Find the coordinates of the midpoint of with endpoints K(–20, 3) and L(12, –2).

55 is the number of soda bottles the machine can make each minute.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, the graph shows the relationship between time and the number of soda bottles a machine can make. Use points ​(4​,220​) and ​(7​,385​)

Since this graph is a straight line graph and also it goes through the origin that means time is directly proportional to the number of soda can manufactures

To prove this theory

the ratio between cans to the time taken by machine = 220/4 = 385/7

Since the ratio is the same for two points.

Thus,

Soda machine makes in 4 hours = 220 cans

Soda machine makes in 1 hours = 220/4 = 55 cans

Therefore, the number of soda bottles the machine can make each minute is 55.

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Answer:

The function rule for this set of ordered pairs is y = 2x + 1.

This can be determined by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) can be calculated by using the formula:

m = (change in y) / (change in x)

For the ordered pair (1, 3) and (3, 7), we can see that change in x = 3 - 1 = 2 and change in y = 7 - 3 = 4, so m = 4/2 = 2.

Then, using any of the point we can find the b which is y-intercept. let's take the point (-2, -3) and substitute the values in the function y = 2x + b

-3 = 2(-2) + b

-3 = -4 + b

b = 1

So, the function rule is y = 2x + 1

The percent of the gas in the tank remaining is equals to the 53.6..

The capacity of Wilon's car's gas tank

= 15 gallons

The amount of gas in Wilon's car's tank

= 8.4 gallon

The amount of gas in tank used on a recent trip = 3.9 gallons

The remaining amount of gas in tank

= amount of gas in Wilon's car's tank before trip - amount of gas in tank used on a recent trip.

= 8.4 gallons - 3.9 gallons

= 4.5 gallons

Percent is calculated as the value diving by total value and then multiply with hundred. Now, the percent of the gas in the tank remaining = (4.5/8.4)× 100

=( 45/84)100

= 4500/84

= 53.57 ~ 53.6 %

Hence, the percent of the gas in the tank remaining is 53.6 .

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Complete question:

Wilon’ car hold 15 gallon of gaoline in it tank. Wilon had 8.4 gallon of gaoline in the tank. He used 3.9 gallon on a recent trip. What is the percent of the gas in the tank remaining?

The error is that the student did not distribute the -3 to the x and 2 inside the parentheses.

The correct answer is 3x - 6

Simplification of an algebraic expression is defined as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression.

The student's error is that the student did not distribute the -3 to the x and 2 inside the parentheses when simplifying the expression.

The correct simplification of the expression is:

-3(x + 2) + 6x = -3x - 6 + 6x = -3x + 6x - 6 = 3x - 6

Therefore, the student's answer is 3x + 2, but the correct answer is 3x - 6.

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The student made error when removing the bracket. The correct simplification of the expression is 3x - 6

We can spot the error of the student by carefully observing the student's answer. This is illustrated below:

-3(x + 2) + 6x = -3x + 2 + 6x = 3x + 2

From the student's work, we can see that the student made an error when removing the bracket.

We can correct the student's error by carefully removing the bracket as shown below:

-3(x + 2) + 6x

Remove bracket by multiplying through by -3

-3x - 6 + 6x

Rearrange by bring the numbers with x variables together

-3x + 6x - 6

3x - 6

Thus, the correct answer to the simplification is 3x - 6

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The experimental probability that a person selected at random is going to City C is 4/25.

Number of responses from destination A = 22

Number of responses from destination B = 40

Number of responses from destination C = 16

Number of responses from destination D = 14

Number of responses from destination E = 8

As we know, the formula of experimental probability is

Probability of an Event P(E) = Total Number of times an event occurs/Total number of trials.

Number of responses from destination C = 16

Total number of responses from all destinations = 100

∴ Probability of an Event P(C) = 16/100 = 4/25

--The given question is incorrect; the correct question is

"The table shows the results of a survey of 100 people selected at random at an airport. Find the experimental probability that a person selected at random is going to City C."--

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The solution to the given inequality expression is; x < 5

We want to solve the inequality expression;

8 - 4x > -12

Add 4x + 12 to both sides using addition property of equality to get;

8 - 4x + 4x + 12 > -12 + 4x + 12

20 > 4x

Divide both sides by 4 using division property of equality to get;

20/4 > 4x/4

x < 5

That expression is what we will have as our final solution to the inequality expression .

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The solution to the equation is described as follows:

The equation says that a number was divided by 5 and that 3 was then subtracted from the quotient, giving the result 2. So, working backward, first add 3 to 2, giving 5. Then multiply that result by 5, giving x = 25.

The equation for this problem is described as follows:

x/5 - 3 = 2.

We must isolate the variable x, hence the first step is adding 3 to 2, as follows:

x/5 = 2 + 3

x/5 = 5.

Then we apply cross multiplication, multiplying the result by 5, as follows:

x = 5(5)

x = 25.

Which is the solution to the equation.

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Answer:300 tires

Step-by-step explanation: I set it up like this 100:45

X : 135

Then I am trying to find x. I cross multiplied. (100 times 135) and (45 times x) which is 45x= 13500 then if you know simple algebra then you get x by itself so you divide 13500 and 45 which equals 300.

The length of string will be used to hang each pennant is 3.9 meters.

The term length in math is defined as the measurement or extent of something from end to end and it is used to identifying the size of an object or distance from one point to the other.

Here we have given that Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school.

And here we have also know that she needs 0. 65 meter of string for the banner and the same length string for each pennant.

the length of the string needed for 5 pennants is calculated as,

=> 0.65 x (5 + 1)

=> 3.9 meter.

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Answer:

????????????????????

Answer:

14sin(55) and

14cos(35)

Step-by-step explanation:

Greetings!!

just remember trigonometric ratios which are

[tex]sin = \frac{opposite}{hypotenus} \\ cos = \frac{adjecent}{hypotenus} \: and \\ tan = \frac{opposite}{hypotenus} [/tex]

following that substitute given values to solve for x.

[tex]sin55 = \frac{x}{14} [/tex]

solve for x

[tex]x = 14 \sin(55) [/tex]

And

[tex] \cos(35) = \frac{x}{14} [/tex]

solve for x

[tex]x = \cos(35) [/tex]

Hope it helps!!!

Answer:

a) the triangles are similar triangles because they are the same shape. The angles in both triangles have the same value.

b) The similarity ratio between the two triangles is 0.5, because the lengths of the sides of the triangle on the right are double the value of the lengths of the sides of the triangle on the left.

c) angle U = angle G. angle V = angle H. angle T = angle F.

UV/GH = VT/HF = TU/FG = 0.5

Answer:1, 3, 9, 27

Step-by-step explanation:

Answer: y=-2x-19

Step-by-step explanation:

First, you should arrange the equation in the form of y=mx+c (that is the standard form of this type of equation)

10x+5y=15

       5y=-10x+15

       [tex]\frac{5y}{5} =\frac{-10x}{5}+\frac{15}{5}[/tex]

         y=-2x+3 (now you got the equation in the simple form)

now you should substitute the given point (-10,1) into the simplified equation

y= 1 & x=-10

1=-2(-10)+c  (the y-intercept must be taken as c )

c= 1 - 20

c= -19

therefore the equation will be : y=-2x-19

it will be the same gradient as the other line for this line too as the lines are parallel, you should only find the y-intercept. The gradient of the other line will stay the same as long as they are parallel lines.

well, let's find the equation of the line through those points then, and let's see

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-6 }{0 +2} \implies \cfrac{ -6 }{ 2 } \implies - 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-2)}) \implies y = - 3 ( x +2) \\\\\\ y=-3x-6\implies \boxed{3x+y=-6} ~~ \ne ~~ 3x-y = 6[/tex]

When I run 5280 feet in 5.00 minutes my speed is 12 miles per hour

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this exercise is:

v = x /t

Where:

Information about the problem:

Applying the velocity formula, we get:

v = x /t

v = 5280 feet / 5 minutes

v = 1056 feet/ minutes

By converting the unit from feet to miles and from hours to minutes, we have:

1056 feet/ minutes * (1 miles / 5280 feet) * (60 minutes / 1 hour) = 12 miles/hour

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Answer:

66?

Step-by-step explanation:

18+18= 36

15+15= 30

30+36= 66

According to Isabella transactions, her present balance in bank statement is -$9.45

The term called transaction in math is defined as  a finalized agreement between a seller and a buyer for transferring goods, services, or financial assets in exchange for money

Here let us consider that Isabella's present balance be X.

According to the problem statements regarding her deposits, there is withdrawals, auto-payments, direct deposit and service charge are also done on the account.

Then those transaction values are calculated as,

=> (1/2)x - (1/3)x -(1/4)x +(1/10x) -$9.29 = x

Here by finding the LCM of common terms, then we get

=> (1/60)x - $9.29 = x

When we solve it for x, then we get the equation like the following,

=> 59x = -$9.29 × 60

=> 59x = -$557.4

Therefore the value of x is -$9.45.

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Answer

undefined

Step-by-step explanation:

Answer:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To find the equation of a line passing through two given points, we can use the slope-intercept form, and use the slope formula:

slope = (y2 - y1) / (x2 - x1)

Given the points (2, -4) and (2, -5), we can see that the x-coordinates are the same, which means that the line is a vertical line.

Since the line is vertical, the slope is undefined, and we can say the line can be represented by the equation x = 2

This is the equation of the line passing through the given points (2, -4) and (2, -5) in slope-intercept form.

The HCF of the numbers 114, 138 and 234 is 6.

The term HCF in math is also know as the greatest common factor or highest common factor of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder.

Here we have given the numbers 114, 138 and 234.

And we need to find the HCF of the numbers.

By using the prime factorization method, here we have identified the factors of the numbers, and it can be written as

The factors of 114 are: 1, 2, 3, 6, 19, 38, 57, 114

The factors of 138 are: 1, 2, 3, 6, 23, 46, 69, 138

The factors of 234 are: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234

While we looking into the given number we have identified that the the greatest common factor is 6.

Complete Question:

Find the HCF of the numbers 114, 138, and 234 by using the prime factorization method.

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The length of the base is 3.1 cm when you subtract 12.6 from btohs ides b is15.7.

There are two equal sides and two equal angles in an isosceles triangle. The word is a combination of the Greek words iso (same) and skelos (leg). Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.

Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.

The equal sides of an isosimple triangle are longer than the base's length.

We know that identical sides are greater, thus 6.3 is one of the identical sides in the perimiter=15.7 equation, which is 2a+b=15,7.

2a denotes the two identical sides: 2(6.3) + b = 15.7

The answer is base=3.1 cm when you subtract 12.6 from btohs ides b=15.7.

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Answer: It is equidistant from the segment's endpoints

Step-by-step explanation:  This can also be called "a locus of point" and this is now the perpendicular bisector theorem.

Answer:

150

Step-by-step explanation:

90/0.6 = 150

Check:

150*0.6 = 90

Then:

90 is 0.6 of 150

The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

        so,   fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

                fg(x)  = -x^4-4x^3

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The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

       so,   fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

              fg(x)  = -x^4-4x^3

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Answer:

Small jet seat capacity: 73

Large jet seat capacity = 90

Step-by-step explanation:

Let x be the number of seats on the small jet

Let y be the number of seats on the large jet

From the word description for last week:

Last week, she worked on flights on 1 small jet and 2 large jets, which could seat a total of 253 passengers

we can formulate the equation
1x + 2y = 253  .............(1)

For the week before:
The week before, she was assigned to flights on 5 small jets and 4 large jets, which could seat a total of 725 passengers

5x + 4y = 725 ...............(2)

Equation (1)  x 2 ==>
2x + 4y = 2(253)

2x + 4y = 506  ..............(3)

So our two equations are:

5x + 4y = 725 . .............(2)
2x + 4y = 506  ..............(3)

Equation (2) - Equation (3) will eliminate the y terms making it possible to solve for x
(5x + 4y) - (2x + 4y) = 725 - 506

5x + 4y - 2x - 4y = 219

5x -2x +4y - 4y = 219

3x = 219

x = 219/3

x = 73

Plugging this value back into equation (1): 1x + 2y = 253 we get
1(73) + 2y = 253

73 + 2y = 253

2y = 253 - 73

2y = 180

y = 180/2

y = 90

Answer
Small jet seat capacity: 73

Large jet seat capacity = 90

It should be noted that the rate will be gotten by dividing the distance by the time taken.

A rate in mathematics is a ratio that contrasts two distinct quantities with dissimilar units. Typically, a rate is defined as the ratio of two quantities expressed in different units. The first quantity is typically written as the numerator of a fraction, and the second quantity is written as the denominator

By reducing them to their simplest form, we can express the rate. By way of illustration, if a person walks 30 steps in 20 seconds, their walking speed is 30 steps/20 seconds, or 3 steps/2 seconds.

The information above was given as your information is incomplete. The table wasn't shown.

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There is a 0.17 percent chance that a student spent 4 hours in class.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. Probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

To determine the probability.

The number of students that has 5 hours is 6

The total number of students are 35.

P(5 hours) = 6/35

P(5 hours) = 0. 17

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Answer:

4x+6y = 46

Step-by-step explanation:

you just add by column

2x+2x

y+5y

9+37

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-6)}) \implies y +7= \cfrac{1}{3} (x +6) \\\\\\ y+7=\cfrac{1}{3}x+2\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-5 \end{array}}[/tex]

Answer:

I think it is y=1/3x -7

Step-by-step explanation:

Answer:

$62.50

Step-by-step explanation:

We multiply 0.25(25% as a decimal) by $250 to get $62.50.