) - 25= -25

-25= -25

5(25) = 100 + 25 - 8(0)

125 = 125

D.

3x + 2y = 6

4x + 5y = -20

-12x - 8y = -24

12x + 15y = -60

7y = -84

y = -12

2(-12) + 3x = 6

-24 + 3x = 6

3x = 30

x = 10

(10, -12)

2(-12) + 3(10) = 6

-24 + 30 = 6

6 = 6

4(10) + 5(-12) + 20 = 0

40 - 60 + 20 = 0

 -20 + 20 = 0

0 = 0

Answer:

  -2

Step-by-step explanation:

You want to know the dilation scale factor that gives triangle A'B'C from triangle ABC.

We notice that point A' is 4 units down and 2 units right of C, whereas A is 2 units up and 1 unit left of C. The ratio of these distances is the scale factor.

If up and right are positive, then ...

  k = (A' -C)/(A -C) = (2, -4)/(-1, 2) = -2

The dilation scale factor is -2.

Answer:

cos(2x)

Step-by-step explanation:

To simplify the expression cos²x - sin²x, we can use the identity cos²x - sin²x = cos(2x).

This identity can be derived by using the double angle formula for cosine:

cos(2x) = cos(x + x) = cos(x)cos(x) - sin(x)sin(x) = cos²x - sin²x

Therefore, the expression cos²x - sin²x can be simplified to cos(2x).

The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed.

The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed. Parallel computing is a sort of computation in which several computations or processes are performed at the same time. Large issues are frequently broken into smaller ones, which may then be tackled concurrently.

Here,

Parallelization can only speed up a program so much. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be ten times regardless of the number of processors employed.

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The terminal point of vector cu lies in quadrant III.

Option B is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

p = (0, 0) and Q = (9, 12)

u = PQ = (9 - 0, 12 - 0) = (9 , 12)

Now,

cu = (9c, 12c)

where c < 0

If c = -1

cu = (-9, -12)

The coordinates (-x, -y) lie in quadrant III.

(-9, -12) is in quadrant III.

Thus,

Vector cu lies in quadrant III.

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In given right triangle ACB, the ratios for sin A and cos A :

sin(A) = 48/50

cos(A) = 14/50

Consider the following diagram.

In a right triangle ACB, the angle ACB = 90 degrees.

We know that in right triangle for an angle θ, the trigonmetric ratios are:

sin(θ) = opposite side of θ/ hypotenuse

cos(θ) = adjacent side of θ / hypotenuse

Here, side AC = 14 units, side CB = 48 units and the hypotenuse AB = 50 units

We need to find the ratios for sin A and cos A

In right triangle ACB for angle A,

sin(A) = opposite side of angle A/ hypotenuse

sin(A) = CB/AB

sin(A) = 48/50

And cos(A) = adjacent side of A / hypotenuse

cos(A) = AC/AB

cos(A) = 14/50

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The percent of fans that are between 18 and 27 years old is 16.80%.

From the information, the average age of a group of fans at a hockey game is 34 years with a standard deviation of 8 years and we want to calculate the percent of fans are between 18 and 27 years old.

It should be noted that this will be Illustrated through the normal curve.

The probability will be:

P(18 ≤ X ≤ 27)

= P(18 - 34/8) ≤ Z ≤ (27 - 34 / 8

= P(-2.0 ≤ Z ≤ -0.875)

= 0.1908 - 0.02275 (From the standard normal calculator)

= 16.80%

The percentage is 16.80%.

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Answer:

SAA

Step-by-step explanation:

Therefore, the inequality problem solution is even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.

Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<

Here,

R should stand for Guliskhan's running seconds, and B should stand for her bicycling seconds.

Guliskhan is said to bike at a pace of 7 meters per second, hence the distance (in meters) that he covers in B seconds will be 7B.

An inequity of 3R + 7B 1000 has been handed to us.

We can observe that 7B reflects the cycling distance covered by Gulkishan in meters in B seconds.

Guliskhan covers a distance of 3R meters in the number of seconds she runs for, where R is the number of seconds she runs for.

Guliskhan moves at a steady pace of 3 meters per second because of this.

B. Since Gulkiskhan 3R plus 7B has traveled a total distance greater than or equal to 1000 meters, her minimum intended distance is 1000 meters.

C. Let's replace R=60 and B=90 in our inequality to see if Guliskhan is capable of traveling this minimum distance.

=>3*60 + 7*90 ≥ 1000

=>180 + 630 ≥ 1000

=>810 ≠> 1000

Therefore, even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.

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Answer:

6 1/4 pounds

Step-by-step explanation:

There are 7 1/2 pounds of potatoes, which is equivalent to 7 1/2 = 7.516=120

120 ounces of potatoes.

If 1/6 of the potatoes are rotten, then 1/6*120 = 20

20 ounces of potatoes are rotten.

Thus, the weight of the good potatoes is 120-20 = 100

100 ounces.

Converting this back to pounds, we get

100/16 = 6 1/4

6 1/4 pounds.

The equation 1.6: n = 0.16 can be written as: [tex]1.6 = 2.511^n[/tex]

And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.

What is an exponent?

An exponent is a mathematical operation that represents the number of times a value is multiplied by itself. It is usually written as a small number raised to the power of a larger number, such as 2^3, which means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.

To write the equation 1.6: n=0.16 using an exponent, we can divide both sides of the equation by 1.6 to get: n = 0.16/1.6 = 0.1

And then we can raise the base 10 to the power of n: [tex]10^n = 10^{0.1} = 2.511[/tex]

Hence, the equation 1.6: n = 0.16 can be written as: [tex]1.6 = 2.511^n[/tex]

And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.

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The equation 1.6: n = 0.16 can be written as: 1.6 = [tex]2.511^n[/tex]

And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.

What is an exponent?

An exponent is a mathematical operation that represents the number of times a value is multiplied by itself. It is usually written as a small number raised to the power of a larger number, such as 2^3, which means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.

To write the equation 1.6: n=0.16 using an exponent, we can divide both sides of the equation by 1.6 to get: n = 0.16/1.6 = 0.1

And then we can raise the base 10 to the power of n: [tex]10^n=10^{0.1}=2.511[/tex]

Hence, the equation 1.6: n = 0.16 can be written as: 1.6 = [tex]2.511^n[/tex]

And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.

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The scale factor of the dilation is 2. An expansion happens when the scaling factor's absolute value exceeds one.

The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the center of dilatation. The scale factor and the center of dilation are used to determine the dilation transformation. The image stretches if the scaling factor is greater than 1.

As per the rule of scale factor

Q'U'/QU = SF

SF= Scale factor

=    (5+5)/5= Scale factor

=      10/5= 2

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Zachary expects to make $40 + $7 x tt (number of tables) in a day when waiting on tt tables

If Zachary waits on 11 tables, he can expect to make an additional $7 in tips for each table, for a total of 11 tables * $7/table = $77 in tips.

When added to his guaranteed wage, Zachary can expect to earn $40 (guaranteed wage) + $77 (tips) = $117 for that day.

To calculate how much Zachary would expect to make in a day when waiting on tt tables, we can use the equation:

Earnings = $40 (guaranteed wage) + $7 (tips/table) x tt (number of tables)

So if tt represents the number of tables Zachary waits on, then he can expect to earn:

Earnings = $40 + $7 x tt

For example, if Zachary waits on 15 tables, he can expect to earn $40 + $7 x 15 = $190.

Zachary can use this equation to calculate his expected earnings for any number of tables he waits on in a day.

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The width of the arch at its base can be found by setting ƒ(x) = 0 and solving for x. This gives  x=12 feet.

Horizontal distance is the length of a straight line between two points, measured only in the horizontal direction. It is typically measured in units such as kilometres, meters, miles, or yards.

No, the box truck will not fit under the arch. The height of the arch at a horizontal distance of 8 feet is ƒ(8) = -0. 5(8)2 + 6(8) = 4 feet, which is less than the height of the truck (13. 5 feet).
The maximum height a truck that is 8 feet wide and is passing under the bridge can be is ƒ(8) = 4 feet.

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The Value of the two constants K and R are 5 and 3 respectively.

a) To find u2, you can substitute u1 = 8 into the term-to-term rule to get:

u2 = 2u1 + 20 = 2(8) + 20 = 36

So u2 = 36.

b) To find the values of k and r, you can use the given values of u1, u2, and u3 to set up a system of equations. Using the term-to-term rule:

Substituting in the given values:

Solving for r and k, we get:

k = 5 and r = 3.

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Answer: 347

Step-by-step explanation:

Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.

Here.

Given : Cosθ = -1/6

To find : Tanθ

Since cosθ is in second quadrant

Thus,

Cosθ = B/H

According to pythagoras theorem,

H²= B²+ P²

=> 6² = 1² + P²

=> 36-1 =P²

=>P= √35

So ,

value of Tanθ comes out to be

=> tanθ = - √35 /1

=>tanθ = - √35

Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

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Answer:

19.95 + .71 × x = 125.74

x = 141.053

x is the answer

We can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division.

The result of a multiplication operation is a product.

There are four different methods for multiplying: addition, long multiplication, grid multiplication, and drawing lines.

So, we have:
5/8 and 4

5/8 is in the form p/q which represents the fraction that must be multiplied by 4.

Now, calculate the product as follows:

5/8 * 4

5/2

Therefore, we can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

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The value of d when F = 0.7 Newton's by solving with inverse variation is 0.61 meters to 2 D.P

Let

F = k/ d²

Where k = constant of proportionality

If F = 0.045 Newtons and d = 2.4 metres

F = k/ d²

0.045 = k / 2.4²

cross product

k = 0.045 × 2.4²

k = 0.2592

Find d when F = 0.7 Newton's

F = k/ d²

0.7 = 0.2592 / d²

cross product

0.7 × d² = 0.2592

0.7d² = 0.2592

divide both sides by 0.7

d² = 0.2592 / 0.7

d² = 0.370285714285714

find the square root of both sides

d = √0.370285714285714

d = 0.6085110634045

d = 0.61 to 2 decimal place.

Therefore, d is equal to 0.61 meters to 2 decimal place if F is 0.7 Newton's.

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The Avogadro's number of every element remains is the same. The number of atoms of 1 mole in every element is Avogadro's number. One mole of an element is 6.02214076×10²³ atoms.

What is an atom?

Each atom is made up of a nucleus and one or more electrons that are linked to it. One or more protons and a significant number of neutrons make up the nucleus. Only the most prevalent type of hydrogen is neutron-free. Atoms that are neutral or ionized make up every solid, liquid, gas, and form of plasma.

The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of  6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.

The number of atoms of one mole substance is 6.02214076 × 10²³ which is Avogadro's number.

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A figure made by two intersecting lines or two rays extending from the same point is called an angle.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays.  Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.

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It is assumed the given figure is a parallelogram.

Use properties of a parallelogram:

Find the missing values:

There are 29.8 students in the running club overall.

The quotient is the number we get when we divide two numbers. For instance, in the case of 8 4 = 2, where the division result is 2, it is the quotient. The divisor is 4, and the dividend is 8.

The remnant is the amount that does not wholly enter the divisor, whereas the quotient is the number of times a division is completed to the fullest extent possible. By way of illustration, 42 is the quotient and 1 is the remainder when 127 is divided by 3 to provide 42 R 1.

Given,

30+9-46 (2/3) % × 30

Multiply

30 + 9 - (46 × 30) × 0.00666666666666667

Calculate quotient,

30 + 9 - 1380 × 0.00666666666666667

Simplifying quotient,

30 + 9 - 9.2

Then we get,

39 - 9.2

Then 29.8

get the result: 29.8

The complete question is:

Thirty 8 th  graders signed up for running club, however nine dropped out before the first practice. If 46 (2/3)  of the club are 8 th graders, how many total students are in the running club?

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The correct option is option (E) 15

To calculate the number of cookies they will need, they first determine the number of students who will be attending the meeting. Since attendance is down by 25%, the number of students attending is 108*(1-0.25) students.

=108 students * 0.75 = 81 students.

To figure out the number of cookies they will need, they multiply the number of students by the number of cookies per student, which is 81 students * 2 cookies= 162 cookies.

Since each recipe makes 15 cookies, they need to make 162 cookies / 15 cookies/recipe = 10.8 recipes.

Since they cannot make partial recipes, they round up and make 11 recipes of cookies for their smaller party.

As 11 is not a given  option, we consider the option which is greater than 11, which is 15.

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Answer: The ship is going to another planet.

Step-by-step explanation:

I hate i-ready,

Your welcome mate

Answer:

Step-by-step explanation:

Let the number be x then:.

According to the question:

6 * (x + 25) = 30

therefore,

x + 25 = 30 / 6

x + 25 = 5

x = 5 - 25 = -20