please view the image and answer the questions.

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

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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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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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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Answer:

9/6=12/x-4

Step-by-step explanation:

An average mean of 1.72 children can be found on every house

One method for making data more comprehensible is to put it in a frequency distribution table. Consider having a list of IQ results for a talented class at a certain elementary school. The frequency of a value in a set of data is how frequently it appears.

Victor, for instance, made nine attempts to obtain a red gumball. The quantity of gumballs in each hue that were produced would be the frequency in this situation. The distribution of observations based on a variable's possible values is displayed in a frequency table.

frequency = 10 + 4 + 2 + 3 + 4 + 2

= 25

Sum of children

= (10 × 0)+(4 ×1)+(2 × 2)+(3 × 3)+(4 × 4)+(2 × 5)

= 43

Mean =  43/25

= 1.72

Thus, An average mean of 1.72 children can be found on every house.

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Answer:

3. (-4/5, -3) 6. (4, 12/-5)

Step-by-step explanation:

3. so first we have

-5x - 10y = 20

-5x - 8y = 14

so first we have to have the x's be opposite so we multiply the top one by -1 which gets us

5x + 10y = -20

-5x - 8y = 14

then we cancel out the x's and subtract 10 by 8 and -20 by 14 so it's now

2y = -6

then we divide by 2 on both sides so it's

y = -3

but now we have to solve for x so we substitute y in on the bottom equation so now it is

-5x - 8(-3) = 20

now we multiply

-5x + 24 = 20

subtract 24 from both sides

-5x = -4

divide by -5

x = -4/5

then put it in coordinates

(-4/5, -3)

6. so we have

x = 4

-4x - 5y = 4

so first we have to substitute the top in for the bottom so now we have

-4(4) - 5y = 4

distribute

-8 - 5y = 4

add 8 to both sides

-5y = 12

divide

y = 12/-5

coordinates

(4, 12/-5)

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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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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The solutions of the quadratic equation are:

m = 1  ± i*√(5)/2

The correct option is b.

Here we want to solve the quadratic equation:

4m² - 8m +9 = 0

Replacing the coefficients on the quadratic formula, we will see that the solutions are:

[tex]m = \frac{8 \pm \sqrt{(-8)^2 - 4*4*9} }{2*4} \\\\m = \frac{8 \pm \sqrt{-80} }{8}\\\\m = 1 \pm\sqrt{-80/64} \\\\m = 1 \pm\sqrt{-5/4} \\\\m = 1 \pm\sqrt{-5}/2\\\\m = 1 \pm\sqrt{5}i/2[/tex]

These are the solutions.

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The polynomial, so d can be any value less than b.

A polynomial is an expression made up of multiple terms, each of which is a number, a variable, or the product of a number and one or more variables. Polynomials are typically used to model real-world scenarios including, but not limited to, population growth, force and acceleration, and angles of elevation. Each term of the polynomial is separated from the others by an addition or subtraction sign.

Given the polynomial 4x^3 + ax^2 + bx + c,
a = 4, b = -3, c = 5, d = -2.
To find the values of a, b, c, and d, we need to compare the coefficients of the polynomial to the given values.
The coefficient of the term with the highest degree (x^3) is 4, so a = 4.
The coefficient of the next degree (x^2) is a, so a = -3.
The coefficient of the next degree (x) is b, so b = 5. The coefficient of the constant term is c, so c = -2. Finally, d is not given in the polynomial, so d can be any value less than 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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Answer: 11 1/4

Step-by-step explanation:

4 1/2 * 2 1/2

= 9/2 * 5/2

= 45 / 4

= 11 1/4

Answer:

See below

Step-by-step explanation:

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 value of the length of side UX for the right triangle formed by sides tangent to the circle is equal to 3.4 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The side XV is perpendicular to the side UV tangent to the circle, which makes the triangle a right triangle.

so by evaluation we derive the value for the hypotenuse UX as follows;

UX = √(3² + 1.6²)

UX = √(9 + 2.56)

UX = √11.56

UX = 3.4

Therefore, the length of side UX for the right triangle is equal to 3.4 using the Pythagoras rule.

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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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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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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.

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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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 vertices of the triangle DEF after the 90º counterclockwise rotation about the point (5,2) are given as follows:

D'(-11, -2), E'(-10, 1) and F'(-6, -3).

The five more known rotation rules are given as follows:

Considering the 90º counterclockwise rotation about the point (5,2), the rule is given as follows:

(x,y) -> (-y - 5, x - 2).

Hence the vertices are given as follows:

D'(-11, -2), E'(-10, 1) and F'(-6, -3).

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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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The distance remained to be covered by amrita to attend a function is 2950 meters or 2.95 kilometers.

Given,

  Total distance to be covered by Amrita = 20 KM = 20000 m

  Distance covered by her car before broken = 17 Km 50 meter = 17050m

We know that,

                        1 Kilometer = 1000 meter

Remaining Distance = (20000 - 17050)m

                                  = 2950 m

                                  = 2.95 KM

Therefore, the distance remaining to be covered by amrita is 2950 meters or 2.95 Kilometers.

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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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Based on the information provided, the length of the rope for the goat to graze over half of the field is 0.5 units.

The radius of a circle can be defined as a straight line that goes from any of the borders of the circle to its center of it.

The radius and the proportion of the field that the goat can graze is proportional. In this case if the length is 1 unit the goat can graze all the field; therefore, if we cut the graze to 0.5 the goat will graze only half of the field.

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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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