A bird flies from the bottom of a canyon that is 72 1/2 feet below sea level to a nest that is 719 2/5 feet above sea level. What is the difference in elevation between the bottom of the canyon and the​ bird's nest?

The missing angle is 90°. So, to obtain the values of the sides given the lengths we will have:

8. PT = 1

   PV = 2

9. VT = 0.76

   PV = 0.66

10. PT = 3

     PV = 6

11. PV =0.58

    PT =1.154

12. PT = 1.73

    VT = 3

13. VT = 3

     PV = 3.5

The given triangle is a scalene triangle because of the three different angles it has which sum up to 180 degrees. The sides will also be different.

For the first triangle whose known side is √3, the missing values can be obtained this way:

sin 60°/ √3 = sin 90/PV

PV = √3 Sin 90/ sin 60

PV = 1.732/0.866

= 2

PT = sin 60/ √3 = sin 30/ PT

PT = √3 sin 30/sin 60

PT = 1

Using this same pattern, the values for the other figures can be obtained.

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The function that is increasing at a faster rate, given the graph shown, is D. g ( x ) increases at a faster rate.

You can find which function is increasing faster by looking at the steepness of the line.

When the slope of a line is positive, it means that as we move from left to right along the line, the y-coordinate of a point on the line increases. This indicates that the line is moving upward and becoming steeper. The steeper the line, the larger the magnitude of the slope.

g ( x ) was more steep in the interval [ 0, 1 ] and so was increasing at a faster rate.

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If Lin's sister dοes nοt make any depοsits οr withdrawals, the balance in her accοunt after 22 days will be -$133.57.

The balance is the sum οwing οn an accοunt in banking and accοunting. The term "balance" in bοοkkeeping refers tο the difference between the tοtal οf debit entries and the tοtal οf credit entries made intο an accοunt οver the cοurse οf a certain financial periοd. The accοunt shοws a debit balance when tοtal debits exceed tοtal credits.

Net debt is represented by an accοunt balance that is less than zerο. An accοunt with a minus sign (-) at the end οf the amοunt typically has a negative balance οr is in debt.

Given,

The fee charged when the balance falls belοw zerο = $5.95/day

The current balance in Lin's sister's accοunt = −$2.67

We are asked tο find her accοunt balance after 22 days if nο transactiοns are made.

Since the current balance in her accοunt is belοw zerο, a fee will be charged.

The fee charged fοr 22 days = 5.95 × 22 = $130.9

Then the current balance = -2.67 - 130.9 = -$133.57

Therefοre if Lin's sister dοes nοt make any depοsits οr withdrawals, the balance in her accοunt after 22 days will be -$133.57.

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144x² - 24x + 1 = 12²x² - 24x + 1 = (12x)² - 2(12x) + 1² = (12x - 1)²

The functions that represent a horizontal dilation of the function y = log x are A and C.

Horizontal dilation, also known as horizontal stretching or compression, is a transformation of a function that changes the shape of its graph by scaling the independent variable (x-axis).

When a function is horizontally dilated, it is stretched or compressed horizontally without changing its vertical position. If the function is stretched horizontally, it becomes flatter and wider, while if it is compressed horizontally, it becomes steeper and narrower.

Horizontal dilation is achieved by multiplying the independent variable x in the function by a positive constant a. If a > 1, the function is horizontally compressed, and if 0 < a < 1, the function is horizontally stretched. If a = 1, the function is not affected by horizontal dilation.

The function that represents a horizontal dilation of the function y = log x is a function of the form y = log(ax), where a is a positive constant. This is because changing the value of a will stretch or compress the graph horizontally.

A. h(x) = log(2x) + 1 represents a horizontal compression by a factor of 2, followed by a vertical translation upward by 1 unit.

B. K(x) = log(x + 1) represents a horizontal translation to the left by 1 unit.

C. f(x) = log(0.3x) represents a horizontal compression by a factor of 1/0.3 = 3.33.

D. g(x) = 5 log(x) represents vertical stretching by a factor of 5.

Therefore, the functions that represent a horizontal dilation of the function y = log x are A and C.

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Answer:

D is the answer trust me

hope helpful! :)

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎

The elevation of the gun will the projectile hit the missile will be 62.18°.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Let 't' be the time. And 'θ' be the angle. Then the measure of the angle is given as,

688t / sin 35° = 548 / sin θ

sin θ = 0.4568

θ = 27.18°

The angle from the base is calculated as,

⇒ 27.18° + 35°

⇒ 62.18°

The elevation of the gun will the projectile hit the missile will be 62.18°.

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Claire will be 20 years old in 16 years. To solve this problem, we use algebra.

Let's represent Claire's current age with the variable x. According to the problem, in 8 years, Claire will be three times her current age. We can write this as an equation:

x + 8 = 3x
Next, we can rearrange the equation to solve for x:

8 = 2x
x = 4
This means that Claire is currently 4 years old. To find out when she will be 20 years old, we can subtract her current age from 20:

20 - 4 = 16

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1) 140

2) T2 = ?

3) $13,786.40

4) $835.88

5) x = 3, y=(0, 1.5)

1) To find the number of pounds of grass seed needed to cover an area of 140,000 ft2, you need to write a proportion and solve it. Set up the proportion using the given information:

20 lb/10,000 ft2 = x lb/140,000 ft2

To solve for x, multiply both sides of the equation by 140000:

20 lb * 140000/10,000 ft2 = x lb

x = 2800 lb

You will need 2800 lbs of grass seed to cover an area of 140,000 ft2. To find out how many whole bags of seed you will need to buy, divide the total number of pounds by the number of pounds in a bag, which is 20 lbs. You will need to buy 140 whole bags of seed.

2) To solve for T2 in the equation ???????????????? ???????? = ???????????????? ????????, divide both sides of the equation by ???????????????? :

T2 = ???????????????? ????????/????????????????

3) To find the cost of the car before the sales tax, subtract the 5% sales tax from the total cost. The formula is:

Cost before tax = Total Cost - (Total Cost * Sales Tax %)

Cost before tax = $14,512 - ($14,512 * 0.05) = $13,786.40

4) To find the list price of the laptop computer, add the 15% off sale to the sale price. The formula is:

List Price = Sale Price + (Sale Price * Discount %)

List Price = $722.50 + ($722.50 * 0.15) = $835.88

5) The x and y intercepts for the equation 3x + 6y = 9 can be found by setting x or y equal to 0 and solving for the other. To find the x intercept, set y = 0:

3x + 6(0) = 9

3x = 9

x = 3

The x intercept is (3, 0). To find the y intercept, set x = 0:

3(0) + 6y = 9

6y = 9

y = 1.5

The y intercept is (0, 1.5).

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Answer:

Below

Step-by-step explanation:

Volume of a cylinder is given by the formula

V = pir^2 h     SUbstitute in the values given for  r , h

V = pi * (17/2)^2 * 42 = 9533 ft^3 =  353 yd^3  

The Big Ideas or Focal Points in the mathematics curriculum in grades 4 are as follows:

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Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.

A triangle is a polygon with three vertices and three angles that has three sides. It is one of the fundamental geometric shapes and has numerous uses in fields like engineering, physics, architecture, and more. The lengths of a triangle's sides and angles can be calculated using a variety of geometric formulas. Triangles come in a variety of shapes, including equilateral, isosceles, scalene, right-angled, acute-angled, and obtuse-angled triangles, each of which has unique attributes.

given

Let x represent the person's height.

Let x represent the streetlight's height.

Let d represent the distance between an individual and a streetlight.

Let s be the size of the shade cast by the subject.

According to the facts provided, x equals 6 feet (height of the person)

d Equals 15 feet (distance from the person to the streetlight)

The shadow's extent, s, is 15 feet.

Finding y's number, or the streetlight's height, is necessary.

The following ratios can be written using the comparable triangles property:

y / (d + s) Equals x / s

Inputting the numbers provided yields:

By condensing and figuring out x, we arrive at:

y = 12 feet

Consequently, the streetlight has a 12 foot height.

We can divide the streetlight's height by the person's height to determine how many times higher the streetlight is:

y / x = 12 / 6 = 2

Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.

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The maximum value of the function z=8x+3y subject to the constraints is 94

The maximum value of the function z=8x+3y subject to the constraints y>=0, x>=4, y<=10, and 5x+2y<=60 can be found using the method of linear programming.

Graph the constraints on a coordinate plane. The constraints y>=0 and x>=4 are vertical and horizontal lines, respectively.

The constraint y<=10 is a horizontal line at y=10, and the constraint 5x+2y<=60 can be rewritten as y<=-5/2x+30 and graphed as a line with a slope of -5/2 and a y-intercept of 30.

Identify the feasible region, which is the area of the graph that satisfies all of the constraints.

In this case, the feasible region is the quadrilateral bounded by the lines x=4, y=0, y=10, and y=-5/2x+30.

Find the vertices of the feasible region. The vertices are the points (4,0), (4,10), (8,10), and (10,5).

Substitute the coordinates of the vertices into the function z=8x+3y to find the maximum value. The maximum value occurs at the vertex (8,10), where z=8(8)+3(10)=94.

Therefore, the maximum value of the function z=8x+3y subject to the constraints y>=0, x>=4, y<=10, and 5x+2y<=60 is 94.

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The key shows that 1|1 represents the score 11.

The stem-and-leaf plot that depicts the data set accurately is as follows:

Season Points for the 2021 Riverside Red Dragon Football

0 | 0 3

1 | 0 1 7 7 7 7 7

2 | 0 0 2 4 8 8

3 | 1 3

Key: 1|1 = 11

The stems represent the tens digit and the leaves represent the ones digit in this stem-and-leaf plot, which accurately depicts the frequency of each score in the data set. For instance, the stem 2 and the leaves 0 and 0 indicate the two instances of the score 20, which appears twice. The score 11 is represented by the key as 1|1.

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Using some rules for interior angles, we will see that:

x = 22.5

y = 22.5

Remember that the sum of the interior angles of any triangle is 180°.

Now, we can see that :

3x + k = 180°

Where k is the missing angle in the left triangle.

k = 180° - 3x

if we add the 3 interior angles, we will get:

2x + y + 180° - 3x = 180°

y - x = 0°

So x and y have the same value.

If now use the top triangle, we can write:

(90 - y) + 3x + 2x = 180

And we know that y = x

90 -x  + 3x + 2x = 180

90 + 4x = 180

4x = 180 - 90  =90

x = 90/4 = 22.5

Then:

x = 22.5

y = 22.5

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The ball is falling at 130 feet per second after 10.9375 seconds.

The height of the ball launched in the air t seconds after it is launched is given by the equation F(t) = 16t^2 – 220t + 19. We need to find the time t when the ball is falling at 130 feet per second. To do this, we need to find the derivative of the function F(t) with respect to time t, which represents the velocity of the ball at any given time t.

The derivative of F(t) with respect to t is F'(t) = 32t - 220. We can set this equal to 130 to find the time when the ball is falling at 130 feet per second:

32t - 220 = 130

32t = 350

t = 350/32

t = 10.9375 seconds

Therefore, the ball is falling at 130 feet per second after 10.9375 seconds.

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Answer:

50: Composite

45: Composite

36: Composite

35: Composite

27: Composite

44: Composite

43: Prime

32: Composite

Answer:

x = 1
y = 1

Step-by-step explanation:

The solutions for the given equations are:

31. x = 4 or x = -2

32. x = 2+√13 or x = 2-√13

33. x = -3+√5 or x = -3-√5

34. x = -0.5+√4.25 or x = -0.5-√4.25

35. x = 1.5+√1.25 or x = 1.5-√1.25

To solve the equations by completing the square, we will use the following steps:

Step 1: Move the constant term to the right side of the equation.

Step 2: Take half of the coefficient of the x term and square it.

Step 3: Add this value to both sides of the equation.

Step 4: Factor the left side of the equation.

Step 5: Take the square root of both sides of the equation.

Step 6: Solve for x.

Let's apply these steps to the given equations:

31. x^2-2x-8 = 0

Step 1: x^2-2x = 8

Step 2: (-2/2)^2 = 1

Step 3: x^2-2x+1 = 9

Step 4: (x-1)^2 = 9

Step 5: x-1 = ±3

Step 6: x = 4 or x = -2

32. x^2-4x-9 = 0

Step 1: x^2-4x = 9

Step 2: (-4/2)^2 = 4

Step 3: x^2-4x+4 = 13

Step 4: (x-2)^2 = 13

Step 5: x-2 = ±√13

Step 6: x = 2+√13 or x = 2-√13

33. x^2+6x+4 = 0

Step 1: x^2+6x = -4

Step 2: (6/2)^2 = 9

Step 3: x^2+6x+9 = 5

Step 4: (x+3)^2 = 5

Step 5: x+3 = ±√5

Step 6: x = -3+√5 or x = -3-√5

34. x^2+x-4 = 0

Step 1: x^2+x = 4

Step 2: (1/2)^2 = 0.25

Step 3: x^2+x+0.25 = 4.25

Step 4: (x+0.5)^2 = 4.25

Step 5: x+0.5 = ±√4.25

Step 6: x = -0.5+√4.25 or x = -0.5-√4.25

35. x^2-3x+1 = 0

Step 1: x^2-3x = -1

Step 2: (-3/2)^2 = 2.25

Step 3: x^2-3x+2.25 = 1.25

Step 4: (x-1.5)^2 = 1.25

Step 5: x-1.5 = ±√1.25

Step 6: x = 1.5+√1.25 or x = 1.5-√1.25

Therefore, the solutions for the given equations are:

31. x = 4 or x = -2

32. x = 2+√13 or x = 2-√13

33. x = -3+√5 or x = -3-√5

34. x = -0.5+√4.25 or x = -0.5-√4.25

35. x = 1.5+√1.25 or x = 1.5-√1.25

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1. Surface area of the pyramid  is 24.36 [tex]ft^2[/tex]

2. Surface area is 259.2 [tex]in^2[/tex]

3. Surface area is 912 [tex]m^2[/tex]

4. Surface area is 1226.08 [tex]yd^2[/tex]

5. Surface area is 204 [tex]ft^2[/tex]

6. Surface area is 67.49 [tex]ft^2[/tex]

7. Surface area is 334.2 [tex]in^2[/tex]

8. Total surface area of the pyramid is 300  [tex]m^2[/tex]

9. Total surface area of the pyramid is 257.43 [tex]yd^2[/tex]

10. Total surface area of the pyramid is 80 [tex]ft^2[/tex]

11. Total surface area is 77.96 ft²

12. Total surface area is 292.55 ft²

13. Total surface area is 429 in²

14. Total surface area is 129 m²

15. Total surface area is 1256.4 yd²

1. The following formula is used to get the surface area of a pyramid having a triangle base:

Surface area = (1/2)P x s + B

where

P is the perimeter of the base,

s is the slant height, and

B is the area of the base.

By using the given values, we have:

B = (1/2) x b x h = (1/2) x 4 x 2 = 4 [tex]ft^2[/tex]

s = [tex]\sqrt{(1/2\times4)^2 + 2^2)} = \sqrt{17}[/tex] ft

P = 12 ft

Surface area = (1/2) x 12 x [tex]\sqrt{17}[/tex]+ 4 = 24.36 [tex]ft^2[/tex]

2.The following formula is used to get the surface area of a pyramid having a square base:

Surface area = (1/2)P x s + B

By using the given values, we have:

B = [tex]s^2 = 12^2 = 144 \:in^2[/tex]

s = [tex]sqrt{(1/2\times16)^2 + 12^2}[/tex] = 14.4 in

P = 16 in

Surface area = (1/2) 1614.4 + 144 = 259.2 [tex]in^2[/tex]

3. By using the same formula as above, we have:

B = [tex]s^2 = 12^2 = 144\: m^2[/tex]

s =[tex]\sqrt{(1/2\times48)^2 + 12^2}[/tex] = 24 m

P = 48 m

Surface area = (1/2)4824 + 144 = 912 [tex]m^2[/tex]

4. By using the same formula as above, we have:

B = (1/2) x b x h = 90 [tex]yd^2[/tex]

s = [tex]\sqrt{(1/2*15)^2 + 12^2} = \sqrt{369}[/tex]  yd

P = 45 yd

Surface area = (1/2)45 [tex]\sqrt{369}[/tex] + 90 = 1226.08 [tex]yd^2[/tex]

5. By using the same formula as above, we have:

B = [tex]s^2 = 6^2 = 36 ft^2[/tex]

s = [tex]\sqrt{(1/2\times24)^2 + 6^2}[/tex]= 12 ft

P = 24 ft

Surface area = (1/2)2412 + 36 = 204 [tex]ft^2[/tex]

6. By Using the same formula as problem 1, we have:

B = (1/2) x b x h  = 10 [tex]ft^2[/tex]

s = [tex]\sqrt{(1/2\times5)^2 + 4^2} = \sqrt{41}[/tex] ft

P = 15 ft

Surface area = (1/2) 15 [tex]\sqrt{41}[/tex] + 10 = 67.49 [tex]ft^2[/tex]

7. By using the same formula as problem 2, we have:

B = [tex]s^2 = 121 in^2[/tex]

s =[tex]\sqrt{(1/2\times16)^2 + 11^2} = \sqrt{185}[/tex] in

P = 16 in

Surface area = (1/2) x 16 x [tex]\sqrt{185}[/tex] + 121 = 334.2 [tex]in^2[/tex]

8. The pyramid's base is a square with long sides. b = 10 m,

so the area of the base is A = [tex]b^2[/tex] = 100  [tex]m^2[/tex]

The lateral area of the pyramid is L = 4 × (1/2 × s × P/4) = 5P [tex]m^2[/tex]

Substituting the given values, we get L = 5 × 40 = 200  [tex]m^2[/tex]

So, the total surface area of the pyramid is then

A + L = 100 + 200 = 300  [tex]m^2[/tex]

9. A side-length equilateral triangle forms the pyramid's base.b = 15 yds,

so the area of the base is

A = ([tex]\sqrt(3)[/tex]/4) × [tex]b^2[/tex] = 97.43 [tex]yd^2[/tex]

The lateral area of the pyramid is L = (1/2 × s × P/3) × h = 160 [tex]yd^2[/tex]

The total surface area of the pyramid is then

A + L = 97.43 + 160 = 257.43 [tex]yd^2[/tex]

10. The base of the pyramid is a square with sides of length

b = P/4 = 16 ft/4 = 4 ft,

A = [tex]b^2[/tex] = 16 [tex]ft^2[/tex]

L = 4 × (1/2 × s × P/4) = 64 [tex]ft^2[/tex]

The total surface area of the pyramid

A + L = 16 + 64 = 80 [tex]ft^2[/tex]

11. The surface area may be computed as follows since the base is square and has sides that are each 5 feet long:

Area of each triangular face = (1/2) x s x h = (1/2) x 7 x 3.64 = 12.74 ft²

Area of the square base = b² = 5² = 25 ft²

Total surface area = 4 x (12.74) + 25 = 77.96 ft²

12. Calculate the length of the altitude by using the Pythagorean theorem:

a² + b² = c², where a = 8 ft,

b = (1/2) x b = (1/2) x 15 ft = 7.5 ft, c = h = unknown height

8² + 7.5² = c²

c ≈ 11.18 ft

Then, we can calculate the surface area as:

Area of each triangular face = (1/2) x b x h  = 83.85 ft²

Area of the triangular base = (1/2) x b x h= 60 ft²

Total surface area = 3 x (83.85) + 60 = 292.55 ft²

13. Surface area can be calculated as:

Area of each triangular face = (1/2) x s x h = 55 in²

Area of the square base = b² = 13² = 169 in²

Total surface area = 4 x (55) + 169 = 429 in²

14. The surface area can be calculated as:

Area of each triangular face = (1/2) x s x h = (1/2) x 8 x 5 = 20 m²

Area of the square base = b² = 7² = 49 m²

Total surface area = 4 x (20) + 49 = 129 m²

15. By using the Pythagorean theorem:

a² + b² = c², where a = 25 yds, b = (1/2) x b = (1/2) x 9 yds = 4.5 yds, c = h = unknown height

25² + 4.5² = c²

c ≈ 25.42 yds

Then, we can calculate the surface area as:

Area of each triangular face = (1/2) x b x h = 381.3 yd²

Area of the triangular base = (1/2) x b x h =112.5 yd²

Total surface area = 3 x (381.3) + 112.5 = 1256.4 yd²

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The zeros and their multiplicities are x=-2/3, multiplicity 5 and x=5, multiplicity 1.

To find the zeros of the function f(x)=(3x+2)^(5)(x^(2)-10x+25), we need to set the function equal to zero and solve for x.

0=(3x+2)^(5)(x^(2)-10x+25)

Since the product of two factors is zero, one of the factors must be zero. We can set each factor equal to zero and solve for x.

(3x+2)^(5)=0

3x+2=0

3x=-2

x=-2/3

The other factor is:

x^(2)-10x+25=0

This is a quadratic equation, which we can solve using the quadratic formula:

x=(-b±√(b^(2)-4ac))/(2a)

x=(-(-10)±√((-10)^(2)-4(1)(25)))/(2(1))

x=(10±√(100-100))/2

x=(10±0)/2

x=10/2

x=5

So the zeros of the function are x=-2/3 and x=5.

To find the multiplicity of each zero, we need to look at the exponent of the factor that contains the zero. The zero -2/3 comes from the factor (3x+2)^(5), which has an exponent of 5, so the multiplicity of -2/3 is 5. The zero 5 comes from the factor (x^(2)-10x+25), which has an exponent of 1, so the multiplicity of 5 is 1.

Therefore, the zeros and their multiplicities are:

x=-2/3, multiplicity 5

x=5, multiplicity 1

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The exact value of cos(2a) is 7/25 and the exact value of sin a/2 is √10/10. Remember to consider which sign is appropriate when using the trigonometric identities.

Given tan a = 3/4, and sin a = -3/5, we can find the exact value of cos(2a) and sin a/2 by using the appropriate trigonometric identities.

a) cos(2a) = 1 - 2sin^2(a) = 1 - 2(-3/5)^2 = 1 - 18/25 = 7/25

b) sin a/2 = √[(1 - cos a)/2] = √[(1 - (4/5))/2] = √[(1/5)/2] = √(1/10) = 1/√10 = √10/10

Therefore, the exact value of cos(2a) is 7/25 and the exact value of sin a/2 is √10/10. Remember to consider which sign is appropriate when using the trigonometric identities.

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The domain and range of C are:
Domain of C: {c, j, e}
Range of C: {h, j, c, a}

The domain and range of a relation C are the set of all x-values and y-values in the ordered pairs of C. The domain of C is the set of all x-values, and the range of C is the set of all y-values. We can find the domain and range of C by looking at the ordered pairs in C={(c,h),(j,j),(j,c),(e,a)}.

The domain of C is {c, j, e} because these are the x-values in the ordered pairs. The range of C is {h, j, c, a} because these are the y-values in the ordered pairs.

Therefore, the domain and range of C are:
Domain of C: {c, j, e}
Range of C: {h, j, c, a}

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Answer:

[tex]\frac{4}{50fx^{30} } :[/tex][tex]\frac{2}{25f^{30} }[/tex]

Step-by-step explanation:

Factor thenumber:4=2\2

[tex]=\frac{2 . 2}{50fx^{30} }[/tex]

Factor the number 50= 2 x 25

[tex]=\frac{2.2}{2.25f^{30} }[/tex]

Cancel the common factor:2

[tex]=\frac{2}{25f^{30} }[/tex]

The expression [tex](2x-1)(2x+2)[/tex] can be expressed as the trinomial [tex]4x^2 + 2x - 2[/tex].

To express the given expression as a trinomial, we need to use the distributive property to multiply the two binomials.

1. Multiply the first term of the first binomial by the first term of the second binomial:

[tex](2x) * (2x) = 4x^2[/tex]

2. Multiply the first term of the first binomial by the second term of the second binomial:

[tex](2x) * (2) = 4x[/tex]

3. Multiply the second term of the first binomial by the first term of the second binomial:

[tex](-1) * (2x) = -2x[/tex]

4. Multiply the second term of the first binomial by the second term of the second binomial:

[tex](-1) * (2) = -2[/tex]

5. Add the four products together:

[tex]4x^2 + 4x + (-2x) + (-2) = 4x^2 + 2x - 2[/tex]

So, the expression [tex](2x-1)(2x+2)[/tex] can be expressed as the trinomial [tex]4x^2 + 2x - 2[/tex].

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The properties of real numbers being used in the equations you provided are as follows:

1. 5−8: This equation does not use any specific property of real numbers. It is simply subtraction of two real numbers.

2. 5.3+2x=2x+36: This equation uses the Commutative Property of Addition, which states that the order in which real numbers are added does not affect the sum. This is why 5.3+2x is equal to 2x+5.3.

3. (a+b)(a−b)=(a−b)(a+b): This equation also uses the Commutative Property of Multiplication, which states that the order in which real numbers are multiplied does not affect the product. This is why (a+b)(a−b) is equal to (a−b)(a+b).

4. 7.A(x+y)=Ax+Ay: This equation uses the Distributive Property, which states that multiplying a real number by a sum is the same as multiplying each term in the sum by the real number and then adding the products. This is why A(x+y) is equal to Ax+Ay.

5. (A+1)(x+y)=(A+1)x+(A+1)y: This equation also uses the Distributive Property, as explained in the previous example.

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The correct options are A, D, and E. Option B is not a valid ordinal number ending, and option C does not match any of the given cardinal numbers.

What is cardinal number ?

A cardinal number is a type of number used to represent the size or quantity of a set or collection of objects. It is a number that expresses how many objects are in a particular set or group, and is used to answer questions like "how many?"

For example, the cardinal number of the set {1, 2, 3} is 3, because there are three objects in the set. The cardinal number of a set can be finite or infinite, depending on whether the set has a definite number of elements or not.

The ordinal numbers corresponding to the cardinal numbers are:

183: 183rd

201: 201st

82: 82nd

Therefore, the correct options are A, D, and E. Option B is not a valid ordinal number ending, and option C does not match any of the given cardinal numbers.

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The side of the unknown side of this right angled triangle is 14cm

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given two sides of the triangle are 17cm and 9cm.

We have to find the unknow side of the triangle.

By Pythagoras theorem we find the length of unknown side.

The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

17²=9²+x²

289-81=x²

208=x²

Take square root on both sides

x=√208

x=14.42 cm

Hence, the side of the unknown side of this right angled triangle is 14cm

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Using the circumference formula of the circle, we know that the area of the shaded region is 2,375 in.

The circumference of a circle is the distance encircling its edge.

The diameter of a circle is the distance measured through its center.

The radius of a circle is the distance from the center to any point on the edge.

The circumference of a circle or ellipse in geometry is its perimeter.

That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

The curve length around any closed figure is more often referred to as the perimeter.

So, the circumference of the inner circle is 125.6 inches.

Then, the radius would be:

C = 2πr

125.6 = 2πr

125.6 = 6.28r

r = 125.6/6.28

r = 20 in

r for the outer circle: r will be 20 + 14 = 34 in

Area of the inner circle:

A = πr²

A = π20²

A = 1256.63706

A = 1257 in

Area of the outer circle:

A = πr²

A = π34²

A = 3631.68111

A = 3632 in

Area of the shaded region:

3632 in - 1257 in = 2,375 in

Therefore, using the circumference formula of the circle, we know that the area of the shaded region is 2,375 in.

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