Let G be the centroid of triangle ABC. If triangle ABG is an equilateral triangle with a side length of 2, then find the area of triangle ABC.

The answer is that the the equation for a cosecant function with vertical asymptotes found at x equals pi over 2 plus pi over 2 times n comma such that n is an integer is, 2 coscec 2x.

Since, Cosecant is one of the trigonometric ratios .

It is calculated as the ratio of the hypotenuse to the perpendicular of a right triangle.

It is also calculated as the reciprocal of the sine function.

Now, here if the vertical asymptotes is x = pi/2 + pi/2 (n).

This is not defined when n=0.

so, when x= pi/2,

sin 2x = sin x = 0

which means w =0 .

and we get the equation for cosecant function to be,

⇒ f(x) = 2 cosec 2x

since cosec x = 1/ sin x.

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The perimeter of the sector in terms of π is (7π+18) cm.

A sector is a shape that is bounded by an arc and two radius.

To calculate the perimeter of the sector, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

Step-by-step explanation:

It has a center at (3,5)  and r=4

Draw your center then go out 4 up, down, left, and right

Domain = [(3-4),(3+4)] = [-1, 7]    this is where the function exists for x

Range = [(5-4), (5+4)] = [1, 9]    this is where the function exists for y

The rational function r(x) with the given features is r(x) = 4(x + 9)(x - 4)²/(x - 3)(x + 5)(x + 2)

We use the given parameters to determine the possible function

So, we have

crosses the x-axis at -9

Factor = (x + 9)

touches the x-axis at 4

Factor = (x + 9)(x - 4)²

Vertical asymptote at x = 3 and at x = -5

Denominator = (x - 3)(x + 5)

A hole at x = -2

This means that the function is undefined at x = -2

So, we have

Denominator = (x - 3)(x + 5)(x + 2)

Horizontal asymptote at y = 4

So, the function becomes

r(x) = 4(x + 9)(x - 4)²/(x - 3)(x + 5)(x + 2)

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The answer of the given question based on the expression is , the value of the summation when m = 3 is 137.

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a set of values. It can be a simple combination of numbers and variables or a more complex combination involving mathematical operations like addition, subtraction, multiplication, division, exponents, and roots. Expressions can be used to represent a wide range of mathematical concepts, from simple arithmetic to complex functions and equations.

To evaluate the summation 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!), where m = 3, we substitute m = 3 and simplify:

1(1!)+2(2!) +3(3!) +4(4!) +3(3!)

= 1(1) + 2(2) + 3(6) + 4(24) + 3(6) (since n! = n(n-1)! for all positive integers n)

= 1 + 4 + 18 + 96 + 18

= 137

Therefore, the value of the summation when m = 3 is 137.

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To find f+g, we need to add f(x) and g(x):

f(x) + g(x) = (2x^(2) +5) + (1/2x)

f+g = 2x^(2) + (1/2)x + 5

To find f-g, we need to subtract g(x) from f(x):

f(x) - g(x) = (2x^(2) +5) - (1/2x)

f-g = 2x^(2) - (1/2)x + 5

To find fg, we need to multiply f(x) and g(x):

f(x) * g(x) = (2x^(2) +5) * (1/2x)

fg = x + (5/2)x^(-1)

To find f/g, we need to divide f(x) by g(x):

f(x) / g(x) = (2x^(2) +5) / (1/2x)

f/g = 4x + 10x^(-1)

y = a(x + 4)^2 + 12

where "a" is a constant that determines the shape of the parabola. To find the value of "a", we can use the y-intercept (0,-36):

-36 = a(0 + 4)^2 + 12

-36 = 16a + 12

-48 = 16a

a = -3

Therefore, the equation of the parabola is:

y = -3(x + 4)^2 + 12

To find the x-intercepts, we can set y = 0 and solve for x:

0 = -3(x + 4)^2 + 12

3(x + 4)^2 = 12

(x + 4)^2 = 4

x + 4 = ±2

x = -4 ± 2

So the x-intercepts are (-6,0) and (-2,0). Therefore, the answer is:

(-6,0), (-2,0)

The solution of the quadratic equation (x - 3)² - 24 = 25 is x = 10, -4.

Given that the quadratic equation is (x - 3)² - 24 = 25

Expanding the left side of the equation, we get:

(x - 3)² - 24 = 25

Simplifying the above equation, we get:

x² - 6x + 9 - 24 = 25

Solving by combining like terms, we get:

x²  - 6x - 40 = 0

We can solve for x by factoring the quadratic equation:

(x - 10)(x + 4) = 0

Therefore, x can be equal to 10 or -4.

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The y-intercept of the graph of this function is 5.

Given information:

The linear function passes through the points (0, 5) and (8, -2).

Here, we have to find the y-intercept.

For that, the definition of y-intercept is given as the point where the graph intersects the y-axis.

To find the y-intercept of the graph of this function, we need to identify,

the point where the graph intersects the y-axis.

The y-axis corresponds to the x-coordinate of 0.

Since the function passes through the point (0, 5), we know that the y-intercept is 5.

Therefore, the y-intercept of the graph of this function is 5.

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Evaluating the exponential equation we can see that after 5 years, the account has 2559.02

Here we need to use the formula:

A=P(1+r/n)^nt

Where P is the initial amount.

r is the percentage in decimal form, in this case 0.06

n is how many times it is compounded, in this case 4

t is the variable, in this case years.

Replacing all that we get:

A = 1900*(1 + 0.06/4)^(4t)

Now we want to evaluate this in t = 5, we will get:

A = 1900*(1 + 0.06/4)^(4*5)

A = 2559.02

That is the amount.

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The total number of beads which Lola use to make 13 bracelets and 8 necklaces is 1340 beads.

An expression will consists of one or more numbers along with one more operation. X + 1 is an example of an expression.

We will use this expression to calculate the number of beads. The number of beads will be: (number of bracelets x beads per bracelet) + (number of necklaces x beads per necklace)

Substituting the values, we get:

= (13 x 44) + (8 x 96)

= 572 + 768

= 1340 beads

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The cost of the 28 inches and 36 inches diagonal Smart TVs, based on the quadratic cost function are;

28 - inch diagonal; $134

36 - inch diagonal; $165

A quadratic function is a function of the form f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The cost of the Smart TV as a function of the diagonal length is C(d) = 0.322·d² - 16.776·d + 351.444

The above function indicates that the cost of a Smart TV that is 28 inches long is; C(28) = 0.322 × 28² - 16.776 × 28 + 351.444 ≈ 134

The cost of a Smart TV with a diagonal of 36 inches is therefore;

C(36) = 0.322 × 36² - 16.776 × 36 + 351.444 ≈ 165

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Since you cannot make a fraction of a round trip, you will need to make 5 round trips (back and forth) between Seattle and Miami to earn a free flight.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Each round trip between Seattle and Miami covers a distance of 2 x 2,724 = 5,448 miles (round-trip distance). To accumulate 25,000 miles, you need to make 25,000 / 5,448 = 4.59 round trips.

Since you cannot make a fraction of a round trip, you will need to make 5 round trips (back and forth) between Seattle and Miami to earn a free flight.

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Answer:

- 3 > - 7
  1 < 4

- 6 < 6

Step-by-step explanation:

From ( - ) to ( + ), it becomes greater as you go right side

Note : -

( + ) > ( - )

This is always true.

The surface area of the box formed by the pattern is given as follows:

72 cm².

The surface area of a figure is calculated as the sum of the areas of all the components of a figure.

The components of the figure in this problem can be defined as follows:

The area of the large rectangle is given as follows:

6 x 10 = 60 cm².

The combined area of the smaller rectangles is given as follows:

2 x 3 x 2 = 12 cm².

Hence the surface area of the figure is given as follows:

60 + 12 = 72 cm².

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Answer:

Step-by-step explanation:

I) In the scatter graph question, D is the most suitable line of best fit for the data. Reason: the line diligently follow the points as they move upwards. Also, the points outside the line(i.e besides the line) are equally divided, on the up and down part of the line unlike in F

II) Here, you trace the values provided on the graph on one axis to get the corresponding value on the other axis.

Therefore, From the graph 600umbrellas = corresponds to 160 days.

III) Same rule in II) applies here.

28 lions = corresponds to 20 hyenas

IV) 50 cm = corresponds to 20kg weight

Answer:

Step-by-step explanation:

[tex]\frac{2}{\sqrt{40} }[/tex]

=[tex]\frac{2}{\sqrt{40} }*\frac{\sqrt{40} }{\sqrt{40} }[/tex]            multiply root on top and bottom

=[tex]\frac{2\sqrt{40} }{40}[/tex]                    reduce fraction outside of root

=[tex]\frac{\sqrt{40} }{20}[/tex]                     break up 40 under root

=[tex]\frac{\sqrt{4*10} }{20}[/tex]                  break up roots to see better

=[tex]\frac{\sqrt{4}\sqrt{10} }{20}[/tex]                 √4 = 2

=[tex]\frac{2\sqrt{10} }{20}[/tex]                   reduce fraction outside of root

=[tex]\frac{\sqrt{10} }{10}[/tex]                    answer

The second pair of numbers with a highest common factor (HCF) of 4 and lowest common multiple (LCM) of 40, other than 4 and 40, could be 8 and 20. Their sum is 28.

The highest common factor (HCF) of two numbers is the largest number that divides both numbers without leaving a remainder. It is also known as the greatest common divisor (GCD). On the other hand, the lowest common multiple (LCM) is the smallest common multiple of two numbers.

For the numbers 4 and 40, the HCF is indeed 4, and the LCM is 40. Let's denote our second pair of numbers as 'a' and 'b'. Given that these two numbers share the same HCF (4) and LCM (40), we could set up these equations:

Given these constraints, the possible pairs ('a', 'b') could be (4, 40) or (8, 20). Since 4 and 40 have been provided as examples, we'll take the second pair. Therefore, the sum 'a' + 'b' = 8 + 20 = 28.

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The ultimate reason that the Bergen-Belsen camp was surrendered to British forces was C. The Nazis worried that if the prisoners escaped, typhus would spread.

One of the last camps to be liberated during World War II was Bergen-Belsen, a concentration camp in Nazi Germany. The camp was overcrowded and in appalling condition by April 1945. There was a possibility of a typhus epidemic, and the convicts were ill and malnourished.

To stop the typhus from spreading, the German army was on the run. The SS leaders agreed to hand over the camp to the British soldiers as a result. When British troops invaded Bergen-Belsen on April 15, 1945, they discovered some 60,000 captives there, the majority of whom were sick and dying.

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The equation of the ellipse graphed in the image is given as ((x-4)²/16) + ((y-6)²/4) = 1.

The standard form equation of an ellipse with center (h,k), horizontal axis of length 2a, and vertical axis of length 2b is,

((x-h)²/a²) + ((y-k)²/b²) = 1

Since the center is given as (4, 6), we have h = 4 and k = 6. The vertex is given as (0, 6) which means the horizontal distance from the center to the vertex is a = 4. Also, the co-vertex is given as (8, 6) which means the vertical distance from the center to the co-vertex is b = 2. Therefore, substituting these values in the equation of an ellipse, we get,

((x-4)²/4²) + ((y-6)²/2²) = 1

Simplifying, we get the equation of the ellipse,

((x-4)²/16) + ((y-6)²/4) = 1

Thus, the equation of the ellipse with center (4, 6), vertex at (0, 6), and co-vertex at (8, 6) is ((x-4)²/16) + ((y-6)²/4) = 1.

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The equation is filled as;

366 · (673 + 518) = 366 · 673 + 366 · 518

PEDMAS is described as a mathematical acronym that is used to represent the different mathematical operations in their order of application.

PEDMAS represents the following;

From the information given, we have that;

366 · (673 + 518)

Using the first rule, expand the parentheses

We have;

366(673) + 336(518)

This is also represented as;

366. 673 + 366. 518

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The shipping container shaped like a cuboid is 9.5 feet tall.

Let's call the height of the shipping container "h".

As per the given information, the shipping container can be described as a cuboid.

We are aware that the container's volume is given by the formula:

V = lwh,

where l stands for length, w for width, and h for height.

Substituting the values provided yields:

3040 = 8 x 40 x h

Simplifying, we get:

3040 = 320h

Dividing both sides by 320, we get:

h = 9.5

Therefore, the height of the shipping container is 9.5 feet.

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Answer:

1/4

Step-by-step explanation:

The probability of tossing tails on a fair coin is 1/2. The probability of rolling a multiple of 2 on a fair six-sided number cube is 1/2 (since there are three multiples of 2: 2, 4 and 6). Since these two events are independent, the probability of both events happening is the product of their individual probabilities: (1/2) * (1/2) = 1/4.

The coordinates of the vectors are, respectively:

Vector A: P = (7, π / 4)

Vector B: P = (7, 3π/ 4)

Vector C: P = (7, 5π / 4)

Vector D: P = (7, 7π / 4)

In this question we have the need of representing four vectors described in the figure given. Each description must be done in polar form:

P = (r, θ)

Where:

Now we proceed to determine the coordinates for each vectors:

Vector A

P = (7, π / 4)

Vector B

P = (7, 3π/ 4)

Vector C

P = (7, 5π / 4)

Vector D

P = (7, 7π / 4)

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The number of tons of cream chees  ordered by each supplier are 20 tones

The given parameters are

x = tons of CCC **AND** BBF (can use same variable for both since these amounts [CCC & BBF] are the same)

y = t

2x+y = 100                         <== tonnage

80x + 65x + 50y = 5900       <== cost

  2x +     y = 100   <== multiply all by -50

145x + 50y =  5900

-100x - 50y = -5000

145x + 50y = 5900

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

  45x  +   0   = 900

Making x the subject of the relation we have

x = 810/45 = 20 tones

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A compound inequality that represent example 5 is -2 < x ≤ 5.

A compound inequality that represent example 6 is -4 < x < 0.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Since the open circle and closed circle are located at -2 and 5 respectively, a compound inequality to represent this is given by;

x > -2

x ≤ 5

By combining, we have:

-2 < x ≤ 5.

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Therefore, we can estimate that approximately 34.1% of values in this distribution fall between 28 and 30 and approximately 99.7% of values in this distribution fall between 24 and 36.

Percent is a unit of measurement that expresses a part-to-whole ratio as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express changes, proportions, and rates in many fields such as mathematics, science, economics, and finance. They are often used to compare values of different sizes and scales, and to convey information in a clear and concise way.

Here,

(a) To find the percentage of values in the distribution between 28 and 30, we need to determine the z-scores corresponding to these values and use the empirical rule to estimate the proportion of values that fall between these z-scores.

First, we calculate the z-score for a value of 28 as:

z = (28 - 30) / 2

= -1

Next, we calculate the z-score for a value of 30 as:

z = (30 - 30) / 2

= 0

According to the empirical rule for a normal distribution, approximately 34.1% of values fall between a z-score of -1 and 0. Therefore, we can estimate that approximately 34.1% of values in this distribution fall between 28 and 30.

(b) To find the percentage of values in the distribution falling between 24 and 36, we need to determine the z-scores corresponding to these values and use the empirical rule to estimate the proportion of values that fall between these z-scores.

First, we calculate the z-score for a value of 24 as:

z = (24 - 30) / 2

= -3

Next, we calculate the z-score for a value of 36 as:

z = (36 - 30) / 2

= 3

According to the empirical rule for a normal distribution, approximately 99.7% of values fall between a z-score of -3 and 3. Therefore, we can estimate that approximately 99.7% of values in this distribution fall between 24 and 36.

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Complete question:

A normal distribution has a mean of 30 and a standard deviation of 2 Use the 68-95-99.7 rule to find (a) the percentage of values in the distribution between 28 and 30 % (b) the percentage of values in the distribution falling between 24 and 36 %.

The solution for the given inequality is x ≥ - 7.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

- 3 - 3x ≤ 18

Adding 3 on both sides, we get -

- 3 - 3x + 3 ≤ 18 + 3

- 3x ≤ 21

Divide by -1 on both sides, we get -

3x ≥ - 21

x ≥ - 7

Therefore, the solution for the given inequality is x ≥ - 7.

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