Differentiate. 6x y = 7 - cot(x)

Number of At-the-Door tickets Anna needs to sell to make her goal = 100

Anna is selling pre-sale and at-the-door tickets.

Let 'x' be the number of pre-sale tickets and 'y' be the number of at-the-door tickets.

Price of a pre-sale ticket = $10

Price of an at-the-door ticket = $20

Total price to be raised = $5000

So the equation corresponding is 10x+20y = 5000-----------(1)

Total number of people the venue can hold = 400

Thus the next equation is x+ y = 400---------(2)

From the graph the line with points (0,250) and (500,0) represent the equation (1) since 10 x 0 + 20 x 250 = 5000 and 10 x 500 + 20 x 0 = 5000.

The line with points (0,400) and (400,0) represent the equation (2) as 0+400 = 400 and 400+0 = 400.

So to find x and y we need to solve equations (1) and (2).

10 x (2) ⇒ 10x+10y = 4000-------(3)

Now subtract (3) from (1)

⇒ 10y = 1000

⇒ y = 100

Hence the number of At-the-Door tickets Anna needs to sell to make her goal = 100

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Answer:

16

Step-by-step explanation:

4x3=12 tins of white paint

12+4=16 total tins

The total number of tins used by the Peony will be 16.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that Peony mixes red paint and white paint in a ratio of 1:3 She uses four tins of red paint.

The Number of red tins,

R = 4 x 1 = 4

The number of white tins,

W = 4 x 3 = 12

Total number of tins,

T = R +W

T = 4 + 12

T = 16

Therefore, the total number of tins used by the Peony will be 16.

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Answer:

2nd option

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here g(x) = \(\sqrt{x}\) + 1

The base graph f(x) has been shifted up 1 unit

Answer:

w`16

Step-by-step explanation:

I think it right

Yes, the function g(x) is continuous at x= 2.
To demonstrate this, we will use the definition of continuity. A function is continuous at x=a if ()=() and ′() exists and is finite.

For g(x) we can see that (2)=() is true because for x = 2, g(2) = 2*2-2 = 2 which is the same as the value of g(x) for any x (1/2x + 1 for x ≤ 2 and 2x -2 for x > 2).
We will now check if ′(2) exists and is finite. To do this, we will calculate the limit of g'(x) as x approaches 2.
g'(x) = {-1/2 for x ≤ 2, 2 for x > 2}
The limit of g'(x) as x approaches 2 is:
lim g'(x) = lim (2) = 2
Since the limit of g'(x) is finite, ′(2) exists and is finite.
Therefore, the function g(x) is continuous at x= 2.

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Answer:

-3x + 4 = 2

just find x

Step-by-step explanation:

x = ⅔

An order for a computer can specify any one of four memory sizes, any one of three types of displays, any one of four sizes of a hard disk, and can either include or not include a pen tablet. Therefore, 96 different systems can be ordered.

How many different systems can be ordered? In order to answer the given question, we need to calculate the total number of different systems that can be ordered. We can do so by multiplying the number of options for each category.

Let's assume the given options for each category:

Memory sizes:

4Types of displays:

3Sizes of a hard disk:

4Pen tablet (yes or no): 2

Now, the total number of different systems that can be ordered is:

4 x 3 x 4 x 2

= 96

Therefore, 96 different systems can be ordered.

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a) A nonzero element X in W is:

X = [ -10  -4 ]
       [   8    6 ]

b) The matrix Y is in V because it's a symmetric 2x2 matrix, but it's not in W since it can't be formed by any linear combination of matrix A.

a. To find a nonzero element X in W, we need to find a linear combination of the given matrix in the span of W. Let's denote the given matrix as A:

A = [ -5  -2 ]
       [  4    3 ]

Since W = span{A}, a linear combination of A would be:

X = k * A

where k is any scalar value. Let's choose k = 2:

X = 2 * A = [ -10  -4 ]
                [   8    6 ]

So, a nonzero element X in W is:

X = [ -10  -4 ]
       [   8    6 ]

b. To find an element Y in V (the vector space of symmetric 2x2 matrices) that is not in W, we need a matrix that cannot be formed by any linear combination of the given matrix A.

A symmetric 2x2 matrix has the form:

Y = [ a  b ]
       [ b  c ]

Let's choose a symmetric matrix that doesn't have the same pattern as A. For example:

Y = [ 1  2 ]
       [ 2  1 ]

This matrix Y is in V because it's a symmetric 2x2 matrix, but it's not in W since it can't be formed by any linear combination of matrix A.

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The regression equation for the given data set is y = -0.51x + 100.12.

To find the regression equation, we need to first calculate the slope and intercept of the regression line. Using the formula for slope (b) and intercept (a) of the regression line, we get:

b = r(Sy/Sx)

a = y-bar - b(x-bar)

where r is the correlation coefficient, Sy and Sx are the standard deviations of y and x respectively, and y-bar and x-bar are the means of y and x respectively.

Using the given data, we can calculate the means, standard deviations, and correlation coefficient. Then, we can substitute these values into the formulas to get the regression equation.

After calculating, we get the equation y = -0.51x + 100.12. This equation represents the line of best fit for the given data, which can be used to predict the value of y for any given value of x.

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The size  of square tablecloth needed to cover the entire square tabletop is 25 ft^2 (Option B).

To determine the size of the tablecloth needed to cover a square tabletop with a perimeter of 20 feet, we will first find the side length of the square and then calculate the area.

Step 1: Determine the side length of the square.
Since the perimeter of a square is equal to 4 times its side length (P = 4s), we can find the side length by dividing the perimeter by 4.
Side length (s) = Perimeter (P) / 4 = 20 ft / 4 = 5 ft

Step 2: Calculate the area of the square.
The area of a square is equal to the side length squared (A = s^2).
Area (A) = Side length (s) ^ 2 = 5 ft ^ 2 = 25 ft^2

So, the size of the tablecloth needed to cover the entire square tabletop is 25 ft^2 (Option B).

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Step-by-step explanation:

1. 5+2+3=5+(2+3) 2. 9a is equivalent to 11a-2a 3. 7a + 04 - 2a is equivalent to 7a + -2a + 4 4. 8a-(8a-8) is equivalent or = to 8.

Answer:

2x^(3) - 4x^(2) - 4x - 4.

Step-by-step explanation:

2x^(3)-3x^(2)-3x^(2)+2x^(2)-4x-9

Bring like terms together:

= 2x^(3) - 3x^(2) - 3x^(2) + 2x^(2) - 4x + 5 - 9

Now simplify:

= 2x^(3) - 4x^(2) - 4x - 4.

Answer:

\(2x^3-4x^2-4x-4\)

Step-by-step explanation:

Subtract the numbers

\(2x^3-3x^2+5-3x^2+2x^2-4x-9\)

\(2^3-3^2-4-3^2+2^2-4\)

Combine like terms

\(2x^3-3x^2-4-3x^2+2x^2-4x\)

\(2^3-4^2-4-4\)

Rearrange terms

\(2x^3-4x^2-4-4x\)

\(2^3-4^2-4-4\)

Solution:

\(2x^3-4x^2-4x-4\)

Answer:

C: 1/2.

Step-by-step explanation:

the answer is 1/2 because I just took it and got it right.

Answer:

-2a

Step-by-step explanation:

Option C represents a modified Hardy-Weinberg equation that incorporates the effects of natural selection on a population. The equation is given as:

$(p-3s)^2 + 2(p-s)q + q^2 = 1$

In this equation, various terms are included to express the impact of natural selection. Let's break down the equation and understand its components.

$p$ represents the frequency of the dominant allele in the population, while $q$ represents the frequency of the recessive allele. These frequencies are determined based on the initial allele frequencies in the population.

The term $(p-3s)^2$ represents the expected frequency of the homozygous dominant genotype in the next generation. The factor $3s$ denotes the selection coefficient, where $s$ represents the frequency of homozygous recessive individuals who do not survive due to natural selection. By subtracting $3s$ from $p$, we account for the reduction in the frequency of the dominant allele due to selection.

The term $2(p-s)q$ represents the expected frequency of the heterozygous genotype in the next generation. This term incorporates both the initial frequency of the heterozygous individuals, represented by $(p-s)$, as well as the transmission of alleles through reproduction, given by $q$. The factor of 2 accounts for the two possible combinations of alleles in the heterozygous genotype.

Finally, $q^2$ represents the expected frequency of the homozygous recessive genotype in the next generation. This term considers the transmission of the recessive allele, represented by $q$, and its squared value accounts for the homozygous recessive genotype.

The equation is set equal to 1, as the frequencies of all genotypes should sum to 1 in a population.

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The missing terms in the given factorized expression are:

3x²y + 12xy² + 9xy = 3xy ( x + 4y + 3 )

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

We have,

_ x²y + _ y² + 9 _ = 3x _ ( _ + 4y + _ )

We need to fill the boxes and make sure that both sides are equal.

We will remove the bracket on the right side.

i.e 3x _ _ + 12xy_ + 3x_ _

Now,

_ x²y + _ y² + 9 _ = 3x _ _ + 12xy_ + 3x_ _

We will make,

_ x²y  and 3x _ _ equal.

_ y²  and 12xy_ equal.

9 _  and + 3x_ _ equal.

So,

(3)x²y = 3x (x)(y)

(12x)y² = 12xy(y)

9 (xy) = 3x(y)(3)

Thus the missing terms in the given factorized expression are:

3x²y + 12xy² + 9xy = 3xy ( x + 4y + 3 )

3x²y + 12xy² + 9xy = 3x²y + 12xy² + 9xy

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\(43\)

Answer:

The slope of the parallel line to the given line is \(-\frac{1}{4}\)

The equation of the parallel line to the given line and passes through the given point is y + 4 =  \(-\frac{1}{4}\) (x + 2)

The y-intercept of the parallel line to the given line and passes through the given point is  \(-\frac{9}{2}\)

Step-by-step explanation:

In the given figure

∵ The given line passes through points (2, 6) and (-6, 8)

∴ x1 = 2 and y1 = 6

∴ x2 = -6 and y2 = 8

→ Substitute them in the rule of the slope above to find it

∵ m = \(\frac{8-6}{-6-2}\) = \(\frac{2}{-8}\) = \(-\frac{1}{4}\)

∴ The slope of the given line is \(-\frac{1}{4}\)  

∵ Parallel lines have the same slopes

∴ The slope of the parallel line to the given line is \(-\frac{1}{4}\)

∵ The parallel line passes through the point (-2, -4)

∴ x1 = -2 and y1 = -4

∵ m = \(-\frac{1}{4}\)

→ Substitute them in the point-slope form above

∵ y - (-4) = \(-\frac{1}{4}\) (x - (-2))

∴ y + 4 =  \(-\frac{1}{4}\) (x + 2)

∴ The equation of the parallel line to the given line and passes through

   the given point is y + 4 =  \(-\frac{1}{4}\) (x + 2)

∵ m = \(-\frac{1}{4}\)

→ Substitute it in the slope-intercept form above

∴ y =  \(-\frac{1}{4}\) x + b

→ To find b substitute x by -2 and y by -4 (coordinates the given point)

∵ -4 = \(-\frac{1}{4}\)(-2) + b

∴ -4 = \(\frac{1}{2}\) + b

→ Subtract  \(\frac{1}{2}\)  from both sides

∴ \(-\frac{9}{2}\) = b

∵ b is the y-intercept

∴ The y-intercept of the parallel line to the given line and passes

   through the given point is  \(-\frac{9}{2}\)

Answer:

What is the slope of the line that is parallel to the given line and passes through the given point?

✔ –1/4

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point?

✔ y + 4 = –1/4(x + 2)

What is the y-intercept of the line that is parallel to the given line and passes through the given point?

✔ –9/2

Step-by-step explanation:

The function is f(x) = 15x + 25 and you would have 6 services if you were charged $25

We know that the hair salon charges a fixed rate of $25.00 for a haircut and then an additional $15 for any other services, therefore:

Let x = number of services, then we can obtain the function as:

f(x) = 15x + 25 (function)

when we further solve the function, we get the answer for how many services one would have if we were charged $25,

f(x) = 15x + 25

115 = 15x + 25

90 = 15x

6 = x

Now, we know that the function is f(x) = 15x + 25 and you would have 6 services if you were charged $25

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The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

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Answer:

Skew (option d).

Step-by-step explanation:

Skew lines are the lines that do not intersect with each other. These lines exist in different planes and hence do not intersect each other and they are also not parallel. For skew lines to exist,  3 -d planes are required.

Here, the lines e and c are skew lines because they do not intersect each other and are lying on different panes. They are also skew line because the planes are co-planer,

Hence, the lines e and c are skew lines.

When lines are not parallel, and they do not intersect, such lines are said to be skewed.

Line AC and RS are skew.

From the diagram, we have two planes.

Line AC is on plane x, while line RS is on plane y

Plane x and plane y are not parallel;

So lines AC and RS are not parallel.

Also, both lines are not parallel.

Using the condition of skewness stated above, we can conclude that line AC and RS are skew.

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Answer:

200 miles

Step-by-step explanation:

1 3/4 can be turned into a decimal as 1.75

Now let’s create fractions to prepare for cross multiplication

1.75/50=7/x

1.75x=7(50)

1.75x=350

/1.75.  /1.75

x=200

200 miles

hopes this helps please mark brainliest

Answer:

3x²+13x-30

Step-by-step explanation:

3x×x =3x²

3x×6= 18x

-5×x = -5x

-5×6=-30

Connect them together to form:

3x²+13x-30

(I got the 13x by doing 18x-5x)

The perimeter of the Christian's sandbox is 24 feet.

The given two quadrialterals are similar

Let us find the remaining lengths of Christian's sandbox

By proportional equation

36/8=18/x=27/y=18/z

4.5=18/x=27/y=18/z

x=18/4.5 = 4

y=27/4.5 = 6

z=4

The perimeter is sum of all the sides

So perimeter of Christian's sandbox is 8+6+4+4

24 feet

Hence, the perimeter of the Christian's sandbox is 24 feet.

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i. For the first subproblem, there are 111 factorial (111!) ways that 111 guests can arrive at the party if they arrive one at a time.

ii. To answer the second subproblem, there are 4 x 12 x 1 = 48 ways to be dealt blackjack.

iii. For the third subproblem, there are 12 ways to be dealt two cards such that the first card is a spade and the second card is a face card.

iv. For the fourth subproblem, there are 2 x 4 x 12 = 96 ways to pick three cards such that the first card is a spade, the second card is a one-eyed jack, and the third card is a face card.

v. Lastly, for the fifth subproblem, the number of ways Bilbo's 111 guests can arrive at the party if they arrive one at a time is 111!.

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The slope of a line would be -6 which is perpendicular to the line whose equation is 2x+12y=−192.

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

We have to determine the slope of a line perpendicular to the line whose equation 2x + 12y = −192.

First, we have to find the slope of the given line

The equation of the line which is given as

2x + 12y = −192

12y = −192 - 2x

Divided by 12 both sides of the above equation to get the slope-intercept form

y = - (1/6)x - 16

Here the slope of the line (m) = -1/6

So the slope of the line perpendicular to the line will be: 1/m = 1/(-1/6) = - 6.

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Answer:

  D(3.4, 20.8)

Step-by-step explanation:

Given points B(-2, 10) and C(8,7), you want the coordinates of point D such that BD has a slope of 2 and CD has a slope of -3.

The equation for the slope between two points is ...

  m = (y2 -y1)/(x2 -x1)

Using this formula and the given points, we can find D(x, y) to satisfy ...

  2 = (y -10)/(x +2)

  -3 = (y -7)/(x -8)

Putting each of these equations in general form, we have ...

  2(x +2) -(y -10) = 0

  2x -y +14 = 0

and

  -3(x -8) -(y -7) = 0

  3x +y -31 = 0

Adding the two equations eliminates the y-variable:

  (2x -y +14) +(3x +y -31) = 0

  5x -17 = 0 . . . . . . simplify

  x -3.4 = 0 . . . . . . divide by 5

  x = 3.4 . . . . . . . . . add 3.4

Substituting for x in the first equation gives ...

  2(3.4) -y +14 = 0

  y = 6.8 +14 = 20.8 . . . . add y

The point D has coordinates (3.4, 20.8).

__

Additional comment

The graph shows the equations of the lines written in point-slope form.