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Answer:

Let x, x + 1, and x + 2 be the three numbers.

x^2 + (x + 2)^2 = x^2 + x^2 + 4x + 4

= 2x^2 + 4x + 4

= 2x^2 + 4x + 2 + 2

= 2(x^2 + 2x + 1) + 2

= 2(x + 1)^2 + 2

In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

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The three things that a personality test can tell you are:

A. How you prefer to interact with others.

C. What you might enjoy in a career.

D. How you recharge your energy.

A personality test is a tool used to assess and measure an individual's traits, characteristics, and patterns of behavior.

It may be a series of questions or statements that the individual must respond to.

The results are used to determine the person's strengths and weaknesses, their communication and social interaction (like if they are extrovert or introvert), how they process information and decision-making, etc.

They can also tell of an individual's preferred methods of finding balance in their lives, like spending time alone or with friends and families, being in nature, etc.

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Answer:

look at the photo

Step-by-step explanation:

The number of unicycles, tandem bikes, and tricycles that IRVS Cycle Rental has are:

The relevant equations, ( assuming that unicycles as U, tandem bikes as T, and tricycles as R ) are:

U + T + 32 + R = 57

U + 2T + 2 x 32 + 3R = 115

U = T

Using substitution, we get:

U + 2T + 64 + 3R = 115

U + 2T + 3R = 51

U + 2U + 3R = 51

3U + 3R = 51

Solving gives:

2U + R = 25

U + R = 17

U = 8

Solving for R, we have :

8 + R = 17

R = 17 - 8

R = 9

U and T are the same so T is 8 as well.

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Answer:

To find out how many 1 1/2 foot boards can be cut from a 12 foot long board, we need to divide the length of the board by the length of each board.

First, we need to convert 1 1/2 feet to an improper fraction.

1 1/2 = (2 x 1 + 1) / 2 = 3/2

So, each board is 3/2 feet long.

Next, we divide the length of the 12 foot long board by the length of each board:

12 / (3/2) = 12 x 2/3 = 24/3 = 8

Therefore, 8 boards of length 1 1/2 feet can be cut from a 12 foot long board.

Step-by-step explanation:

The triangles are not similar. Triangle EFG and Triangle QRS are not similar. ΔEFG not ~ ΔQRS

From the question, we are to determine if the given triangles are similar

From one of Triangle similarity theorems, AA (or AAA) or Angle-Angle Similarity theorem.

The Angle-Angle similarity theorem states that If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other

In the given diagram,

In triangle EFG

m ∠E = 104°

m ∠F = 45°

m ∠G = 180° - (104° + 45°) = 31°

In triangle QRS

m ∠R = 100°

m ∠Q = 45°

m ∠S = 180° - (100° + 45°) = 35°

Since no two angles of one of the triangles are equal to any two angles of other triangle, the triangles are not similar

Hence,

ΔEFG not ~ ΔQRS

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From a stem-and-leaf plot,

1. The minimum value = 13

2. The maximum value = 62

3. The number of data with values greater than 25 = 16

4. The number of data with values of at least 40 = 4

5. The percentage of the data with value less than 15 = 6.25%

We know that on a stem and leaf plot, the minimum is the first value and the maximum is the last value.

From the stem-and-leaf plot,

a) the minimum value is 13

b) the maximum value is 62

c) the number of data with values greater than 25:

26, 27, 28, 28, 31, 31, 32, 34, 34, 35, 38, 39, 42, 43, 47, 62

So, the number of data with values greater than 25 = 16

d) the number of data with values of at least 40:

42, 43, 47, 62

So, the required number = 4

e) the percentage of the data with value less than 15:

the data with values less than 15 are: 13, 14

So, the number of  the data with values less than 15 are: 2

The total number of data values = 32

So, the required percentage would be,

P = (2/32) × 100

P = 6.25%

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We can factor each of the given terms so that 4x^2 shows up

8x^5 = 4x^2*2x^3

12x^3 = 4x^2*3x

20x^2 = 4x^2*5

This shows how 4x^2 is the GCF of 8x^5, 12x^3, and 20x^2

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

Here's how to find the GCF of terms involving variables.

First, find the GCF of the coefficients 8, 12 and 20.

List the prime factorizations

Then circle "2*2" since it is found in all three factorizations. Do not circle 3 because it's not found in 8 or 20. Do not circle 5 since it's not found in 8 or 12.

Therefore, the GCF of {8,12,20} is 2*2 = 4.

As for the variable terms, we look for the smallest exponent.

The exponents for x^5, x^3, x^2 are 5,3,2 in that order. The smallest exponent is 2, so x^2 is part of the GCF.

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

Summary:

We found the GCF of the coefficients was 4.

The GCF of the variable terms was x^2

That's how we arrive at the GCF of 4x^2

The probability of getting hearts or face cards is 25/52.

We know that, Probability of an event = Number of favorable outcomes/Total number of outcomes.

Total number of outcomes = 52 cards

Number of hearts = 13

Number of face cards = 12

Probability getting hearts = 13/52

Probability getting face cards = 12/52

P(Hearts or Face card) = 13/52 + 12/52

= 25/52

Therefore, the probability of getting hearts or face cards is 25/52.

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Answer:

28+36+y=180

64+y=180

y=180-64

y=116°

Answer:

x ≤ [tex]\sqrt[2]{2}[/tex]

Step-by-step explanation:

x² ≤ 8

[tex]\sqrt{x^{2} }[/tex] ≤ [tex]\sqrt{8}[/tex]

x ≤ [tex]\sqrt[2]{2}[/tex]

Answer:

  569 square units

Step-by-step explanation:

You want the surface area of the 8-sided shape that has a square "base" 7 units on a side, and a "height" of 20 units.

The slant height of each triangular face is the hypotenuse of a right triangle with legs 7/2 units and 20 units. That height is ...

  h = √(3.5² +20²) = √412.25 ≈ 20.304 units

The area of one triangular face is ...

  A = 1/2bh

  A = 1/2(7)(20.304) . . . one face

There area 8 congruent triangular faces, so the total area is ...

  A = 8(1/2)(7)(20.304) = 8(7)√412.25 ≈ 568.51 ≈ 569

The total surface area is about 569 square units.

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The value of x which I suppose is the angle M is calculated to be 32°

In a right-angled triangle KLM, it is a known fact that the sum of the three angles in any triangle is 180°.

Since angle L is a right angle and has a measure of 90°, we can find angle M by subtracting the sum of angles K and L from 180°.

Thus,

angle M = 180° - angle K - angle L

= 180° - 58° - 90°

= 32°

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Answer:

The answer is (0,2) (1,-1) (2,-4)

Step-by-step explanation:

The slope is -3.

Because of this, you go down 3 and to the side 1 (it's also called rise/run).

I REALLY HOPE THIS HELPS!!!!

1. AB is a tangent, the triangle is a right triangle

2. AB is  not a tangent, the triangle is not a right triangle and hence not a Pythagorean triple

3. arc RS = 100 degrees

4. arc ST =  80 degrees

5. arc RTS = 260 degrees

6. arc RST = 180degrees

7. x = 3

8. x = 7

A tangent will obey Pythagorean triple hence we have that

AB^2 = AC^2 + BC^2

1. AB^2 = 24^2 + 10^2 = 676

AB = sqrt (676) = 26. hence AB is a tangent

2. AB^2 = 8^2 + 11^2 = 185

AB = sqrt (185) = 13.6. hence AB is not a tangent

Length of arc

3. arc RS = 100 degrees (central angle equals intercepted arc)

4. arc ST = 180 - arc RS = 180 - 100 = 80 degrees

5. arc RTS = 180 + arc ST = 180 + 80 = 260 degrees

6. arc RST = 180degrees (semicircle)

Value of x

7. x + 8 = 5x - 4

8 + 4 = 5x - x

12 = 4x

x = 3

8. 4x + 5 = 6x - 9

4x - 6x = -9 - 5

-2x = -14

x = 7

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The solution is the two dimensions will be 2121.32 by 1414.2.

Here, we have,

let X and Y be the two dimensions.

Area will be X times Y.

XY = 3000000

Y = 3000000 / X

Perimeter = 2x + 3y

substituting the values:

Perimeter = 2x + 3*3000000 / x

         = 2x + 9000000 / x

so, we get,

2 = 9000000 / x^2

x^2 = 9000000 / 2 = 4500000

x = sqrt(4,500,000)

= 2121.32

 = 1000 sqrt (4.5)

y = 3000000 / 2121.32

 = 1414.2

 = 1000 sqrt(2)

so the dimensions will be 2121.32 by 1414.2 .

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complete question:

A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

Answer: 0.15

I don't really know how to show you work on here but you can think about it like this. if 5 x 3 is 15, and if there is a decimal like 0.3 x 0.5 it would result in the answer getting smaller as you're multiplying decimals if that makes sense... so it would result in the answer being 0.15. Sorry if it wasn't a good explanation.

Let's call the height of the second building "x". We can use trigonometry to solve for x.

First, let's draw a diagram to help visualize the problem:

A        B

\      /

 \    /

  \  / x

   \/

   C

Where:

A is the top of the 200 meters high building

B is the bottom of the second building

C is the point from which the angles of depression and elevation are measured

x is the height of the second building

From the diagram, we can see that:

angle BCA = 20 degrees (angle of depression)

angle BAC = 10 degrees (angle of elevation)

AB = 200 meters

Using the tangent function, we can write:

tan(20) = x / AB (tangent of angle BCA)

tan(10) = x / (AB + x) (tangent of angle BAC)

We can solve these equations for x:

x = AB * tan(20) (multiply both sides by AB)

x = (AB * tan(10)) / (1 - tan(10)) (multiply both sides by 1 - tan(10), then simplify)

Plugging in the values we know:

x = 200 * tan(20)

x = (200 * tan(10)) / (1 - tan(10))

Using a calculator:

x ≈ 67.35 meters

Therefore, the height of the second building is approximately 67 meters (to the nearest hundred meters).

Answer: 9

Step-by-step explanation:-1 plus 9 equals 8

Answer: y = 9

Step-by-step explanation:

First of all, you right out your equation

x + y = 8

Secondly, you sub in the values you have

-1 + y = 8

Then you can swap your answer and y

-1 + 8 = y

Work out the answer

-1 + 8 = 9

Answer is y = 9

The Perimeter of the given figure rectangle will be 60m. The correct option is 1.

Perimeter refers to the total length of the boundary of a two-dimensional shape or object. It is the distance around the edge of a shape. To find the perimeter of a shape, you add up the lengths of all its sides.

The perimeter of a rectangle is given by the formula:

P = 2(l + w)

where P is the perimeter, l is the length, and w is the width.

Using the values you provided, we can substitute them into the formula:

P = 2(18 + 12) = 2(30) = 60 meters

Therefore, the perimeter of the rectangle with a length of 18 meters and a height of 12 meters is 60 meters.

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The value of length y is,

y = 4 cm

And, The area of the shaded part is, 20 cm²

We have to given that;

A figure is shown in image.

Hence, We get;

The value of y is,

y = 4 cm

And, The area of the shaded part is,

⇒ 4 × 5

⇒ 20 cm²

Thus, The value of length y is,

y = 4 cm

And, The area of the shaded part is, 20 cm²

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The solution to a trignometric equation sin²x - 1 = 0 is x = { π/2,  3π/2}

Consider a trignometric equation,

sin²x - 1 = 0

We need to solve this trigonometric equation  for all values of angle x such that 0≤ x < 2π

Consider equation,

sin²x - 1 = 0

sin²x = 1

Takin square root,

sin(x) = ±1

when sin(x) = 1, then x = π/2

and when sin(x) = -1 then x = 3π/2

Therefore, required values of angle x = { π/2,  3π/2}

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Answer:

i believe the answer would be option D

Step-by-step explanation:

Answer:

  total deposits: $35,100

Step-by-step explanation:

You have the value of an annuity earning 5% with payments of $65 a month for 45 years as $131,718.42. You want to know the total value of payments.

12 payments per year of $65 for 45 years will have a total value of ...

  12·65·45 = 35100

Total deposits will be $35,100.

Answer:

C. complementary

Michel-Eugène Chevreul discovered that placing complementary colors next to each other can create the greatest contrast and vibrancy in color perception. This is because complementary colors are located opposite each other on the color wheel and, when placed side by side, they enhance each other and create a strong visual impact. For example, placing yellow next to violet or blue next to orange can create a dynamic and eye-catching effect. In contrast, placing tertiary colors (colors made by mixing primary and secondary colors) or arbitrary colors next to each other may not create as much contrast or visual interest. Overall, understanding color theory and the relationships between different colors can be helpful for creating visually appealing designs, artworks, or other color-based projects.

Answer:

  0.67 million miles per day

Step-by-step explanation:

You want the average rate of change of the function d(t) = ∛(6t²) on the interval [4, 8], where d is in millions of miles, and t is in days.

The average rate of change of the function on the interval [a, b] is given by ...

  rate of change = (d(b) -d(a))/(b -a)

As the table in the attachment shows, this is approximately ...

  rate of change = (7.268 -4.579)/(8 -4) ≈ 0.67

The average rate of change on the interval 4 ≤ t ≤ 8 is about 0.67 million miles per day.

__

Additional comment

Mercury has an orbit of about 88 days at a distance of roughly 36 million miles from the Sun. Already at that distance, the General Theory of Relativity comes into play, making predictions from Newtonian physics somewhat problematic. It is unlikely this formula has any relation to reality for t much less than 200.

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The future value or the total amount due at time t for the loan is $5112.50.

To find the future value or the total amount due at time t for a loan with a principal P, a simple interest rate r, and a period of time t, we can use the formula for calculating simple interest;

A=P + (P × r × t)

where; A = future value or total amount due at time t

P = principal amount

r = simple interest rate

t = time period (in years)

Given the values; P = $5000

r = 4.5% (or 0.045 as a decimal)

t = 6 months (or 0.5 years)

We can substitute these values into the formula and calculate the future value;

A = 5000 + (5000 × 0.045 × 0.5)

A = 5000 + 112.5

A = $5112.50

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Answer: 200

Step-by-step explanation: 20% of 200 is 40

Answer:

200

Step-by-step explanation:

Since 20% of the movie is equal to 40 minutes of the entire movie, simply just keep adding 40 repeatedly until you hit 100%.

40+40+40+40+40=200

^      ^     ^     ^     ^

20+20+20+20+20=100