I need help with this graph what is the root or factored form of this? Thank you!

The equation y = (13 / 4) · x - 19 / 2 represents the perpendicular bisector of the line segment.

In this problem we need to determine the equation of the line perpendicular to a line segment whose endpoints are known. The equation of the line is represented by a first grade polynomial of the form:

y = m · x + b

Where:

And the relationship between the slopes of two perpendicular lines:

m · m' = - 1

Where:

And the slope of the original line can be found by the secant line formula:

m = Δy / Δx

And the midpoint of a line segment between two endpoints is defined below, necessary for the location of the bisector:

M(x, y) = 0.5 · A(x, y) + B(x, y)

Where:

First, find the slope of the line segment by secant line formula:

m = [- 1 - (- 5)] / (- 5 - 9)

m = - 4 / 13

Second, find the slope of the perpendicular bisector by the slope relationship between two perpendicular lines:

m' = - 1 / m

m' = - 1 / (- 4 / 13)

m' = 13 / 4

Third, determine the midpoint of the line segment by the midpoint formula:

M(x, y) = 0.5 · (9, - 5) + 0.5 · (- 5, - 1)

M(x, y) = (4.5, - 2.5) + (- 2.5, - 0.5)

M(x, y) = (2, - 3)

Fourth, find the intercept of the perpendicular bisector by means of the equation of the line:

b = y - m' · x

b = - 3 - (13 / 4) · 2

b = - 3 - 26 / 4

b = - 3 - 13 / 2

b = - 19 / 2

The equation for the perpendicular bisector is y = (13 / 4) · x - 19 / 2.

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The blanks in this two-column proof should be completed (filled) as follows:

Statements                                             Reasons_______________

m∠RST = 5x° and m∠UVW = 7x°                Given

∠RST and ∠UVW are supplementary

m∠RST = 5x° + m∠UVW = 180           definition of supplementary angles

5x + 7x = 180                                       substitution property of equality

12x = 180                                              addition property of equality

x = 15                                                    division property of equality

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this context, we can logically deduce that the sum of angles RST and UVW are supplementary angles:

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Using the relation between standard deviation and variance it is concluded that the standard deviation for the population for the given variance is 7.1

In statistics, the two most crucial metrics are variance and standard deviation. While the variance is a measurement of how data points vary from the mean, standard deviation is a measure of the distribution of statistical data.

The square root of the variance yields the standard deviation, i.e.

Standard deviation = [tex]\sqrt{variance[/tex]

Given that sample, the variance is 49.7 and we have to calculate the standard deviation.

Standard deviation (σ) = [tex]\sqrt{variance[/tex]

= [tex]\sqrt{49.7}[/tex]

= 7.0498

=7.1

Hence, the standard deviation for the population for the given variance is 7.1

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The statement that is true is All rational numbers can be written as the quotient of Integers

Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.

In a rational number, the denominator cannot be zero.

Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers

Quotients refers to the end product of division example 2 ÷ 1 = 2/1

2/1 is the quotient, both 2 and 1 are integers

All decimals are rational - A counter example to this is √2

It has decimal and not a rational number because it cannot be represented as a fraction

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The statement that is true is All rational numbers can be written as the quotient of Integers

What are rational numbers ?

Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.

In a rational number, the denominator cannot be zero.

Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers

Quotients refers to the end product of division example 2 ÷ 1 = 2/1

2/1 is the quotient, both 2 and 1 are integers

All decimals are rational - A counter example to this is √2

It has decimal and not a rational number because it cannot be represented as a fraction

For emission of a surface, the average absorptivity of this surface at 1040 K is 0.899705900025.

Knowing that ε1 =0.15 and ε2 = 0.9, we first solve for the average emission, e, as follows:

ε = ε1 [tex]f_λ[/tex] [ λT]  +   ε2 [1- [tex]f_{λ}[/tex](λT)]

is also solved for reference in calculating fλ

(λ*T) = (5 μm)(1040 K)

       = 5200 μm K

[tex]f_{λ}[/tex]= 0.0003921333  when referencing this to a blackbody function.

Moving on, we solve for T1040 using the equation above:

ε = ε1 [tex]f_{λ}[/tex][λT] + ε2[1 -[tex]f_{λ}[/tex]( λT)]

  =0.9 + (0.15-0.9)0.0003921333  

  =0.899705900025

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In a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that For every unit increase in x1, the predicted mean of Y rises by 2 units holding [tex]x_{2}[/tex] constant.

Given data,

Slope b1 = +2

Mutiple regression which means,

Use multiple linear regression to determine the relationship between two or more independent variables and one dependent variable.

The value of the dependent variable at a specific level of the independent variables (For instance, the crop's anticipated yield at specific levels of temperature, rainfall, and fertilizer application).

[tex]y = b_{0} +b_{1}x_{1}+b_{2}x_{2}+b_{3}x_{3}+....[/tex]

[tex]b_{1}[/tex]=2 means

The estimated mean of Y increases by 2 units for each increase of 1 unit of [tex]x_{1}[/tex], holding [tex]x_{2}[/tex] constant.

Hence, the expected mean of Y increases by two units for every unit increase in x1.

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If a baseball diamond is a square that measures 90ft on each side. The  expression for the distance from 2nd base to home plate in square root form isc =√ (90)² + (90)²   and the distance is 127ft.

Using the Pythagoreans theorem formula

c= √ a²+b²

Where:

c = length of hypotenuse

a and b =  length of the sides of the right triangle

Let plug in the formula

c =√ (90)² + (90)²

c =√ 8100 +8100

c =√16200

c = 127.3

c = 127 ft (Approximately)

Therefore the distance is 127ft.

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the number of Red sweets=14

Let the probability of getting a red sweet be = P(R)

Let the probability of getting a Blue sweet be = P(B)

Let the probability of getting an orange sweet be = P(O)

Let the probability of getting a yellow sweet be = P(Y)

Let the number of Red sweets be represented as = n(R)

Let the number of Yellow sweets be represented as = n(Y)

Let the number of Orange sweets be represented as = n(O)

Let the number of Blue sweets be represented as = n(B)

Let the total number of sweets in the jar be represented as = n(T)

P(B) = 0.5

P(E) = 0.2

P(R) = 2 x P(O)

The formula of probability =

Number of the Sweets of a color/Total number of sweets in the jar

then,

P(B)=n(B)/ n(T)

P(B)=0.5 (Given in question)

n(B)=20 (Given in question)

So,

0.5 = 20/n(T)

5/10 = 20/n(T)

5/10 x 1/20 = 1/n(T)

cross multiplying

n(T)=10/5 x 20

dividing 10 by 5 =2

n(T) = 2 x 20

n(T) = 40

P(Y)=0.2 (Given in question)

Applying the formula of probability

P(Y) = n(Y)/n(T)

putting values

0.2=n(Y)/40

2/10=n(Y)/40

2/10 x 40 =n(Y)

Dividing 40 by 10 = 4

n(Y)= 2 x 4

n(Y)= 8

P(R)=2P(O)

Applying the formula of probability

n(R)/n(T)=2n(O)/n(T)

Cancelling out n(T) with n(T)

So,

n(R)=2 x n(O) -(i)

n(T) = n(O)+n(R)+n(B)+n(Y)

putting values

40=n(O)+n(R)+20+8

40=n(O)+n(R)+28

40-18=n(O)+n(R)

From -(i)

22=2n(O)+n(O)  

22=3n(O)

n(O)=22/3

Since,

n(R)=2xn(O)

n(R)=2x22/3

n(R)=44/3

n(R)=14.6

the number of Red sweets=14.6

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Answer:

Unclassified

Step-by-step explanation:

Which questions would you like answered?

Answer:

-5 with the exponet of 11

Answer:

-1/5 or -0.2 if you are going by fraction or decimal

The parent function is y = x ; shift 2 units downwards.

Given,

In the question:

The function is :

g(x) = x - 2

Now, According to the question ;

Let's know

What is the Parent function and transformation?

The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. Reflection. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.

According to the above statement is;

g(x) = x -2

Hence, The parent function is y = x ; shift 2 units downwards.

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It takes almost 5.7 hours the same hose to fill an aquarium measuring 26 inches by 33 inches by 35 inches.

First, we must determine how quickly the hose operates.

By dividing the volume of the first aquarium by the length of time it took to fill it, we may determine that.

The following formula can be used to determine the volume of the first aquarium: V =L*B*H

where the aquarium's length is L and its width is B

Its height is H.

Thus, the first aquarium's volume is:

V =L*B*H = 3*8*11 = 264 inches^3

We have the filling rate as:

264/3 inches ^3 per minute,

Let's now determine the second aquarium's volume.

The first formula is what we employ.

The volume is as follows:

V =L*B*H = 26*33*35 = 30030 inches ^3

Now, we divide the capacity of the second aquarium by the pace of the first aquarium to obtain the amount of time.

According to mathematics, that is:

30030 * 3/264 = 341.25 minutes = 5.7 hours approximately

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Sherry needs to invest 2000$ in mutual fund and 13200$ in bond to earn 548$ at the end of the year.

A percentage is just one of the many ways that a number, ratio, or fraction can be expressed. It is a number or ratio expressed as a fraction of 100.

Given:

Sherry has 15200$ to invest in mutual funds and in bonds.

Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.

Here we need to find how much does she need to invest in each type of account if she wants to earn 548 at the end of the first year.

Here we have total amount = 15200$

So, let us consider x be the amount invested in mutual funds, then the amount invested in bonds will be 15200 - x.

It can be written in the following matrix

[x     15200-x ]

We know that the total amount earned at the end of the year is 548.

So, it can be written as

amount invested x percentage = final amount

[tex]\left[\begin{array}{cc}x&15200-x\\\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}1/100\\4/100\\\end{array}\right][/tex] = 548

We can simply it as

[x*1/100 + (15200 - x)*4/100] = 548

⇒ x/100 + 60800/100 - 4x/100 = 548

⇒ x + 60800 - 4x = 54800

⇒ -3x = 54800 - 60800

⇒ -3x = -6000

⇒ x = 2000

⇒ 15200 - 2000 = 13200

Therefore, Sherry invests 2000$ in mutual funds and 13200$ in bond to earn 548 at the end of the year.

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The equation that could be used to find q is q = 110-0.15(110) where q equal the price of a quarter-page ad after the markdown.

According to the question,

We have the following information:

Cost of a quarter-page ad cost = $110

Mark down in the price = 15%

Now, q represents the price of a quarter-page ad after the markdown.

(Note that when we remove the sign of % means that the number has to be divided by 100.)

So, the equation will be the difference of the markdown price from the original price:

q = 110-(15/100)110

q = 110-0.15*110

q = 110-0.15(110)

Hence, the correct option is the third one.

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The distance driven in city is 386.4 miles and same in highway is 213.6 miles.

Let the distance driven in city be x and driven in highway be y.

Now given that the mileage in city is 46 miles per gallon and in highway same is 51 miles per gallon.

The car is driven 621 miles in 13 gallon.

So suitable system of linear equations in two variables to solve this is,

x+y = 621 ……(1)

x/46+y/51 = 13 …….(2)

From (2) we get,

51x+46y = 30498

5x+46(x+y) = 30498

5x+46*621 = 30498

5x = 30498-28566

5x = 1932

x = 386.4

So from (1) we get,

y = 621-x = 621-386.4 = 213.6

Hence the car drove 386.4 miles in city and 213.6 miles in highway.

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If the container's height is 20 cm , the amount of water that should be added to fill it completely is 1 liter .

In the question ,

it is given that

the base area of the rectangular container is = 200 cm²

the total height of the container = 20 cm

the height at which the water if filled = 15 cm

the height of water that is needed to be filled = 20 - 15 = 5cm

So , the volume of water to be added is = base area × height

= 200 × 5

= 1000 cm³

= 1 Liter            .... because 1000cm³ = 1 Liter

Therefore , If the container's height is 20 cm , the amount of water that should be added to fill it completely is 1 liter .

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Answer:

i = 7/2

ii = -7/3

Step-by-step explanation:

The line intersects one of the two axis when the vale of the other axis is 0

When x=0:

2y - 7 = 0

2y = 7

y = 7/2

When y = 0

-3x - 7 = 0

-3x = 7

x= -7/3

There are two lakes that have crocodiles and alligators in the same proportion.The two lakes are Lake Winnipeg and Lake Champlain.

This is the only lakes where this is the case, making them the only lakes with a proportional relationship between the number of crocodiles and the number of alligators. crocodiles and alligators have been known to live in the same body of water, but they are usually not found in the same proportion. In these two lakes, however, they are found in equal numbers.

Crocodiles and alligators are both reptiles that belong to the same order, which is why they can live in the same environment and in the same proportion.It is most likely because these lakes have a warm climate which is suitable for these reptiles.

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The given alternate possible way given in the question is not good as the sample does not follow the conditions of the definition of SRS in the study.

SRS is a group or sample size of "n" objects in a population of "n" objects in which all the possible samples would have equal chances to occur or happen.

In the alternate case, There 200 trees sample is taken from near the highway, that can have fewer chances to be infected or can have more infected.

The fact that the sample was not taken randomly and has not been selected in such a way that each tree has equal chances to happen.

Hence we get the required answer.

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There is a 0.990025 probability that this area won't experience a major earthquake in the next two years.

In the field of mathematics called probability theory, random occurrences are studied. The outcome of a random event can take any number of distinct shapes, but it cannot be anticipated before it occurs. The outcome is believed to have been decided by chance.

Given,

In a region where large earthquakes of magnitude 7 or higher have occurred about once every 200 years,

First, the likelihood of an earthquake with a magnitude of 7 or higher is 1/200 = 0.005.

The likelihood of there not being an earthquake is then requested, and it is 1-0.005 = 0.995.

The likelihood that there won't be an earthquake in two years is then

0.995 x 0.995, or.0990025.

The probability that we will not have a big earthquake in this region in the next two years is 0.990025.

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Answer:

a. 87 b. 9 c. 4

Step-by-step explanation:

The probability of a foot of male being between 10 and 12. 5 inches is 59%.

The z score of the distribution is found as-

z = (x - μ)/σ

In which,

μ = mean = (11)

σ = standard distribution (1.5)

The likelihood that a male's foot measures between 10 and 12. 5 inches.

P(10 < x < 12.5)

For x = 10

z = (10 - 11) / 1.5

z = -0.67

check the p-value fro z score table.

p (z = -0.67) = 0.2514

For x = 12.5

z = (1.5 - 11)/1.5

z = 1

p (z = 1) = 0.8413

P(10 < x < 12.5)  = 0.8413 - 0.2514

P(10 < x < 12.5)  = 0.5899

P(10 < x < 12.5)  = 58.99%

P(10 < x < 12.5)  = 59%.

Thus, the likelihood of a male's foot being between 10 and 12. 5 inches is 59%.

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The complete question is attached in figure.

Step-by-step explanation:

to create a vertical asymptote (a tangent of the curve in infinity) at x = n we define e.g.

f(x) = 1/(x - n)

the cost x gets to n, the much closer the function gets to 1/0 and infinity.

so, the part to get us the asymptote at x = -4 is

1/(x + 4)

the part to get us the asymptote at x = 2 is

1/(x - 2)

and the part that gives us a zero solution at x = 3 is

(x - 3)

because that is what the point (3, 0) is : when x = 3. then y = 0.

now we only need to multiply all 3 parts to combine them :

f(x) = 1/(x + 4) × 1/(x - 2) × (x - 3)

Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.

A mathematical assertion in which you use mathematical symbols to demonstrate that two sums are equal.

As per specified data-

Let 'x' be the number of weeks required to complete the amount.

The equation becomes.

378 = 15.75x

For the number of week required.

x = 378/15.75

x = 24

Thus, Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.

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The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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The translation T due to the transformation is (5,3)

Translation can be defined as movement in a straight line

Given the rule: (x,y) → (x + 3, y + 1) as seen in the image. That means  (x,y) translated to (x + 3, y + 1). This is what we use to solve this problem.

From the figure, the value of  (x, y) can be read i.e. (x, y) = (2,2)

Thus the translation will be:

(x,y) → (x + 3, y + 1)

(2,2) → (2 + 3, 2 + 1) = (5, 3)

Therefore, the  translation T of the transformation shown in the graph is (5, 3)

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Answer:

Step-by-step explanation:

I think this is the answer you were looking for but im not 100% sure

If we buy all the same type of folders, the maximum amount we can afford for an individual folder is $ 3.3

To buy : A notebook for = $ 3

number of folders required = 5

The amount of money we can spend is $ 10

The above mentioned problem is a problem of algebra because we would have to use a variable to find out the unknown value.

The individual folders price can be calculated by the equation

3x = 10

divide both sides by 3 and we will get

x = 3.3

Thus the individual folder prices we can afford is $ 3.3

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