Find sine, where is the angle shown.
Give an exact value, not a decimal approximation.
8
17
8

By using the fact that the triangles are similar, we can write and solve an equation to find that t = 11.

Here we know that K is the midpoint of GJ and I is the midpoint of HJ, this means that triangle JKI is similar to JHG, but dilated by a factor 1/2.

That means that we can write:

(1/2)HG = IK

We know that:

GH = t + 47

IK = -5t + 84

Replacing these in the equation above, we will get:

(1/2)*(t + 47) = -5t + 84

t + 47 = 2*(-5t + 84)

t + 47 = -10*t + 168

t + 10t = 168 - 47

11t = 121

t = 121/11 = 11

The value of t is 11.

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You will save as much as $1000 each year if you start recycling with the company.

If your current order of 150 boxes of paper per year costs $50 per box, and in exchange of starting recycling with the company, the recycling company will donate 20 boxes of new paper each year to your business, then you will save as much as $1000 each year.

Determine how much you will save by multiplying the amount of boxes of paper the recycling company will give to your business with the cost of each box of paper.

20 boxes of new paper x $50 per box = $1000

Therefore, the amount you will save if you start recycling with the company will be as much as $1000 each year .

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Answer:

[tex]\mathrm{Slope } = \dfrac{2}{3}[/tex]

Step-by-step explanation:

To find the slope take any two convenient x, y value combo.

Find the difference between the two y-values(we call it rise).

Find the difference in the corresponding x-values (we call this the run)

[tex]\dfrac{rise}{run} = slope[/tex]

Take points (3, 1) and (6,3). I could choose any two points but working with positive numbers makes it easier

Rise = 3- 1 = 2

Run = 6 - 3 = 3

[tex]\mathrm{Slope } = \dfrac{2}{3}[/tex]

Just for the heck of it let's take two other points to make sure we haven't goofed

Take points (-1, - 5/3) and (1, -1/3)

rise = -1/3 - (-5/3) = -1/3 + 5/3 = 4/3

run = 1 - (-1) = 2

rise over run = 4/3 ÷ 2 = 4/3 x 1/2 = 2/3

Answer:

See below

Step-by-step explanation:

the equation that can be used to determine the value of the artwork in "x" year is A = 1500(1 + 0.0128)^x.

An equation that can be used to determine the value of the artwork in "x" years is a compound interest equation. This type of equation is used to calculate the value of an investment over time, taking into account the initial investment amount and the interest rate.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It can be contrasted with simple interest, which is calculated only on the principal amount.

Compound interest is considered to be more beneficial for savers and investors, as it allows for interest to be earned on previously earned interest, leading to faster growth of the principal.

In this case, the artwork appreciates by 1.28% in value every year and was purchased for $1500. The formula for compound interest is:

A = P(1 + r)^n

Where:

A = the future value of the artwork

P = the initial investment (the purchase price of $1500)

r = the interest rate (1.28% per year)

n = the number of years

To use this equation, we need to convert the interest rate from a percentage to a decimal. We do this by dividing the interest rate by 100. So, 1.28% as a decimal is 0.0128.

Now we can substitute the values into the equation:

A = 1500(1 + 0.0128)^x

Therefore, the equation that can be used to determine the value of the artwork in "x" year is A = 1500(1 + 0.0128)^x.

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The table for the function c{b} is -

{b} :     1      2     3       4

c{b} : 3.5   7.0   10.5  14  

Given is that the number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b.

We can write the table for the function c{b}  as -

b          c{b}  

1           3.5

2          7.0

3          10.5

4          14

Therefore, the table for the function c{b} is -

{b} :     1      2     3       4

c{b} : 3.5   7.0   10.5  14  

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Answer:

n=8

Step-by-step explanation:

40=5n

40=5x8

Answer:n=8 I hope this helps mark brainlist if correct

Step-by-step explanation:

40=5n

Swap the sides of the equation

5n=40

Divide both sides of the equation by 8

n=8

This equation divides the total number of paper clips (8100) by the number of boxes (90)

An equation is a mathematical statement that asserts the equality of two expressions. It is usually expressed using an equals sign (=), with the expressions on either side of the sign separated by the equation symbol. Equations are used to describe relationships between different variables, or to solve for unknown values. Equations are also used to explain physical phenomena, such as Newton's second law of motion, which states that force equals mass times acceleration (F = ma).

The equation that would be used to determine how many paper clips each box will contain is 8100 ÷ 90 = 90.

This equation divides the total number of paper clips (8100) by the number of boxes (90) in order to determine that each box will contain 90 paper clips.

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Answer:

112 chocolate bars

Step-by-step explanation:

Given that the chocolatier made 16 batches of salted caramel chocolate bars, each batch consisted of 42 bars and he sent an equal number of bars to each of its 6 stores,

What is asked: To determine how many bars did each store receive.

Method of solving: Using elementary operations as multiplication and division.

Start considering each batch as the following box:

So it suggests that to find the total number of chocolates produced is equal to the product

Before multiplying, now see that the chocolatier is equally dividing them to its 6 stores, which means that he will take this quantity and divide equally into 6 boxes.

Therefore, this process is the same as dividing by 6, therefore

Is the expression that gives the result desired.

Simplifying the fraction and multiplying the terms gives

This is the amount of chocolate bars each store received.

The sum of 4 and 5 is 9

We know that the sum or also called a summation, is nothing but the result of arithmetically adding numbers.

In simple way we can say that the sum is a way of putting all things together.

The sum is nothing but the whole number which is obtained when two or more numbers have been added together.

and the numbers that are added are known as the addends.

When we add the numbers a plus symbol '+' is used.

Let us assume that we need to find the sum of numbers p and q then we write it as p + q, where p, q are addends.

Here, we need to find the sum of numbers 4 and 5.

4 + 5 = 9

so, the sum is 9

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The range formula determines the difference between the highest and the lowest values in a given set of numbers.

The range formula is mostly used in statistics where the range is the spread of the numbers or data from the lowest to the highest value and it is commonly used in variability. Let's learn more about the range formula and solve a few examples.

The range formula is highly used in statistics to consider the range given in a particular data set. The formula assists in determining the center of the set by finding the difference between the lowest and the highest number. In distribution, the big range means more variability whereas the less range means low variability. The range formula has the other aspects of statistics such as mean, median, and mode. Therefore, the formula to calculate the range is:

R = Highest Value (H) - Lowest Value (L)

Range Formula

R = H - L

In this context,

R is the range

H is the highest value

L is the lowest value

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Answer:

Step-by-step explanation:

The range formula determines the difference between the highest and the lowest values in a given set of numbers. The range formula is mostly used in statistics where the range is the spread of the numbers or data from the lowest to the highest value and it is commonly used in variability. Let's learn more about the range formula and solve a few examples.

The range formula is highly used in statistics to consider the range given in a particular data set. The formula assists in determining the center of the set by finding the difference between the lowest and the highest number. In distribution, the big range means more variability whereas the less range means low variability. The range formula has the other aspects of statistics such as mean, median, and mode. Therefore, the formula to calculate the range is:

R = Highest Value (H) - Lowest Value (L)

Range Formula

R = H - L

In this context,

R is the range

H is the highest value

L is the lowest value

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The slope of the line containing the points A(-8,6) and B(11,2) is given as follows:

m = -0.2105.

The angle of the line is given as follows:

θ = -11.89º.

The two points on the line are given as follows:

A(-8,6) and B(11,2).

Given two points, the slope is obtained by the division of the change in y by the change in x, hence:

m = (2 - 6)/(11 + 8)

m = -0.2105.

The slope represents the tangent of the angle, hence the angle is the arc tangent of the slope, thus:

θ = arctan(-0.2105)

θ = -11.89º.

The problem asks for the slope and for the angle of the line containing points A and B.

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The figure represents the angle of refraction

The angle of refraction is represented by the angle θ2 

Light rays that are refracted change their direction as they travel through different media. Light changes direction when it travels from one medium to another.

The refracted beam will bend toward the normal if the incident light is moving from a less dense to a denser material. Here, the angle of refraction (hence, "r") is always smaller than the angle of incidence. (In line with the diagram)

Similar to this, the refracted ray will bend away from the normal if the incident light is moving from a denser medium to a less dense material. In this situation, the angle of incidence is never greater than the angle of refraction, or "r."

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In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4).

Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.

The midpoint formula is used to find the midpoint between two points whose coordinates are known to us. The midpoint formula is also used to find the coordinates of the endpoint if we know the coordinates of the other endpoint and the midpoint. In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4). Let us learn more about the formula of the midpoint, and different methods to find the midpoint of a line.

(3, 8 )

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

(x+x /2  ,y+y/2  )

here (x₁, y₁ ) = P (1, 6 ) and (x₂, y₂ ) = Q (5, 10 ) , then

midpoint = (1+5/2 ,++10/2  ) = ( 6/2 , 16/2 ) = (3, 8 )

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The maximum value of the linear equation on the given interval is:

y = 11

We want to find the maximum of the linear function:

y = 2x + 1

On the interval [3, 5]

Notice that we have a line with a positive slope, thus, this is an increasing line.

Then the maximum is just what we get when we evaluate the function on the maximum value of the interval:

y = 2*5 + 1

y = 10 + 1

y = 11

The maximum value is 11.

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Answer: x = 26

Step-by-step explanation: All you need to do is to add up given two unknown angles. Then, you can solve the equation for 180 degree. Because in this case, these angles are complementary to 180 degrees.

If you add them up:

[tex]8x - 28 = 180\\x = 26[/tex]

So, the answer is 26.

If you purchase the car with this loan, you will have to pay a total of $5,400 in interest.

To calculate the interest rate used for this loan, we can use the formula:

Interest rate = (Monthly payment x 12) / Principal

Plugging in the given values, we get:

Interest rate = ($450 x 12) / $10,000 = 0.54 or 54%

To calculate the total interest paid on the loan, we can use the formula:

Total interest = Principal x Interest rate

Plugging in the given values, we get:

Total interest = $10,000 x 0.54 = $5,400

So if you purchase the car with this loan, you will have to pay a total of $5,400 in interest.

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Answer:

75x = 300

x = 4

So he has

4 quarters

3x = 3*4 = 12 dimes

4x = 4*4 = 16 nickels

Step-by-step explanation:

The mean is dividing the sum of all values in a data set by the number of values.

Average is another word for "mean." For instance, if we say that the average height of the 9th grade class is 150 cm, it signifies that this is the mean of all of the kids' heights. The statistical notion of mean, which is employed in a variety of financial areas and corporate appraisal, has significant financial implications. The three statistical measurements of a data set's central tendency are mean, median, and mode.

The mean, which measures the central tendency of the data, is the average or computed central value of a set of numbers. The statistical metric known as central tendency identifies the complete collection of data or distribution by a single value. It offers a precise description of the entire set of facts. The ratio of the sum of all observations to the total number of observations is another way to define the mean in statistics.

Given a data set, X = {x₁,x₂, . . . ,xₙ}, the mean (or arithmetic mean, or average), denoted X, is the mean of the n values x₁,x₂, . . . ,xₙ.

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Graph y=-7 by plotting y-intercept (0,-7) and all points have y=-7, it is a horizontal line.

What is graph ?

A graph is a mathematical structure used to represent relationships between objects. In a graph, objects are represented by vertices (or nodes) and relationships are represented by edges (or arcs). Graphs can be used to model a wide variety of real-world systems, including networks of roads, social networks, and the internet.

To graph y = -7, you can start by plotting the y-intercept, which is the point at which the line crosses the y-axis. In this case, the y-intercept is (0, -7) because when x = 0, y = -7.

To graph the line, you can then pick any other x-value, substitute it into the equation, and find the corresponding y-value. For example, if you pick x = 1, then y = -7. So, you can plot the point (1,-7) on the graph.

You can repeat this process with different x-values and plot more points on the graph.

Graph y=-7 by plotting y-intercept (0,-7) and all points have y=-7, it is a horizontal line.

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Answer: 11 1/4

Step-by-step explanation:

4 1/2 * 2 1/2

= 9/2 * 5/2

= 45 / 4

= 11 1/4

For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.

The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.

Given a right triangle with base = 8 and an angle = 24°

Using angle sum property of triangle

24 + 90 + angle L = 180

L = 66°

Using Sohcahtoa

Tangent: tan(θ) = Opposite / Adjacent

tan(24°) = LK/8

0.445 = LK/8

LH = 8 × 0.445

LK = 3.56

LM = [tex]\sqrt{MK^2 + LK^2}[/tex]

LM = [tex]\sqrt{8^2 + 3.56^2}[/tex]

LM = 8.75

Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

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For given equation of circle radius is 6 unit and center is at (-2,1).

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

Now,

As shown in graph the graph by taking two points on graph

(-2,7) and (-2,-5)

Center will be at (-2-2)/2, (7-5)/2

i.e. (-2,1)

And for radius take magnitude of points from y-coordinate

(7+5)/2=6 unit

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The perimeter, in units, of the parallelogram exists 48.

Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. The coordinate plane allows us to graph points, lines, and more.

A coordinate plane is a framework for describing and graphing points and lines. The coordinate plane is composed of two axes, one vertical (y) and one horizontal (x). The coordinate plane has four quadrants. The origin is the location where these lines converge (0, 0).

Therefore, the correct answer is option C) 48.

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Logarithm and exponential functions are inverse as log(ex)=x and elogx=x.

Knowing that logarithms were once a tool for multiplication when ships employed celestial navigation may be helpful to the layperson. The product of two numbers' logarithms is equal to the total of their individual logarithms. Numerous log tables were published and utilized mechanically.

In 1958, this was an excellent supplemental math topic. The slide rule converts multiplication to addition of lengths using one axis graphs of an exponential function and a graphic log table as a physical correlate. As a result, the logarithm of a product is equal to the sum of the logarithms of its components.

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The correct option A:  The solution cannot include x = 3  and x = (-1/2) as it will make the equation as indeterminate form, whose solution is not possible.

For the stated equation.

6 / (2x + 1) - 1 / (x - 3) = 0.

When putting x = x = 3  and x = (-1/2), the denominator part will become zero.

This makes the whole equation as indeterminate form,whose solution is not possible.

Thus, the solution cannot include x = 3  and x = (-1/2) as it will make the equation as indeterminate form, whose solution is not possible.

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Therefore, the burglar's initial theft was $12,000.

To begin, we may express the data in the problem using algebra.

Let x represent the original sum that the burglary victim took.

The thief was left with x/2 + 2000 after giving the first guard the other half of the money plus $2,000, according to the issue.

He had (x/2 + 2000)/2 + 2000 when he gave the same sum to the second guard.

He also handed the third guard the same amount, leaving him with

((x/2 + 2000)/2 + 2000)/2 + 2000.

However, because we are certain that he left with $9,000 more than when he came, we may state:

((x/2 + 2000)/2 + 2000)/2 + 2000 = x + 9000

We can now determine x:

x = (900022*2 - 6000)/3

x = 36000/3

x = 12000

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As the person wanted the fountain to be the same distance from each edge of the pond and the incenter of the triangle is equidistant

From the information, the person is placing a fountain in a triangular koi pond and want the fountain to be the same distance from each edge of the

pond.

The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It can be thought of as the intersection of the triangle's internal angle bisectors. The fountain is equally spaced from each edge of the pond because the person wanted it to be, and the triangle's incenter is also evenly spaced.

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The probability that the counter removed is red is given as follows:

18/55.

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

The probabilities of a red counter being removed from Bag B is obtained considering these following scenarios:

Hence the probability that the counter removed is red is calculated as follows:

p = 4/11 x 6/10 + 3/11 x 4/10 = 36/110 = 18/55.

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Solve each equation in steps:

Answer:

Step-by-step explanation:

1) 2(3b + 6) = 78, value of b?

→ 2(3b + 6) = 78

→ 6b + 12 = 78

→ 6b = 78 - 12

→ 6b = 66

→ b = 66/6

→ [ b = 11 ]

Hence, the value of b is 11.

2) -2(6c - 3) = -72, value of c?

→ -2(6c - 3) = -72

→ -12c + 6 = -72

→ -12c = -72 - 6

→ -12c = -78

→ c = (-78)/(-12)

→ c = 78/12

→ [ c = 6.5 ]

Hence, the value of c is 6.5.