The senior classes at Portland High School and Biddeford High School planned separate
trips to New York City. The senior class at Portland High School rented and filled 1 van
and 6 buses with 372 students. Biddeford High School rented and filled 4 vans and 12
buses with 780 students. Each van and each bus carried the same number of students. How
many students can a van carry? How many students can a bus carry?

As per the given function, the equation of tangent line is y - e = e(x -1)

The term tangent line in math referred as a function y=f(x) can be calculate the slope by taking derivative m=f′(x) then at a given point (x1,y1) equation of tangent line is given by the formula y−y1=m(x−x1)

Here we have given the expression y = eˣ/x

Now, we have to calculate the tangent line for the given function,

Let us consider, Slope of the tangent line is written as,

=> m = dy/dx

Now, we have written it as,

=> dy/dx = eˣ/x

then the equation is equate with the slope, then  we get,

=> m = eˣ/x

When we put the value of x as 1, then we get

=> m = e

Here we know that the point value is (1, e)

Therefore, the equation of the tangent line is written as,

=> y - e = e(x -1)

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The number of student tickets sold is 40 and the number of adult tickets sold is 60.

Define System of equations

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Each student ticket sells for = $4

Each adult ticket sells for = $8

Total tickets sale = 100

Revenue from the sale of 100 tickets = $640

Let, x = number of student tickets sold

and, y = number of adult tickets sold

so, let's form a equation

x + y = 100             ------(i)

4x + 8y = 640        -------(ii)

Rewrite eq(i),

x = 100 - y

Now, substitute x value in eq(ii)

4(100- y) + 8y = 640

400 - 4y + 8y = 640

4y = 640 - 400

y = 240 / 4

y = 60

Now, put y value in eq(i)

x + 60 = 100

x = 40

Hence, the number of student tickets sold is 40 and the number of adult tickets sold is 60.

Now, to solve graphically

Let's rewrite the eq(i) and eq(ii)

y = 100 - x

y = 80 - (1/2) x

Plot these lines on graph as mentioned below.

And, the solution is the point of intersection(40,60)

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The two solutions to the equation x² + 5x + 6 = 0 are x = -2 and x = 3. This means that when we substitute either of these values into the equation, the left-hand side of the equation will be equal to 0.

To find the roots of a quadratic equation, we need to set the equation equal to 0 and then solve for x. In this case, we have the equation x² + 5x + 6 = 0. we can use the quadratic formula. The quadratic formula states that the two solutions for x are given by x = (-b ± √(b² - 4ac))/2a. For our equation, this gives us x = (-5 ± √(5² - 4(1)(6)))/2(1). Once we simplify this, we get x = (-5 ± √(-19))/2. Since the square root of a negative number is not real, we can discard this solution. This leaves us with x = -2 and x = 3. This means that when we substitute either of these values into the equation, the left-hand side of the equation will be equal to 0.

x = (-5 ± √(5² - 4(1)(6)))/2(1)

= (-5 ± √(-19))/2

= (-5 ± i√19)/2

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Answer:

1:1

Step-by-step explanation:

Since the surface area of A is 4 times the surface area of B, and the volume of B is 125 times the volume of C, we can write the following proportion:

(surface area of A) / (surface area of B) = (volume of B) / (volume of C)

(height of A)^2 / (height of B)^2 = (height of B)^3 / (height of C)^3

We can then cross-multiply and simplify to find the ratio of the heights:

(height of A)^2 / (height of C)^2 = (height of B)^3 / (height of B)^3

(height of A)^2 = (height of C)^2

Therefore, the ratio of the height of A to the height of C is 1:1, or simply 1.

The expression 3x²y + xy² + 2x + 5 has in its entirety 4 term.

First let's define what algebraic expressions are.

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

The terms of an expression are identified by the fact that they are separated by means of an addition and subtraction operation:

As we can see the expression has addition operations so it has more than 1 term:

this expression has 4 terms.

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The resultant answer after solving the given equation by taking x as the subject is x = (12 + 3y)/2.

The concept of an equation in algebra is a mathematical statement that shows the equality of two mathematical equations.

For example, the equation 3x + 5 = 14 comprises the two equations 3x + 5 and 14, which are divided by the 'equal' sign.

So, we have the equation:

2x - 3y = 12

Now, solve the equation by taking x as the subject as follows:

2x - 3y = 12

2x = 12 + 3y

x = (12 + 3y)/2

Therefore, the resultant answer after solving the given equation by taking x as the subject is x = (12 + 3y)/2.

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Correct question:
How do you work out 2x - 3y = 12?

The inequality that represents the most no. of music played is,

C ≤ 4,  J ≤ 1 and 4C + 0.25C ≤ 12

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, the radio station plays at most 12 hours of music per day. Let C denotes classical music, J denotes jazz music, and 25% of 4 hours be 1 hour.

The inequality representing this situation is

C ≤ 4 and J ≤ 1.

4C + 0.25C ≤ 12.   (less than or equal to is at most)

4.25C ≤ 12.

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Answer:

(x=2, y=3) and (x=12, y=1/2)

Step-by-step explanation:

14 - 4[tex]\sqrt{6}[/tex] = ([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])^2

14 - 4[tex]\sqrt{6}[/tex] = ([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])

14 - 4[tex]\sqrt{6}[/tex] = [tex]\sqrt{x}[/tex]([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex]) - 2[tex]\sqrt{y}[/tex]([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])  ==> distribute ([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex]) to [tex]\sqrt{x}[/tex] and

                                                                           2[tex]\sqrt{y}[/tex]

14 - 4[tex]\sqrt{6}[/tex] = ([tex]\sqrt{x}[/tex] * [tex]\sqrt{x}[/tex]) - ([tex]\sqrt{x}[/tex] * 2[tex]\sqrt{y}[/tex]) - (2[tex]\sqrt{y}[/tex] * [tex]\sqrt{x}[/tex]) - (2[tex]\sqrt{y}[/tex] * (-2[tex]\sqrt{y}[/tex])) ==> use

                                                                                            distribution property

14 - 4[tex]\sqrt{6}[/tex] = (x) - (2[tex]\sqrt{xy}[/tex]) - (2[tex]\sqrt{xy}[/tex]) - (-4[tex]\sqrt{y}[/tex] *[tex]\sqrt{y}[/tex]) ==> simplify

14 - 4[tex]\sqrt{6}[/tex] = (x) - (4[tex]\sqrt{xy}[/tex]) - (-4y)

14 - 4[tex]\sqrt{6}[/tex] = (x) - (4[tex]\sqrt{xy}[/tex]) + 4y  ==> subtracting by a negative number is

                                               equivalent to adding by a positive number

14 - 4[tex]\sqrt{6}[/tex] = x + 4y - 4[tex]\sqrt{xy}[/tex]   ==> notice any similarities?

x + 4y = 14

[tex]\sqrt{xy}[/tex] =  [tex]\sqrt{6}[/tex]

xy=6  ==> solve for x

x = 6/y  ==> isolate x by dividing by y on both sides

6/y + 4y = 14  ==> plugin 6/y for x in x + 4y = 14

(6/y + 4y = 14) * y  ==> multiply the equation by y to remove fractions

6 + 4y^2 = 14y

4y^2 - 14y + 6 = 14y-14y

4y^2 - 14y + 6 = 0

2y^2 - 7y + 3 = 0  ==> divide both sides by 2 to simplify the equation

2y^2 - 1y - 6y + 3 = 0  ==> -1y - 6y = -7y

y(2y - 1) - 3(2y - 1) = 0  ==> factor the equation

(y - 3)(2y - 1) = 0

y - 3 = 0 ==> y=3

2y - 1 = 0 ==> 2y = 1  ==> y = 1/2

y=3: 3x = 6 ==> plugin 3 for y in xy = 6

x = 2 ==> divide both sides by 3

y=1/2: x/2 = 6 ==> plugin 1/2 for y in xy = 6

x = 12  ==> multiply both sides by 2

When y=3, x=2.  When y=1/2, x=12

Hence, the answers are (2, 3) and (12, 1/2).

The expression will be simplified as x + 4y + 4√x√y -14 + 4√6 = 0.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 14 - 4√6 = ( √x - 2√y)². The given expression will be simplified as below,

14 - 4√6 = ( √x - 2√y)²

14 - 4√6 = (√x )²  + (4√x√y) + 4(√y)²

14 - 4√6 = x + 4√x√y + 4y

x + 4√x√y + 4y -14 + 4√6 = 0

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Answer:

20/3 cups of milk

Step-by-step explanation:

Take 5/6 time 8 = 40/6 = 20/3

So, Jessica drinks 20/3 cups of milk after 8 days

Graphs and the correlation coefficients are mentioned below-

A scatter plot uses dots to represent values for two different numeric variables. There are three types of scatter plots or charts -

There are the three most important correlations as -

Given are the scatter plots and the associated correlation coefficient.

        [tex]$r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]

        r = correlation coefficient

        [tex]$x_{i}[/tex] = values of the x-variable in a sample

        [tex]$\bar x[/tex] = mean of the values of the x-variable

        [tex]$y_{i}[/tex] = values of the y-variable in a sample

 [tex]\bar y[/tex] = mean of the values of the y-variable

The graph and their corresponding values of [r] are mentioned below -

Therefore, graphs and the correlation coefficients are mentioned below-

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The median of the data set would be affected as the median points per game decreases. That is option C.

The median of a data set is defined as the value of a data set the is found in the middle of a data after it has been arranged in an ascending order.

The first number line plots points per game;

= 16, 17 ,18 ,19 ,20 ,21 = 18+19 = 37/2 = 18.5

The second number line plots points per game;

= 21, 22, 23, 24 = 22 + 23 = 45/2 = 22.5

The third number line plots points per game:

= 9 points through 35 points

= 22 as the median.

Therefore, the scores of the next two games led to a decrease in the median determined per game point.

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Answer:

C) 5.25s^2

Step-by-step explanation:

1. Multiply 1.5s x 3.5s = 5.25.

2) Because 1.5 has one s, and 3.5 has another s, these 2 s combine (s+s)=s^2. Meaning there is 2 s in the equation. s^2 happens when you multiply two numbers that each have an s. Multiplication in this problem is brought by the use of parenthesizes surrounding these 2 numbers.

Answer:

Step-by-step explanation:

If it is the greatest common factor then it would be 5 I think.

Step-by-step explanation:

first of all, remember for life :

the sum of all angles in a triangle is always 180°.

so, in this right-angled triangle we have therefore

180 = b + 90 + 71

b = 180 - 90 - 71 = 19°

and then regarding a and b :

the sum of all angles around a single point on one side of a line is also always 180°.

why ? because the line can be seen as the extended diameter of a circle, with that point being the center of the circle. and one side of the line is representing half of that circle. and a half-circle is 180°.

so,

a + b = 180

a + 19 = 180

a = 180 - 19 = 161°

FYI, the reason for the first principle (all angles in a triangle are together 180°) is also based on a half-circle concept : any right-angled triangle can be seen as inscribed into a half-circle, with the Hypotenuse (the baseline opposite of the 90° angle) being the diameter of the circle, and the center of the circle being the midpoint of the Hypotenuse.

The vertical asymptotes of the graph of f(x) = (2x² + 7x - 4)/(x² + 5x + 4) is x = -1

The equation of the function is given as

f(x) = 2x² + 7x - 4/x² + 5x + 4

Introduce bracket, to differentiate the numerator and the denominator

So, we have

f(x) = (2x² + 7x - 4)/(x² + 5x + 4)

Next, we plot the graph of the function

The asymptotes are the points on the graph is a line that acts as the limit of another line or curve

From the graph, we have the asymptotes to be

x = -1 and y = 2

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Complete question

What is the vertical asymptote of the graph of f X?

f(x) = 2x² + 7x - 4/x² + 5x + 4

Answer: 25 weeks

Step-by-step explanation:

Let W represent the number of weeks

Judy equation is

12W + 300

Cassie equation is

20W + 100

Now let's solve it! Our system of equation is

12W + 300 = 20W + 100

Subtract 300 from both sides

12W = 20W -200

Subtract 20W from both sides

-8W = -200

W = 25 weeks

So, it takes 25 weeks for Judy and Cassie to have the same amount saved.

Answer:

let judy = 300 + 12W

cassie = 100 + 20W

300 + 12W =  100 + 20W

300 - 100 = 20W - 12W

200 = 8W

W = 25

300 +  12(25) = 100 + 20(25)

300 + 300 = 100 + 500

600 = 600

Therefore, it will take 25 days for Judy and Cassie so that they have the same amount saved.

THE GRAPH IS IN THE PICTURE,line graph

Step-by-step explanation:

The trapezoid has 4 sides and 1 set of parallel

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Answer:

17.0

Step-by-step explanation:

pythag theorem is a^2 + b^2 = c^2

12^2 + 12^2 = c^2

144+144=288=c^2

[tex]\sqrt{288}[/tex]= 16.97056275

round to nearest tenth, 17.0

The mean and the median of the given data are 210 and 170.

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.

The four-hour service call costs

$30  + $40(4) = $90

(a) The given table summary details and finds the cost of the service cells

Statics      Hour of service call       cost of service call

Mean          4.5                                  30 + 40(4.5) = 210

Median       3.5                                  30 + 40 (3.5 = 170

SD               1.2                                  30 + 40 (1.2) = 78

TQR            2.0                                  30 + 40 (2.0) = 110

Minimum    0.5                                  30 + 40 (0.5) = 50

(b) The service call corresponding score is 1.50

z score = 138-4.5/1.2 = 113.75

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An equation that depicts a straight line on a graph is said to be linear line.

What is linear line?

Linear refers to a straight line. Straight-line graphs called linear graphs are used to show the relationship between two values. The single straight lines on this graph assist to represent a result. The phrase "linear" refers to a straight line and excludes the usage of curves, dots, bars, etc.

A linear line can include more than one variable. Linear lines with two variables, for example, are those that have two variables in them.

2x - 3 = 0 and 2y = 8 are few examples of linear lines.

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Answer:

okay he can make 62 packages with 1 bagel left over

Step-by-step explanation:

Answer:

Step-by-step explanation:

381/6 = number of packages = 63 packages

63 * 6 = 378; 381-378 = 3 bagels left over

No. The GCF of 6 and 35 is 1.

To determine the biggest factor that perfectly divides both 6 and 35, i.e. 1, we must factor each number separately (factors of 6 are 1, 2, 3, 6; while factors of 35 are 1, 5, 7, 35).

What is Factors of 35?

Factors of 35 are the list of integers that we can split evenly into 35. It has a total of 4 factors of which 35 is the biggest factor and the positive factors of 35 are 1, 5, 7 and 35. The Prime Factors of 35 are 1, 5, 7, 35 and its Factors in Pairs are (1, 35) and (5, 7).

Factors of 35: 1, 5, 7 and 35

Negative Factors of 35: -1, -5, -7 and -35

Prime Factors of 35: 5, 7

Prime Factorization of 35: 5 × 7 = 5 × 7

Sum of Factors of 35: 48

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Answer:

[tex]m=\frac{1}{2}[/tex]

Step-by-step explanation:

The average rate of change (m) for the given line segment can be found with

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Given the graph, the following values can be recorded:

[tex](x_1,y_1)=(-1,-5)\\(x_2,y_2)=(1,-4)[/tex]

So,

[tex]m=\frac{(-4)-(-5)}{(1)-(-1)}\\m=\frac{-4+5}{1+1}\\m=\frac{1}{2}[/tex]

This answer makes sense in both sign and scale with the given image.

Answer:

--------------------------------

The height of the tower is the leg of the isosceles right triangle, since one of angles is 45 degrees.

The horizontal distance from the to the point where you dropped your keys is same as the vertical distance, 156 meters, because it is the other leg of the triangle.

The outcome of the complex number given is 7i+8/10 in its most basic form. Option C

Complex numbers are referred to as the square root of negative numbers. For instance √-1 = i.

In this expression 'i" is a complex number.

Given the expression below;

-7+8i / 10i

Rationalise

-7+8i / 10i * 10i/10i

= 10i(-7+8i)/10(i²)

= -70i+18(-1)/10(-1)

= -70i - 18/-10

= 7i+1.8

Hence the result of the given complex number in its simplest form is 7i+8/10

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They are the three methods of mean -  Direct Method. Assumed Mean Method. Step-deviation Method.

What does the mode mean?

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

              A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                    Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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The level of a line's slope indicates its steepness, y = (2/3)x - 4 is the slope intercept form of the inequality 2x - 3y = 12.

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

The above equation is a standard straight-line equation, and we are asked to change it to slope-intercept form, which is given as y = mx + c. "m" denotes the slope of the line and "c" denotes its intercept.

Now, it is given that,

2x - 3y = 12

or, - 3y = 12 - 2x

or, 3y = 2x - 12

or y = (2/3)x - 4

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The complete question is as follows:

What is the slope intercept form of the inequality 2x - 3y = 12.  

The zero of the graph is x = -4

From the question, we have the following parameters that can be used in our computation:

Major points on the graph are (minus 4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).

Express the points, properly

So, we have the following representation

Major points on the graph are (-4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).

Write out the points

(-4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).

The zeros of the graph are the point where y = 0

In this case, the points are

(-4, 0)

So, we have

x = -4

Hence, the zero is x = -4

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Arthur Schlesinger Jr. introduced the term "judicial activism" in a January 1947 Fortune magazine article titled "The Supreme Court: 1947".

What is judicial activism?

Judicial activism is a judicial philosophy that is sometimes referred to as "legislating from the bench". It is an exercise of judicial review and generally refers to the willingness of a judge to strike down legislative or executive actions regarding constitutional issues. Judicial restraint is generally thought of as the opposite of judicial activism.[1]

Earlier in the january of 1947 ,Arthur Schlesinger Jr. introduced the term "judicial activism" .An article by Keenan Kmiec says that in its early usage, it was sometimes used with a positive connotation akin to the term "civil rights activist".

Thus , Arthur Schlesinger Jr. introduced the term "judicial activism" in a January 1947 Fortune magazine article titled "The Supreme Court: 1947".

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The quotient of 1065 ÷ 33 is [tex]32\ \frac{3}{11}[/tex] .

1065 ÷ 33 = 32.2727272727

Dividend = 1065

divisor = 33

quotient = 32

balance = 9

answer as a mixed number  [tex]32\ \frac{9}{33} = 32\ \frac{3}{11}[/tex]

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