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A Drama Club is planning a grand opening musical for the new auditorium! It can hold up to 1000 people. They plan on charging $6 for a student ticket (x) and $10 for an adult ticket (y). If they need to make $3500 to cover all of their expenses, answer the following:

a) Write an inequality to represent the number of tickets

b) Write an inequality to represent the amount of money brought in

c) Give ONE combination of student and adult ticket sales that would satisfy both inequalities

d) Give ONE combination of student and adult ticket sales that would satisfy ONE, but NOT both inequalities

Answer:

  6 inches

Step-by-step explanation:

You want to know the uniform width of border around a 3 ft square coffee table that would have an area of 7 square feet.

The area of the border is x feet wide by 3 feet long along each of the 4 sides, together with 4 corner squares that are x ft square.

  A = 7 = 4(3x +x²)

Completing the square, we have ...

  x² +3x +9/4 = 7/4 +9/4 . . . . . . divide by 4, add (3/2)² to both sides

  (x +3/2)² = 4 . . . . . . . . . . . . simplify

  x +3/2 = √4 = 2 . . . . . . square root

  x = 1/2 . . . . . . . . . foot

The width of the border should be 6 inches.

The rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

To find the rational roots of the polynomial, we can use the Rational Root Theorem. This theorem states that if a polynomial of the form a_n*x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 has a rational root, then that root must be of the form p/q, where p is a divisor of a_0 and q is a divisor of a_n.

In this case, the polynomial is

f(x) = 20x^4 - 8x^3 - x^2 + 12x,

so a_0 = 12 and a_4 = 20. The divisors of 12 are 1, 2, 3, 4, 6, and 12. The divisors of 20 are 1, 2, 4, 5, 10, and 20. Therefore, the possible rational roots of the polynomial are

p/q = +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

We can then test each of these values to see if they are actually roots of the polynomial. If a value is a root, then substituting it into the polynomial will result in a value of 0.

Therefore, the rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

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This theorem states that if a polynomial of the form a_n*x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 has a rational root, then that root must be of the form p/q, where p is a divisor of a_0 and q is a divisor of a_n.

f(x) = 20x^4 - 8x^3 - x^2 + 12x,

p/q = +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

Therefore, the rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

Answer:

15/8

Step-by-step explanation:

The ratio is 45:24

45/24 simplify by 3

15/8

So, the ratio in simplest form is 15/8

3x + 2y = 5; 2x - 3y = 7. Hence, the given lines are intersecting. So, the given pair of linear equations has exactly one solution and therefore it is consistent.

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

If a system has no solution, it is said to be inconsistent . Represent parallel lines.

if Both line slope are same and parallel to each other.

So,  no solution

System is  inconsistent.

if Both equation represent the same line. So, infinite many solution.

System is consistent.

if Both lines are parallel. So, no solution.

System is inconsistent.

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Using trigonometric ratio, the height of the building is 72 feet

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

In this question, we need to use trigonometric ratio to find the height of the building.

Using tangent of the angle;

tan θ = opposite / adjacent

tan 45 = x / 52

x = 52tan45

x = 52

From the top of the building to the window level of the other building, the distance is 52 feet.

The height of the building = 52 + 20 = 72 feet

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Answer:

29

Step-by-step explanation:

You have 1,500 Kilometers and 32 15- kilometer races.

Step 1: Divide 1,500 by 15

step 2: Multiply the answer by 10

step 3:  

To find the quotient of a polynomial, first divide the polynomial by the divisor. Then use polynomial long division to divide the polynomial by the divisor. The quotient is the result of the polynomial long division.

1. Identify the polynomial to be divided and the divisor.

2. Divide the highest degree term of the polynomial by the divisor.

3. Multiply the divisor by the result from the previous step and subtract this from the polynomial.

4. Bring down the next term in the polynomial.

5. Repeat steps 2-4 until all terms in the polynomial have been divided.

6. The result is the quotient (the answer) of the polynomial division.

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Answer:

2

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

since there are 7 numbers, divide it by 2. Then you will get 3 remainder 1. Now, count 3 numbers from the first number and the very next number will be your median.

Answer:

B - 50

Step-by-step explanation:

the exterior angle is 105, and as it's on a straight line, the interior angle is 180-105=75

75+55=130

angles in a triangle are 180

180-130=50

Answer:50 degrees

Step-by-step explanation: The 105degrees angle forms a supplementary angle with the missing degrees in the triangle

so the missing value which is not requested is 180degrees-105 degrees=75 degrees

No we have two angles inside the triangle. We can now work out the missing angle for x

We know that a triangle adds up to 180 degrees

So x=180-55-75=50 degrees as the answer

Answer:

yes

Step-by-step explanation:

We require both to ascertain whether the findings are independent, this criterion is applied.

Statistics frequently employs the binomial distribution as a discrete distribution. When compared to a binomial distribution, the normal distribution is continuous. The chance for 'x' success of an investigation in 'n' trials is represented by the binomial distribution.

As per the given information in the question,

The normal distribution can be used to approximate the binomial distribution. The situation when performing a normal approximation is as follows:

np ≥ 10 and,

np(1 - p) ≥ 10

This criterion is used to determine whether the results are independent.

We are aware that when n and p are combined, the results are independent.

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The solution of the given system of equation is (3, 2).

In the given question we have to find the solution to the system of equations:

y = 4x − 10 and y = 2

We can solve the system of equation using the substitution method.

In substitution method we have to put the the value of one variable from one equation to the other equation.

We have to equations:

y = 4x − 10........................(1)

y = 2...................................(2)

Now putting the value of y from the equation 2 in equation 1

2 = 4x − 10

Add 10 on both side, we get

4x = 12

Divide by 4 on both side, we get

x = 3

Now putting the value of x in equation 1

y = 4(3) − 10

y = 12 − 10

y = 2

Hence, the solution of the given system of equation is (3, 2).

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The right question is:

What is the solution to the system of equations y = 4x − 10 and y = 2?

Answer:

y= -1/3x+7

i graphed it so it should be right

The phone's cost that varies directly with time are given as follows:

Both Mark and Nikiya.

The variation of the functions can have two classifications, given as follows:

Mark's cost starts at (0, 20) and goes through (3, 40), meaning that when the input increases from zero to 3, the output increases from 20 to 40, hence it has a direct variation.

Nikiya's cost starts at (0, 0) and goes through (2, 30), meaning that when the input increases from zero to 2, the output increases from 0 to 30, hence it has a direct variation.

The problem asks for whom's function varies directly with time.

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Answer:

Based on the graph shown to the right, whose phone cost varies directly with the amount of time spent talking?  

✔ Nikiya’s only

Mark’s cost does not vary directly with time spent talking because

✔ the cost of 0 hours is not 0 dollars

For Nikiya’s plan, the value of the constant of variation is

15,

which represents Nikiya’s

✔ cost per hour

Step-by-step explanation:

Hope this helps :)

The solution of the linear equations 2x + y = 8 and y = 3x - 2 will be (2, 4).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

2x + y = 8             ...1

y = 3x - 2             ...2

From equations 1 and 2, then the value of the variable 'x' is calculated as,

2x + 3x - 2 = 8

5x = 10

x = 2

Then the value of the variable 'y' will be calculated as,

y = 3(2) - 2

y = 6 - 2

y = 4

The solution of the linear equations 2x + y = 8 and y = 3x - 2 will be (2, 4).

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Answer:

y=(2/3) x+7

Step-by-step explanation:

2/3 is the slope which would be parallel

There are nine numbers in this set, so the median is the fifth number. The fifth number in this set is 14, so the median is 14.

The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 13, 16, 12, 14, 19, 12, 14, 13, 14. When we order this set from least to greatest, we get 12, 12, 13, 13, 14, 14, 14, 16, 19. There are nine numbers in this set, so the median is the fifth number. The fifth number in this set is 14, so the median is 14.

To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are nine numbers in the set, so the median is the middle number.

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The surface area of the soccer ball to the nearest square centimeter is 744.68 square centimeters .

Given :

The volume of a soccer ball is 1,930. 75 cubic centimeters .

we know that ,

shape of soccer ball is same as the sphere

Volume of sphere = 4 / 3 * pi * r^3

1930.75 = 4 / 3 * 3.14 * r^3

1930.75 = 4.18 * r^3

r^3 = 1930.75 / 4.18

= 462

r = 7.7 cm

Surface area  of soccer ball = 4 * pi * r^2

= 4 * 3.14 * 7.7^2

= 12.56 * 59.29

= 744.68 square centimeters

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If in the past month Kaylynn rented one video game in for DVDs. the total amount that Kaitlyn spent on video game and DVD rentals in the past month. is : $7.60.

We would have to make use of this formula to find the total amount that Kaitlyn spent on video game and DVD rentals in the past month.

Total amount = (Number of video game × Video game rental price ) + Rental price for DVD

Let plug in the formula

Total amount = (1 × $3.30) + $4.30

Total amount = $3.30 + $4.30

Total amount = $7.60

Therefore we can conclude that the total amount is $7.60.

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Answer:

64

Step-by-step explanation:

What is the median of the data 46 64 87?

Median: center most value when values are arranged in numerical order so:

46 , 64 , 87

The percent that the average score on the test increased during the two months is 12.5%.

It should be noted that mean simply means the average of a set of numbers that are given. In this case, the average test score of RSM students in September increased by 10%. In October it increased by another 15%..

The average of the increase will be:

= (10% + 15%) / 2

= 25% / 2

= 12.5%

The average is 12.5%.

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A dilation is a type of transformation causes the image to be larger or smaller than the pre-image.

A dilation is a type of transformation that changes the size of a figure without changing its shape. Dilations can make a figure larger or smaller.

In a dilation, the original figure is called the preimage. The dilated figure is called the image. Figures are dilated from a fixed point, called the center of dilation.Dilations also scale all sides of a figure by the same factor. As a result, dilations preserve angle measures and the ratio between corresponding parts.When dilating a figure, the different parts of the figure are multiplied by the scale factor.

In a dilation, the scale factor refers to the ratio between the corresponding sides of the preimage and the image. Therefore, the scale factor, k, can be calculated by dividing the length of one part in the image with the corresponding part in the preimage. The length of the preimage part should always be in the denominator as it belongs to the original figure.

A dilation is a type of transformation causes the image to be larger or smaller than the pre-image.

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Answer: -6

Step-by-step explanation:

If x:(x+3) = 2:3, we can set up the following equation:

x / (x+3) = 2/3

Next, we can multiply both sides of the equation by 3 to get rid of the fraction on the right side:

3 * (x / (x+3)) = 3 * (2/3)

This gives us:

x / (x+3) = 2

Finally, we can multiply both sides of the equation by (x+3) to get rid of the fraction on the left side:

x = 2 * (x+3)

We can then solve for x by rearranging the terms on the right side of the equation:

x = 2x + 6

Subtracting 2x from both sides gives us:

x - 2x = 6

This simplifies to:

-x = 6

Finally, we can divide both sides of the equation by -1 to solve for x:

x = -6

Therefore, x = -6.

Answer:

m = -3/5

Step-by-step explanation:

The slope is rise/run or (y2 - y1) / (x2 - x1)

We see the y increase by 3 and the x decrease by 5, so the slope is

-3/5

So, m = -3/5

__________________________________________________________

Hello! In this question, we are going to find the slope of the line with the coordinates given to us in the question.

__________________________________________________________

Explanation:

In the question, we were given the points:

In order to find the slope of the line, we will use the slope formula:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

We will plug our coordinates into the equation and solve.

__________________________________________________________

Solve:

Plug in the coordinates into the equation and solve.

[tex]m=\frac{-3-(-6)}{2-7} \\\\m=\frac{-3+6}{2-7} \\\\m=\frac{3}{2-7} \\\\m=\frac{3}{-5}\\\\\boxed{m=-\frac{3}{5}}[/tex]
Therefore, our slope for the given coordinates would be [tex]-\frac{3}{5}[/tex]

__________________________________________________________

Answer:

[tex]\boxed{m=-\frac{3}{5}}[/tex]

__________________________________________________________

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The roots of the quadratic equation 2x² + 5x - 2 = 0 are -2.7 and 1.3.

The quadratic equation is 2x² + 5x - 2 = 0.

We can solve this equation using the Quadratic Formula:

x = [-b ± Â√(b² - 4ac)] / 2a

Where a = 2, b = 5, and c = -2.

Substituting these values into the formula, we get:

x = [-5 ± Â√(5² - 4(2)(-2))] / 2(2)

x = [-5 ± Â√41] / 4

x = [-5 ± Â√41] / 4

x = [-5 ± 6.4] / 4

x = -2.7 or 1.3

Therefore, the roots of the quadratic equation 2x² + 5x - 2 = 0 are -2.7 and 1.3.

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The value of  ZLMN is 58.

What is bisects?

Bisection in geometry is the division of an object into two equal or congruent halves, typically by a line, which is subsequently referred to as a bisector. The segment bisector and the angle bisector are the two forms of bisectors that are most frequently used. 

LMO+NMO = LMN,

x+34 + NMO = 6x-28

But, MO bisects LMN, so LMO=NMO

x+34 + x+34 = 6x-28

2x+68 = 6x-28

4x = 96

x = 24

That would makem it

24 + 34 =58 T NMO = 6(24)-28

58 + nmo = 144 - 28 = 119

116- 58 = 58

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Python's Transform function returns a self-produced data frame with transformed values after applying the function specified in its parameter. This data frame has the same length as the passed data frame.

Now, According to the question:

Python's Transform function returns a self-produced data frame with transformed values after applying the function specified in its parameter. This data frame has the same length as the passed data frame.

What does transform () do?

The transform CSS property lets you rotate, scale, skew, or translate an element. It modifies the coordinate space of the CSS visual formatting model.

The transform() function is used to call function on self producing a Series with transformed values and that has the same axis length as self. Function to use for transforming the data.

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Answer:

[tex]y=-3x+7[/tex]

Step-by-step explanation:

[tex]=\frac{4-1}{1-2}=-3 \\ \\ y-4=-3(x-1) \\ \\ y-4=-3x+3 \\ \\ y=3x+7[/tex]