Describe the graph of the proportional relationship represented by the equation y = 7.5x.

The graph is a line that goes through points (0, 0) and (7.5, 7.5).
The graph is a line that goes through points (0, 0) and (15, 2).
The graph is a line that goes through points (0, 0) and (7.5, 1).
The graph is a line that goes through points (0, 0) and (1, 7.5).

[tex]\textit{arc's length}\\\\ x = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =\frac{\pi }{3} \end{cases}\implies x=10\cdot \cfrac{\pi }{3}\implies x\approx 10.47[/tex]

Solution set of the equation is -3,-1, and 2 by simplifying the equation we get m³+2m²-5m-6 = 0

There are many different ways to define an equation. 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.

Mathematical algebraic equations typically have one or more variables.

Given equation is: (6/m)+2 = (m+3)(m-1)

multiply with m both sides,

⇒6+2m = m(m²+2m-3)    

⇒m³+2m²-3m = 6+2m

So we get,

m³+2m²-5m-6 = 0

Solving we get, m = -3, m = -1, m = 2 as solution of given equation.

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Answer:

Answer in image

Step-by-step explanation:

average speed = 3 3/4 km/h

In order to find how many kilometers the hiker will walk in 5 hours, you'll need to multiply the average speed by the hiker's hours.

[tex]3\dfrac{3}{4} \times5[/tex]

[tex]=\fbox{18.75 km}[/tex]

Answer:

9/12

Step-by-step explanation:

The easiest way to do this would to multiply the numerator and the denominator.

We need to find out how to get the numerator (3) to 9.

We can do this equation.

3 × 3 = 9

Now that we have multiplied the numerator by 3, we now need to multiply the denominator by 3.

4 × 3 = 12

The new fraction is 9/12.

Answer: 840 ways

Step-by-step explanation:

[tex]\displaystyle\\C_{10}^1*C_9^3=\\\\\frac{10!}{(10-1)!1!} *\frac{9!}{(9-3)!3!}=\\\\\frac{9!10}{9!1} *\frac{6!*7*8*9}{6!*1*2*3}=\\\\10*\frac{7*8*9}{2*3} =\\\\10*84=\\\\840\ ways[/tex]

Answer: 840 ways

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Step-by-step explanation:

Answer:

Step-by-step explanation:

The total tax Kala paid on the CDs was $1.30/CD * 6 CDs = $1.3*6=7.80.The total cost of the CDs before tax was $97.20 - $7.80 = $97.2-7.8=89.40.The price of each CD before tax was $89.40 / 6 CDs = $89.4/6=14.90/CD. Answer: 14.90.

The equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.

What is two point equation form?

The equation of the line passing through two points is

(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)

Here, (x₁,y₁) ∈ (7, -2)

(x₂, y₂) ∈ (5, 3).

y - (-2) / 3 -(-2) = x - 7/ 5 - 7

(y + 2) / 5 = x-7 / -2

-2y - 4 = 5x - 35

5x + 2y - 31 = 0

Hence, the equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.

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The distance between the points C = (-9, 7) and Q = (-1, 3)  in the coordinate plane will be;

⇒ D = 10

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

Two points on the coordinate plane are C = (-9, 7) and Q = (-1, 3).

Now,

Since, Two points on the coordinate plane are C = (-9, 7) and Q = (-1, 3).

Hence, The distance between the points C = (-9, 7) and Q = (-1, 3)  in the coordinate plane will be;

⇒ D = √(3 - 7)² + (- 1 - (-9))²

⇒ D = √ (-4)² + (8)²

⇒ D = √36 + 64

⇒ D = √100

⇒ D = 10

Thus, The distance = 10

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The required amount of $799.90 will reduce the amount by $842.

Given that,
The amount will reduce the amount due on an invoice of $ 9410.25 by $ 842 if the terms of the invoice are 5/10, n/30 and the payment was made during the discount period is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
For 5/10  and n /30
The discount would be 5% if paid in the 30-day span,
Amount = amount invoiced [1 - 5%/100]
Amount = $842[0.95]
Amount = $799.9

Thus, the required amount of $799.90 will reduce the amount by $842.

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Sasha's balance after 12 years, if she makes no other deposits or withdrawals would be $ 4, 598. 07

Sasha's balance after 12 years will be the future value of her savings after 12 years at a rate of 2. 3% per year.

This future value can be found by the formula :

Amount after 12 years = Amount deposited by Sasha x ( 1 + annual compound interest ) ^ number of years

= 3, 500 x ( 1 + 2 .3 % ) ¹²

= 3, 500 x 1.3137344983996021269289886802331

= $ 4, 598. 07

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The total cost to transport 12 tons of sugar is $9600.

From the information, Sugar Sweet company is going to transport its sugar to the market. It will cost $7500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported.

Let C represent the total cost ( in dollars)

Let s represent the amount of sugar.

The equation to find the total cost to transport 12 tons of sugar will be:

C = 7500 + (175 × s)

C = 7500 + 175s

C = 7500 + (175 × 12)

C = 7500 + 2100

C = 9600

The cost is $9600.

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The value of m in the equation m=-(4+m)+2 is -1.

How are linear equations solved step-by-step?

One of the easiest methods for resolving a system of linear equations is graphing. Simply plot each equation as a line on a graph and identify the point or points where the lines converge to find the value. These equations are simple to graph because they are already expressed in slope-intercept form.

m = -(4+m)+2

m = -4 -m + 2

m = -2 - m

m + m = -2

2m = -2

m = -1

Hence, the value of m in equation m=-(4+m)+2 is -1.

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The box plot indicates that the interquartile range (IQR) of the data 0, 25, 50, 75, and 100 is 100.

Find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1. We use the median to summarize a typical value rather than the mean when a data collection contains outliers or extreme values. The interquartile range, which is the difference between the first and third quartiles, is a statistic that is frequently used to summarize variability in data sets with outliers.

Here,

The first and third quartiles would need to be located initially. Then, to obtain the IQR, you would divide the third quartile by the first.

IQR, in my opinion, is 100.

The interquartile range (IQR) of the data 0, 25, 50, 75, 100 will be 100 by the given box plot.

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a) The linear function that best represents the red line is given as follows: y = -4x + 4.

b) The linear function that best represents the blue line is given as follows: y = x - 2.

c) Two coordinates of the red line are given as follows: (0,4) and (1,0).

d) The coordinates of the blue line are given as follows: (0,-2) and (2,0).

The slope-intercept definition used to define a linear function from it's graph is given as follows:

y = mx + b.

In which the coefficients are listed as follows:

For the red line, two points are given as follows:

(0,4) and (1,0)

Hence the parameters are of:

Thus the equation is of:

y = -4x + 4.

For the blue line, the equation is of:

y = x - 2.

As:

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The mean of the temperatures is 29°C, which corresponds to answer B.

For convenience reasons we are going to avoid the use of the Celsius symbol (°C) during the calculations.

[tex]19+22+30+45=116[/tex]

There are 4 values of temperature.

[tex]\frac{116}{4}=29[/tex]

The mean of the temperatures is 29°C, which corresponds to answer B.

The non-real complex number is  [tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex].

We have,

To find a non-real complex number,

What is not a real number?

Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers. Now, which numbers are not real numbers? The numbers that are neither rational nor irrational are non-real numbers, like, √-1, 2 + 3i, and -i.

A non-real complex number is an imaginary number containing negative numbers in the root.  

Here,

[tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex]

In this option, it includes the negative term that is in the root so this is imaginary, therefore, the answer is "Option B".

Hence, the non-real complex number is  [tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex].

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Answer:

2((2x+2)+3x)=124 units

Step-by-step explanation:

We know that the formula for perimeter is 2(b+h) and since we know this, we just substitute the values for this and solve.

Hello, Elyna. ,

The formula would be:

200+200x=b

Step-by-step formula:

1.) x equals hours, whereas b equals bacteria.

2.) There are 24 hours in one day.

3.) 24*5= 120

4.) Connect it.

5.) 200+200(120)= 6.) 24200= 5 bacterium days

Hope I could help.

x/2 + 4 is  an equivalent expression .

What is an expression in maths?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

                          This mathematical operation may be addition, subtraction, multiplication, or division. An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.

                            An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases.

= 1/2(X+8)

= x/2 + 8/2

= x/2 + 4

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Answer:

Below

Step-by-step explanation:

See image below:

the center of the circle is at (5, 1) and the radius is approximately 5.48 units.

Why it is and what is perimeter of a circle?

The standard equation of a circle with center (a,b) and radius r is:

(x - a)²2 + (y - b)²2 = r²2

Comparing this equation to the given equation, we can see that the center of the circle is (5, 1) and the radius is the square root of 30. Therefore, the center of the circle is at (5, 1) and the radius is approximately 5.48 units.

The perimeter of a circle is also known as its circumference, and it can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.

Alternatively, you can also use the formula:

C = πd

where d is the diameter of the circle.

So if you know the radius or diameter of a circle, you can use either of these formulas to calculate its circumference (perimeter).

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The equation of a line that represents the table is y = 6x - 5.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

To obtain the linear equation first we need slope(m) = (y₂ - y₁)/(x₂ - x₁)

= (1 + 11)/(1 + 1) = 12/2 = 6.

Now, we'll take any one of these coordinate points and construct an equation in slope-intercept form,

- 11 = 6(-1) + b.

- 11 = - 6 + b.

b = - 5.

∴ y = 6x - 5 is our equation.

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Answer:

If you need the answer as f by simplifying both sides of the equation and then isolating the variable, the answer would be:

[tex]xf=\frac{3x^2}{5}-\frac{f(x)}{5}[/tex]

Or, if you need to evaluate the function itself, the answer would be:

[tex]f(x)=3x^2-5xf[/tex]

Python is a dynamic, high-level, free open source, and interpreted programming language.

#definition of "median" function

def median(list):

#checking median condition to make sure the list returns zero if empty

if len(list) == 0:

return 0

#sort the list

list.sort()

#find middle element

mid = len(list) / 2

#check the condition

if len(list) % 2 == 1:

return list[mid]

else:

return (list[mid] + list[mid - 1]) / 2

#definition of "mean" function

def mean(list):

#checking mean condition to make sure the list returns zero if empty

if len(list) == 0:

return 0

#sort the list

list.sort()

#set the value

total = 0

#initiate a for loop

for num in list:

#then we calculate the total

total += num

#return the value

return total/ len(list)

#definition of "mode" function

def mode(list):

#checking mode condition to make sure the list returns zero if empty

if len(list) == 0:

return 0

#declare the variable

num_Dictionary = {}

#check the condition

for digit in list:

num = num_Dictionary.get(digit, None)

if num == None:

num_Dictionary[digit] = 1

else:

num_Dictionary[digit] = num + 1

#getting the maximum value

max_Value = max(num_Dictionary.values())

mode_List = []

for k in num_Dictionary:

if num_Dictionary[k] == max_Value:

mode_List.append(k)

return mode_List

#definition of main function

def main():

#set the list

num_list = [7, 4, 8, 10, 9]

#call the "mean" function with a parameter

print ("Mean of the given list: ", mean(num_list))

#call the "mode" function with a parameter

print ("Mode of the given list:", mode(num_list))

#call the "median" function with a parameter

print ("Median of the given list:", median(num_list))

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Relations on the set (1,2,3,4), decide whether it is reflexive, whether it is symmetric, whether it is anti symmetric, and whether it is transitive.

Given :

a )

=  { ( 2, 2 ),( 2, 3 ),( 2, 4 ),( 3, 2 ),( 3, 3 ) ,( 3, 4 ) }

Not reflexive because we do not have (1, 1), (3, 3), and (4, 4).

Not symmetric because while we we have (3, 4), we do not have (4, 3).

Not anti symmetric because we have both (2, 3) and (3, 2).

Transitive because if we have (a, b) in this relation, then a will be either 2 or 3. Then (2, c)

b )

{(1, 1),(1, 2),(2, 1),(2, 2),(3, 3),(4, 4)}

Reflexive because (a, a) is in the relation for all a = 1, 2, 3, 4.

Symmetric because for every (a, b), we have a (b, a).

Not antisymmetric because we have (1, 2) and (2, 1).

Transitive because while we have (1, 2) and (2, 1), we also have (1, 1) and (2, 2) in the relation.

c )

{(2, 4),(4, 2)}

Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.

Symmetric because for every (a, b), we have a (b, a).

Not antisymmetric because we have both (2, 4) and (4, 2).

Not transitive because we are missing (2, 2) and (4, 4)

d )

{(1, 2),(2, 3),(3, 4)}

Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.

Not symmetric because we do not have (2, 1),(3, 2), and (4, 3).

Antisymmetric because for every (a, b), we do not have a (b, a).

Not transitive because we do not have (1, 3) for (1, 2) and (2, 3)

e )

{(1, 1),(2, 2),(3, 3),(4, 4)}

Reflexive because we have (a, a) for every a = 1, 2, 3, 4.

Symmetric because we do not have a case where (a, b) and a 6= b.

Antisymmetric because we do not have a case where (a, b) and a 6= b.

Transitive because we can satisfy (a, b) and (b, c) when a = b = c.

f )

{(1, 3),(1, 4),(2, 3),(2, 4),(3, 1),(3, 4)}

Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.

Not symmetric because the relation does not contain (4, 1), (3, 2), (4, 2), and (4, 3).

Not antisymmetric because we have (1, 3) and (3, 1).

Not transitive because we do not have (2, 1) for (2, 3) and (3, 1).

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We have "No Solutions" or "Infinite Solutions" case.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the unit cost of Craft paper be x.

let the unit cost of boxes of markers be y.

let the unit cost of glue sticks be z.

So, the system of equations are

2x+ 4y + 5z= 36

6x+ 4y +2 z = 32

3x+ 2y+ z= 16

Now, solving the above three equation we get using Matrix method

All determinants are zero we have "No Solutions" or "Infinite Solutions" case.

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Answer:

The first one, due to the x being raised to the power of 2

Step-by-step explanation: