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By trigonometry x is equal to 2 radian. An area of mathematics that researches connections between triangle side lengths and angles.

The Greek mathematician Hipparchus created the first chord chart sometime around 140 BC. Hipparchus is said to have authored twelve books of chord tables, yet none of these tables have survived. Thus, Hipparchus is credited as the discovery of trigonometry. A subfield of mathematics known as trigonometry studies how angles and length ratios relate to one another. Applications of geometry to astronomical research led to the field's emergence in the Hellenistic civilization during the third century BC.

tanx = 29/14

tanx = 0.036

x= tan¯1(0.036)

x = 2

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Answer:

$1.35

Step-by-step explanation:

15% of $9

= [tex]\frac{15}{100}[/tex] × $9

= 0.15 × $9

= $1.35

Answer:

5 is what the answer will end up being

because a it's is adding a negative to a positive

a) The factored function is given as follows: f(x) = 4(x + 1.25)(x - 3).

b) The x-intercepts are given as follows: x = -1.25 and x = 3.

c) The end behavior is given as follows: Due to the positive leading coefficient, the function increases to left and right.

d) The graph of the function is given by the image presented at the end of the answer.

The quadratic function for this problem is defined as follows:

f(x) = 4x² - 7x - 15.

The coefficients are given as follows:

a = 4, b = -7, c = -15.

Inserting these coefficients into a quadratic function calculator, the roots, which are the x-intercepts, are given as follows:

x = -1.25 and x = 3.

Considering the leading coefficient of 4 and the linear factors of the function, the factored function is given as follows:

f(x) = 4(x + 1.25)(x - 3).

The x-coordinate of the vertex is given as follows:

x = -b/2a = 7/8.

Hence the coordinates of the vertex are:

(7/8, f(7/8)).

Then the graph is made considering:

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Compare to last year the population of the Boom town increased by 25%  which is equal to 6000 then population of the last year is 4800.

As given in the question,

Present year population of the Boom town is equal to 6000

Let us consider 'y' be the population of Boom town last year.

Percentage of increase in population = 25%

Equation formed for the given condition is :

y + 25%y = 6000

⇒ y + (25/100)y = 6000

⇒ (100 + 25 / 100 )y = 6000

⇒ y  =  ( 600,000 / 125 )

⇒ y  = 4,800 population of Boom town last.

Therefore, last year population of the Boom town is equal to 4,800.

The above question is incomplete, the complete question is:

Compared to last year, the population of Boom Town has increased by 25%. The population is now 6,000. What was the population last year?

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To represent 2 is greater than 1 in math is presented as 2 > 1.

In math, there is a certain symbol to describe a certain condition of comparison. Here some of them:

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Answer:

Step-by-step explanation:

It is not possible to determine which system of inequalities is shown without a graph or more information about the inequalities. Without a graph, it is not possible to determine the region that is being represented by the system of inequalities. Additionally, without more information about the inequalities, it is not possible to determine which inequality is the upper bound and which is the lower bound. Therefore, the answer is "not enough information."

The solution of the system of inequalities is,

y > x and y > 2

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The graph of inequality is shown.

Now, We get;

The first graph is, y > x

And, The second graph is, y > 2

Thus, The solution of the system of inequalities is,

y > x and y > 2

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The value of the expression  is 512x³-9x²

You should be aware that an expression is a mathematical statement that is not an equation but have variables. It is also an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

The given expression is

8x to the third power -9x

This is expressed as follows

(8x)³-9x²

In this expression, every term inside the bracket is raised to the third power

⇒8³ * x³ - 9 *x

= 512*x  - 9x²

= 512x³-9x²

In conclusion, the value of the expression is 512x³-9x²

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On the plan  student are seated in following manner

A-  Emily

B-   Ben

C-  Cath
D-  Adam

E-   Darren

Direction is a particular way to move one place to another place, Commonly we have four directions like, North, South, East, West.

Given information,

Ben is North-East of Adam

Cath is East of Ben

Darren is South-East of Emily

After following instructions given in problem,

we can draw the conclusion,

Sitting arrangement is like this,

A-  Emily, B-   Ben, C-  Cath, D-  Adam, E-   Darren

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For monthly use of phone calls more than 170 minutes, plan a will cost more than plan b.

In plan a, the customer pays 7 cents per minute of use with no monthly fee.

So, the cost of x minutes call is given by, y = 0.07x ............. (1)

Again, in plan b, there is a charge of 5 cents per minute of use and in addition, the customer pays a monthly fee of 3.40.

So, the cost for x minutes call is given by, y = 3.4 + 0.05x  ........... (2)

Now, we have to find the value of x for which plan a costs plan b will be

0.07x > 3.4 + 0.05x

⇒ 0.02x > 3.4

⇒ x > 170 minutes.

So, for monthly use of phone calls more than 170 minutes, plan a will cost more than plan b.

The complete question is,|
A phone company offers two monthly charge plans. In plan a, there is no monthly fee, but the customer pays 7 cents per minute of use. In plan b, the customer pays a monthly fee of 3.40 and then an additional 5 cents per minute of use. For what amounts of monthly phone use will plan a cost more than plan b

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The measures of the angle are a = 84°,  b = 84°, c = 96°, d = 58°, e = 38° and f = 142°

Angle geometry is a branch of mathematics that deals with the properties and relationships of angles in geometric figures.

Check the attached image for labeling

d = 180 - 122 = 58°    (sum of angles on a straight line)

c = 96°   (vertically opposite angles are equal)

a = 180 - 96 = 84°    (sum of angles on a straight line)

b = a  (vertically opposite angles are equal)

b = 84°

e = 180 - b -d  (sum of angles in a triangle)

e = 180 - 84 - 58 = 38°

f = 180 - e     (sum of angles on a straight line)

f = 180 - 38 = 142°

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A system whose answer is (6, -8).

Elimination, substitution, and graphing are the three techniques for resolving equation systems.

Graphing the provided equations and identifying the point(s) at which they all meet is all that is required to solve a system by graphing. You can get the values of the variables you're solving for by finding this point's coordinate.

Elimination, substitution, and graphing are the three techniques for resolving equation systems.

Y = 1/3x - 10 and 2x + y = 4 together form a system whose answer is (6, -8).

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The solution to the system of equations y is x = -5, y = 4

Elimination, substitution, and graphing are the three techniques for resolving equation systems.

Graphing the provided equations and identifying the point(s) at which they all meet is all that is required to solve a system by graphing. You can get the values of the variables you're solving for by finding this point's coordinate.

To solve the system of equations y = 1/3x + 10 - 2x and y = 4,  we can use following method:

We can begin by isolating the variable y in the first equation: y = 1/3x + 10 - 2x.

Next, we can substitute the value of y from the second equation into the first equation: 4 = 1/3x + 10 - 2x

Now we can solve for x by combining like terms and isolating x: 4 = 1/3x + 10 - 2x => 4 = -4x + 10 => x = -5

Substitute x = -5 back into either of the equations to find y:

For example, y = 1/3x + 10 - 2x => y = 1/3(-5) + 10 - 2(-5) => y = 4

So the solution is x = -5, y = 4

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The 2 with an exponent of 1 is represented as 2¹ and the value of 2 with an exponent of 1 is 2 .

When the number "a" is multiplied by itself "n" number of times , then it can be represented in Exponential Form as "aⁿ " , the number "a" is called the base and the number "n" is called the exponent or power .

we have to find the value of 2 with an exponent of 1 ;

So , it is represented as ⇒  2¹ ;

and the value of this exponential expression is ⇒ 2 .

Therefore , the value of 2 with an exponent of 1 is 2 .

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The linear equation 5x - y = -5 have x - intercept is at x = -1 and y - intercept is at y = 5.

The x-intercept of a linear equation is the point at which the line crosses the x-axis. It can be found by setting y equal to 0 and solving for x. The y-intercept of a linear equation is the point at which the line crosses the y-axis. It can be found by setting x equal to 0 and solving for y.

x - intercept is when y = 0 and;

5x - 0 = -5

5x = -5

x = -5/5 {divide through by 5}

x = -1

y - intercept is when x = 0 and;

5(0) - y = -5

-y = -5

y = -5/-1 {divide through by -1}

y = 5

Therefore, the linear equation 5x - y = -5 have x - intercept is at x = -1 and y - intercept is at y = 5.

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Increasing or decreasing the size of a figure (referred to as the preimage) to produce a new figure is a type of transformation termed dilation. How much the dilation image will enlarge or reduce in size relative to the preimage is determined by the scale factor, r. Every time, k will have a value larger than 0.

A transformation in geometry is an action that shifts, rotates, or modifies an existing shape to produce a brand-new shape.

Increasing or decreasing the size of a figure (referred to as the preimage) to produce a new figure is a type of transformation termed dilation.

How much the dilation image will enlarge or reduce in size relative to the preimage is determined by the scale factor, r.

A two-scale factor dilation has been applied to Image A in relation to its origin. It is important to note that every coordinate point in the dilation picture is twofold that of the preimage.

The notation shown below can be used to represent a dilation with a scale factor close to the origin:

Dk (x , y ) = (kx, ky)

there will always be a number greater than 0 in the equation.

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Taking the subject A and solving the equation, the resultant value of A will be 1,150.

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.

So, we have the equation:

4/5*A=920

Now, calculate the equation taking A as the subject:

4/5 * A = 920

4A  = 920 * 5

4A = 4,600

A = 4,600/4

A = 1,150

Therefore, taking the subject A and solving the equation, the resultant value of A will be 1,150.

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In slope-intercept form, the equation of a line is represented as y = mx + b. So the equation in slope-intercept form is y = (1/2)x + 2

Slope is a measure of the steepness of a line or a linear function. It is often represented by the letter "m" and is calculated as the ratio of the change in the y-coordinates of two points divided by the change in the x-coordinates of those same two points. In other words, it is the ratio of the "rise" to the "run" of the line. The slope of a line can be positive, negative, zero, or undefined.

The slope-intercept form of a linear equation is a way to represent the equation of a line in the form of y = mx + b, where m is the slope and b is the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, and it is represented by the value of b. This form of the equation is useful because it allows us to easily identify the slope and y-intercept of a line, as well as to graph the line using these values.

The first step is to add 12y to both sides:

6x - 12y + 12y + 24 = 12y

6x + 24 = 12y

The next step is to divide both sides by 12 to get y by itself on one side:

y = (6/12)x + (24/12)

y = (1/2)x + 2

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The zeroes of the polynomial x5-x3+2x-2 are 0.618033988749895 and -1.618033988749895.

The given polynomial is x5-x3+2x-2. To find the zeroes of the polynomial, it should be set equal to zero.

Thus, x5-x3+2x-2 = 0

To solve this equation, the quadratic formula can be used. The quadratic formula is x = [-b ± √(b2 - 4ac)]/2a.

In this equation, a = 1, b = -1 and c = -2.

Thus, x = [-(-1) ± √((-1)2 - 4(1)(-2))]/2(1)

x = [1 ± √5]/2

The zeroes of the equation are

x = 0.618033988749895 and x = -1.618033988749895

Therefore, the zeroes of the polynomial x5-x3+2x-2 are 0.618033988749895 and -1.618033988749895.

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The perimeter of the square is 16√5 inches.

A square is a quadrilateral with 4 sides equal to each other. The opposite sides of a square is parallel to each other.

The perimeter of a square is the sum of the whole sides of the square.

Let's find the length of the square using the length of the diagonal.

Using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

x² + x² = (4√10)²

2x² = 160

x² = 160 / 2

x = √80

Hence,

perimeter of a square = 4l

where

perimeter of the square = 4 × √80

perimeter of the square = 4 × 4√5

perimeter of the square = 16√5 inches

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the value of t is found to be 16.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Li has t toy bricks only red and blue She picks two bricks one after the other If the first is red the probability of the second brick being red 2/3.

If the first is blue the probability the second brick is red is 7/10.

Let the number of red bricks be x.

So, the number of blue bricks would be t - x

We have 6x-6 = 5x

x =6

and we get t-1 =15

t =16.

Hence the value of t is found to be 16.

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The length of  the outside arc of each piece compared to the inside arc is 5.57 inches

Length of outer track = sum of length of 10 pieces = circumference of the outer circle

if R is the Radius of outer circle then...

Circumference of the outer track = 2pi*R

Similarly the circumference of the inner track (with radius r) = 2pi*r

length of each outer piece is 3.5 inch more than length of inner piece

So total outer length is 10*3.5 =35 inches more than the inner length.

=> Outer Circumference - Inner Circumference = 35 inches

=> 2pi*R - 2pi*r = 35

=> 2pi(R -r) = 35

=> R-r = 35/2pi = 5.57 inches

=> R-r = Width of the track = 5.57 inches

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A collection of two or more inequalities in one or more variables is known as a system of inequalities.

Two or more inequalities in one or more variables make up a system of inequalities. When a problem calls for a variety of answers and those answers are constrained by multiple factors, systems of inequalities are used.

The intersection region of every solution in the system of inequalities is the system's solution.

Comparable to solving a system of linear equations, solving a system of linear inequalities involves locating the point (or points) of intersection, however this is not the case with inequalities. Instead, the area that fulfils each linear inequality will make up the solution set.

An inequality system's graph shows how the inequalities are resolved.

The system of inequality needs to be fixed by [tex]$y > \frac{2}{3}$ \\ and $x \leq \frac{16}{3}$[/tex]

Following is a description of the inequality system:

[tex]$y > 2 x+4$$x+y \leq 6$[/tex]

The charts for these are in the attached.

[tex]$y > 2 x+4$ and $x+y \leq 6$[/tex]

The graph shows us:

[tex]$y > \frac{2}{3}$$x \leq \frac{16}{3}$[/tex]

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If the hypotenuse is c = astartroot 2 endroot, then 6 = astartroot 2 endroot then the value of a in inches would be 3.

What is right triangle ?

A right triangle is a triangle in which one angle is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse, and the two other sides are called the legs. The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs.

The given information is that the hypotenuse, represented by c, is equal to the square root of 2. If we set c = √2 and 6 = √2, we can solve for the value of the other side of the right triangle, represented by a.

To solve for a, we can square both sides of the equation 6 = √2:

[tex]6^{2}[/tex] = [tex](\sqrt{2} )^{2}[/tex]

36 = 2

So a = 6/√2 = 6/√2 = 3,

If the hypotenuse is c = astartroot 2 endroot, then 6 = astartroot 2 endroot then the value of a in inches would be 3.

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Answer: The correct answer to this question is 3 square root 2

Step-by-step explanation: Lincoln Edge 2023

The solution to the implicit differentiation problem is dy/dx = -16x/2y.

To solve this problem, we must use implicit differentiation. This means that we must differentiate both sides of the equation with respect to the independent variable, x. We can do this by taking the derivative of both sides of the equation.

The derivative of 8x^2 is 16x and the derivative of y^2 is 2y dy/dx.

Therefore, the equation becomes: 16x + 2y dy/dx = 0

We can then solve for dy/dx by dividing both sides by 2y, which gives us dy/dx = -16x/2y.

Therefore, the solution to the implicit differentiation problem is dy/dx = -16x/2y.

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The length of each leg from the given triangle is  13 [tex]\sqrt{2}[/tex], 13 [tex]\sqrt{2}[/tex]  respectively.

What is triangle ?

triangle can be defined as figure which contains three sides and three angles and the sum of three angles could be 180 degrees.

Given triangle is right angled triangle,

with given hypothenuse 26.

let other two sides be x and y.

so,

tan45 = x/y

1= x/y

x = y.

from the figure we can say that ,

[tex]\sqrt{ x^{2} + y^{2} }[/tex] =  26

[tex]\sqrt{x^{2} +x^{2}}[/tex]  = 26

2[tex]x^{2}[/tex] = 26*26

[tex]x^{2}[/tex] = 13*13*2

x = 13 [tex]\sqrt{2}[/tex]

Hence the other two sides be 13 [tex]\sqrt{2}[/tex], 13 [tex]\sqrt{2}[/tex] respectively .

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The product of two numbers, x and x + 3 , is 550, then x²+3x = 550: Option C

You should be aware that a quadratic equation is an equation whose highest power of its variable is two. A quadratic equation in the form x can be written as ax²+bx+c = 0 where a, b and c are positive or negative integers

The given expression is

The product of two numbers, x and x + 3 , is 550

this implies x(x+3) = 550

Opening the brackets to get

x²+3x = 550

This in conclusion means that the best option is x²+3x = 550

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The trigonometric function cotθ is undefined for B)0.

What is trigonometric functions?

The simplest definition of a trigonometric function is the function of an angle in a triangle, often known as a circular function. It implies that these trigonometric functions can be used to determine the relationship between a triangle's angles and sides.

Now given trigonometric function is cotangent.

This function is undefined for infinitely many points in the real number system, specifically any time sin(x)=0 which occurs for any integer n at

x = nπ.

If n is 0 you get x=0 so yes that is one value where cot(x) is undefined. Big question is what domain you are restricted to.

For example, if on [0,π), zero is the only value in that interval where cot(x) is undefined.

Hence the correct option is B) 0.

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The equations can be used to solve for y, the length of the room are  y2 – 5y = 750 , (y + 25)(y – 30) = 0,  – y(y – 5) = 0

The formula for calculating the area of a rectangle is expressed as;

A = wl

Given that the parameters are;

From the information given, we have that;

Now, substitute the values, we get;

750 = (y-5)y

expand the bracket

750 = y² - 5y

This can also be written as;

y² - 5y -750 = 0

Hence, the correct option for the expression is  y2 – 5y = 750

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Answer:

$43

Step-by-step explanation:

each friend:

$165/5 = $33

Maria:

$33 + $10 = $43

Answer: $43

Step-by-step explanation:

First, divide the money amongst the friends.

165/5 = 33

Then add the ten.

33 + 10 = 43