what is the formula in finding the area of rectangel square triangle circle
gr 6

The proportion is solved and the height of the tower is H = 117 m

Given data ,

A pole that is 3m tall casts a shadow that is 1.17 m long

And , a nearby tower casts a shadow that is 45.5m long

So , the proportion is given by

Let the height of the tower be H

And , 3 / 1.17 = H / 45.5

On simplifying the equation , we get

Multiply by 45.5 on both sides , we get

H = 116.6667 m

H = 117 m

Hence , the height of the tower is H = 117 m

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Step-by-step explanation:

this is because if the acute angle is equal to or less than 45° it will be less than or equal to 90° but it the angle is more than 45° then it will be a obtuse angle if it is doubled .

eg.

acute angle is 44°

then if it is doubled it will be 44 ˣ 2

= 88°

But if the angle is 46 °

then if it is doubled it will be 46  ˣ 2

= 92°

hope this helps you.

Answer: B

Step-by-step explanation:

Ex: Shortest to smallest.

The 7th term of the binomial expression given can be found to be 8.136 × 10^7 × x^(-4)

To find the 7th term of (3x - 4/x²)¹⁴, we can use the binomial theorem, which states that for any positive integer n and any real numbers a and b:

(a + b)ⁿ = ∑(C(n, k) x a^(n-k) x b^k)

Using the binomial theorem formula, the 7th term can be calculated as follows:

Term_7 = C(14, 6) x (3x)^(14-6) x (-4/x²)^6

First, let's find C(14, 6):

C(14, 6) = 14! / (6! x (14-6)!)

C(14, 6) = 14! / (6! x 8!)

C(14, 6) = 3003

Now, we can put everything together:

Term 7 = 3003 x (3x)^8 x (4096 / x¹²)

Term 7 = 8.136 × 10^7 × x^(-4)

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Thus, the given system of equation has one unique solution (-3, 6).

Two or even more equations with the same variables are referred to be a system of equations. The intersection of the lines is the location where an equation system has a solution. Systems of equations can be solved using one of four techniques: graphing, substitution, elimination, or matrices.

Given:  system of equations:

y = 3x + 15  ...eq 1

3x + 3y = 9 (divide by 3)

x + y = 3

y = 3 - x  ..eq 2

equation eq 1 and eq 2

3x + 15  = 3- x

3x + x = 3 - 15

4x = -12

x = -3

y = 3 - (-3) = 3 + 3 = 6

Solution - (-3, 6)

Thus, the given system of equation has one unique solution (-3, 6).

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a) The distance value is the leverage value from the output which is 0.004

b) The 99% prediction interval is [7.676, 9.146]

a) We are interested in finding and reporting the prediction interval on the output.

Thus, the prediction interval on the output is [7.9188, 8.9025]

Let us consider the estimated value for y as yₓ

We have

x₁ = 3.7, x₂ =3.9, x₃ = 6.5, β₀= 7.5891, β₁ = -2.3577, β₂= 1.6122, β₃= 0.5012

We know that yₓ = β₀ +β₁x₁ + β₂x₂ + β₃x₃

By substituting the value

x₁ = 3.7, x₂ =3.9, x₃ = 6.5, β₀= 7.5891, β₁ = -2.3577, β₂= 1.6122, β₃= 0.5012 into the above equation we get

yₓ =7.5891-(2.3577*3.7)+(1.6122*3,9)+(0.5012*6.5) = 8.411

Let us calculate the value for the prediction interval

The 100 (1 - a) \% prediction interval is

yₓ ±(tₐ/₂ * x * s* √ 1+distance value )

The distance value is the leverage value from the output which is 0.004

We have yₓ =8.411, t₀.₀₀₅.₂₆ =3.067 and s = 0.235. By substituting these values we find that the 95% prediction interval is

8, 411 + (2.3788 * 0.235sqrt(1 + 0.04)) = [7.841, 8, 981]

b) If Enterprise Industry's plan to have in inventory of the number of bottles implied by the upper limit of the prediction interval, which is approximately 9, it can be very confident that it will have enough bottles to meet demand for detergent in the future sales period.

Thus, the bottles are approximately 9

By multiplying the number of bottles implied by the lower limit of the prediction interval, that is approximately 8, by the price of the detergent that is $3.7. we get the minimal revenue from detergent in the future sales period that is $29.6

We are interested in calculating a 99% prediction interval for the demand of detergent in the future sales period

We have yₓ =8.411, t₀.₀₀₅.₂₆ =3.067 and s = 0.235 By substituting these values, we find that the 95% prediction interval is as follows

8, 411 ± (3.067 * 0.235sqrt(1 + 0.04)) = [7.676, 9.146]

Therefore the 99% prediction interval is [7.676, 9.146]

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The value of (f∘g)(x) is 3x² - 2.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: f(x) = √x²-4 and g(x) = 3x²

We have to find the value of (f∘g)(x).

(f∘g)(x) = f(g(x))

(f∘g)(x) = f(3x²)

f(3x²) = √9x⁴- 4

f(3x²) = 3x² - 2

Hence, the value of (f∘g)(x) is 3x² - 2.

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Answer:

? = 7.5

Step-by-step explanation:

the angle between the tangent and the radius at the point of contact is 90°

thus the triangle is right

using Pythagoras' identity in the right triangle

?² = 4.5² + 6² = 20.25 + 36 = 56.25 ( take square root of both sides )

? = [tex]\sqrt{56.25 }[/tex] = 7.5

The limits of the end-behavior of this graph are listed below

The limits that describe the end behavior of a graph are the values that the function approaches as x goes to positive or negative infinity.

The graph has a hole at (-4, 2), then the function is not defined at x = -4, but the limit as x approaches -4 exists and is equal to the value of the function at that point (since the function is continuous except at the hole).

The graph touches the x-axis at x = 2 to x = 6, this means that the function has roots or zeros at x = 2 and x = 6.

The horizontal asymptote is y = 1, this means that the function approaches 1 as x goes to positive or negative infinity.

To summarize, the end behavior of the graph can be described as follows:

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The perimeter of the paperboard that remains after the semicircle is removed is 93.12 inches

Information given in the problem includes:

A rectangular paperboard measuring 26in long and 16in wide

information for the semicircle are

Width = 16 inches

Radius = 16 / 2 = 8 inches

Length = 26 inches

Circumference of the semi circle is calculated using the formula

= π * radius

Where the radius is 8 inches and π = 3.14.

Substituting in to the formula and solving for the circumference of the semicircle which same as perimeter of the semicircle gives:

= 8 x 3.14

= 25.12

The perimeter would be

26 inches + 26 inches + 25.12 inches + 16 inches

= 93.12 inches

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To find the ordered pair solutions for the system of equations y = -x² + 2 and y = x, we can set the two equations equal to each other:

-x² + 2 = x

Now we can rearrange this equation into standard quadratic form by moving everything to one side:

-x² + x + 2 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = -1, b = 1, and c = 2

Plugging these values into the formula, we get:

x = (-1 ± √(1 - 4(-1)(2))) / 2(-1)

x = (-1 ± √9) / (-2)

x = (-1 ± 3) / (-2)

So the solutions for x are x = -1 and x = -2.

To find the corresponding values of y, we can plug these values of x into either of the original equations. Let's use y = x:

When x = -1, y = -1

When x = -2, y = -2

Therefore, the ordered pair solutions for this system of equations are (-1, -1) and (-2, -2).

The calculated value of the area of the rhombus is 35 sq units

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

The rhombus

Also, we have

x = 3, y = 5 and h = 4

Using shape decomposition, we have the following

Shapes = Rectangle and 2 triangles

So, the area is

Area = Rectangle + 2 triangles

Using the area formulas, we have

Area = 1/2 * xy + 1/2 * xy + hy

substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 3 * 5 + 1/2 * 3 * 5 + 4 * 5

Evaluate

Area = 35

Hence, the area is 35 sq units

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Answer:

lesser x = 9

greater x = 11

Step-by-step explanation:

(x-10)² - 1 = 0

(x-10)² = 1

(x-10) = +- root1 (positive and negative root1)

So (x-10) = +1 and (x-10) = -1

Firstly

X - 10 = 1

X = 11

Secondly

X - 10 = -1

X = 9

So you have x = 9, and x = 11

The smaller one is the lesser x (9)

The larger one is the greater x (11)

The equation that represent the graph is C) y=3x.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here let us take the two points [tex](x_1,y_1)=(1,3) , (x_2,y_2)=(3,9)[/tex].

Now using slope formula then,

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

=> m = [tex]\frac{9-3}{3-1}=\frac{6}{2}=3[/tex].

Now using equation formula then,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-3=3(x-1)

=> y-3 = 3x-3

=> y=3x.

Hence the equation that represent the graph is C) y=3x.

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The wildlife group can estimate that there are 100 wild hogs in the area. The answer is C.

The basic idea behind this method is that if we capture a random sample of animals from a population, tag them, and release them back into the population, then later capture another sample of animals, the ratio of tagged to untagged animals in the second sample can be used to estimate the total population size.

To estimate the total population of wild hogs in the area, we can use the capture-recapture method.

In this case, the wildlife group tagged and released 20 wild hogs, and later counted 8 wild hogs out of the 40 they saw. We can set up a proportion to estimate the total population size:

(Tagged hogs in first sample) / (Total population size) = (Tagged hogs in second sample) / (Number of hogs in second sample)

Putting the values,

⇒ 20 / x = 8 / 40

Simplifying and solving for x, we get:

⇒ x = (20 × 40) / 8 = 100

⇒ x = 100

Therefore, the wildlife group can estimate that there are 100 wild hogs in the area. The answer is C.

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Answer:

S - S - P

Step-by-step explanation:

(S) Statistic - The opinion of just those employees who were there on time one morning about a new training program would be a statistic as it represents a sample of the entire population of employees in the company.

(S) Statistic - The range of employees' salaries in a study about a small company with 25 employees would be a statistic as it represents a characteristic of a sample of employees from the company.

(P) Parameter - The average decrease of all the homes sold in Gwinnett in a study about the value of American homes in 2012 would be a parameter as it represents a characteristic of the entire population of American homes in Gwinnett.

The 50th partial sum of the given arithmetic sequence is 4600

From the question, we are to calculate the 50th partial sum of the given arithmetic sequence

The given arithmetic sequence is

-6, -2, 2, 6, ...

To find the 50th partial sum of the sequence, we will find the sum of the first 50 terms in the sequence.

The sum of n terms of a sequence is given by the formula,

S = n/2(a + l)

Where a is the first term

and l is the last term

l is given by

l = a + (n - 1)d

Where d is the common difference

In the given series

a = -6

d = -6 -(-2) = -6 + 2 = 4

Thus,

l = -6 + (50 - 1)4

l = -6 + 49×4

l = -6 + 196

l = 190

Then,

S = 50/2(-6 + 190)

S = 25(184)

S = 4600

Hence,

The sum is 4600

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Answer:

Z = 60

Step-by-step explanation:

60+60+z=180

120+z=180

z=180-120

Z = 60

Answer:

If Kiran's cat eats 1/2 cup of food each day, then in a week (7 days), the cat can eat:

1/2 cup/day x 7 days = 3.5 cups

So Kiran's cat can eat 3.5 cups of food in a week.

The perimeter of the quadrilateral PQRS is calculated as:

= 180 units.

Recall that if two tangents meet outside a circle, their length will be the same based on the tangents theorem.

Therefore, note that every line segments that appear tangent and intersect each other outside the circle have the same length.

Thus, we have:

Perimeter of the quadrilateral PQRS = 52.5 + 37.5 + 23 + (37.5 - 23) + 27.1 + (52.5 - 27.1)

Perimeter of the quadrilateral PQRS = 180 units.

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Answer:

Step-by-step explanation:

To find the total cost of interest, we first need to find the total payment over the life of the loan:

Total payment = Monthly payment x Number of payments

Total payment = $370.41 x (30 x 12)

Total payment = $133,347.60

Next, we need to subtract the principal (loan) amount to find the total interest paid:

Total interest = Total payment - Principal

Total interest = $133,347.60 - $69,000

Total interest = $64,347.60

Rounding to the nearest whole dollar, the total cost of interest is $64,348.

Answer:

-4z

Step-by-step explanation:

Simply add the z, which is a variable together.

Answer:

-4z

Step-by-step explanation:

The limits on the vertical asymptotes of the function are given as follows:

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

On a graph, at the vertical asymptotes, the graph just approaches the point, it does not cross the point.

Hence the vertical asymptotes are given as follows:

x = -6, x = -2 and x = 2.

We must observe the limits to the left(denoted by the - sign) and to the right (denoted by the + sign) of each asymptote.

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Answer:

3 7/8 - 1/4 = 3 5/8 times mile = 3.625 miles

Thats how its done

Step-by-step explanation:

The statements true of function f given by f(Θ) = tan(Θ):

A: Since the tangent function has a repeating pattern, it is a periodic function.

B: The domain of the tangent function is restricted because it has vertical asymptotes at certain values of Θ (specifically, odd multiples of π/2).

C: The range of the tangent function is not all real numbers, but rather all values except for its vertical asymptotes.

D: The period of the tangent function is 2π, because the pattern repeats every 2π radians.

E: The period of the tangent function is not π.

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The line segment XY is tangent to circle Z by using the Pythagorean theorem to find the radius of the circle, and the formula for the distance between a point and a line to find the distance between the center of the circle and the line.

Now let's look at the information given in the problem. We are given the length of line segment XY, which is 3.6 units. We are also given the lengths of two line segments that connect the endpoints of XY to the center of the circle Z: YZ, which is 1.8 units, and ZX, which is 2.7 units.

To determine if XY is tangent to circle Z, we need to check if it is possible for a circle with center Z and radius r to pass through points X and Y. If it is not possible, then XY must be tangent to the circle.

In this case, we can use the lengths of YZ and ZX as the legs of the right triangle, and r as the hypotenuse. We can set up the following equation:

r² = YZ² + ZX²

Substituting the given values, we get:

r² = 1.8² + 2.7²

r² = 7.29

r = √7.29

r ≈ 2.7

Now that we know the radius of circle Z, we can check if it is possible for it to pass through points X and Y. To do this, we need to find the distance between the center of the circle and the line XY. If this distance is equal to the radius of the circle, then XY is tangent to the circle.

To find the distance between the center of the circle and the line XY, we can use the formula for the distance between a point and a line. This formula is:

distance = |Ax + By + C| / √(A² + B²)

where A, B, and C are constants that depend on the equation of the line, and x and y are the coordinates of any point on the line.

In this case, we can use the equation of line XY, which is:

y = 0

Substituting this into the formula, we get:

distance = |A(0) + B(1) + C| / √(A² + B²)

distance = |B| / √(B²)

distance = 1 / √1

distance = 1

Since the distance between the center of circle Z and line XY is 1 unit, and the radius of circle Z is also 1 unit, we can conclude that XY is tangent to circle Z.

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Volume of solid generated when the trapezoid is rotated about side DE=549.8.

A trapezoid is a quadrilateral with only one pair of parallel sides. It is also known as a trapezium in some countries.

The volume of a solid is the amount of space it occupies in three-dimensional space.There are different formulas to calculate the volume of different types of solids, such as cubes, spheres, cylinders, and cones.

Given trapezoid DEFG formed when right angle HGD is cut by line FE.

Volume of solid generated about side DE:

[tex]V_{GDH}[/tex]=1/3×πr²h

=1/3×π(5+5)²(6)

=200π

[tex]V_{FEG}[/tex]=1/3×π×r²h=1/3×π×(5)²×3

=25π

Volume of Solid=[tex]V_{GDH}[/tex]-[tex]V_{FEH}[/tex]

=200π-25π=175π

=549.78 ≈549.8

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The equation of the line that is parallel to the given line and passes through the point (7,-4) is y = -2x + 10.

The equation of the line that is perpendicular to the given line and passes through the point (7,-4) is y = 1/2x - 15/2.

The equation of a line that is parallel to a given line is calculated as follows;

y = -2x + 6

slope of this line = - 2

Any line that is parallel to this line will also have a slope of -2.

The equation of the line that is parallel to the given line and passes through the point (7,-4):

y - y1 = m(x - x1)

y - (-4) = -2(x - 7)

y + 4 = -2x + 14

y = -2x + 10

The slope of the line perpendicular to the line = 1/2

y - y1 = m(x - x1)

y - (-4) = (1/2)(x - 7)

y + 4 = (1/2)x - (7/2)

y = 1/2x - 7/2 - 4

y = 1/2x - 15/2

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