A circular sheet of paper of radius 6 inches is cut into 3 equal sectors, and each sector is formed into a cone with no overlap. What is the height in inches of the cone

ΔXYZ was reflected to form ΔLMN, hence ΔXYZ ≅ ΔLMN, ∠X ≅ ∠L and XZ ≅ LN

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Reflection is a rigid transformation, hence it produces congruent figures with congruent angles.

∠Y + ∠X + ∠Z = 180 (angle in a triangle)

86 + 38 + ∠Z = 180

∠Z = 56°

Also:

∠N + ∠M + ∠L = 180 (angle in a triangle)

86 + 56 + ∠L = 180

∠L = 38°

ΔXYZ was reflected to form ΔLMN, hence ΔXYZ ≅ ΔLMN, ∠X ≅ ∠L and XZ ≅ LN

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Answer:

x = -2

Step-by-step explanation:

you can fist distribute -5 into the parenthesis

25x - 15 - 5x + 5 = -50

then combine like terms

20x - 10 = -50

add 10 to both sides

20x = -40

lastly divide both sides by 20

x = -2

that is your answer

Answer:

 The triangle is not acute because 2² + 4² < 5².

Step-by-step explanation:

Answer:

The triangle is not acute because 2² + 4² < 5²

Step-by-step explanation:

got it correct on my quiz

Answer:

$2,649.50

Step-by-step explanation:

s

Answer:

she has 23 points

Step-by-step explanation:

hope this helps and mark brainliest please

Hello!

The numbers should be written as :

1,750,064

one million, seven hundred fifty thousand, sixty-four

218,502

two hundred eighteen thousand, five hundred two

384,057

three hundred eighty-four thousand, fifty-seven

4,012,923

four million, twelve thousand, nine hundred twenty-three

Yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010

Statement 1: The population of Town C in 2000 was 2/3 of the population in 2005

This tells us the population change from 2000 to 2005 since we need to know the population change from 2000 to 2010, this statement is not sufficient.

Statement 2: The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.

Since statement 2 provides no information about the population change from 2000 to 2005, there is no to answer this question with certainty. thus, statement 2 is not sufficient

Statement 1 and Statement 2 combined:

Let X= the population in 2000

Let Y= the population in 2005

Let Z= the population in 2010

From statement 1, we can write: X=[tex]\frac{2}{3}[/tex]Y

Multiply both sides by 3 to get [tex]3X=2Y[/tex]

Divide both sides by 2 to get [tex]\frac{3}{2}X=Y[/tex]

=>[tex]Y=1.5X[/tex]

As per statement 2, let's first determine the increase in the number of people from 2000 to 2005

If [tex]Y=1.5X[/tex], we know

X= the population in 2000

1.5X= the population in 2005

[tex]1.5X-X=0.5X[/tex]

So, the population increased  [tex]0.5X[/tex] from 2000 to 2005

So,  from 2005 to 2010, the population increased at least 0.5X

1.5X= the population in 2005

[tex]1.5X+0.5X=2.0X[/tex]

So, the population in 2010 was at least 2.0X

In other words, the population at least doubled from 2000 to 2010

So, the answer to the target question is yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010

Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010?

(1) The population of Town C in 2000 was 2/3 of the population in 2005.

(2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.

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A slope is also known as the gradient of a line. The slope of the given linear table is $250 per car.

A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the linear table is,

m = ($4,000 - $2,500)/(12-6) = $250 per cars

Hence, the slope of the given linear table is $250 per car.

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The coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).

In order to determine the coordinates of the circumcenter of triangle ABC with the given vertices, let its circumcenter be P(x, y). Thus, PA = PB = PC.

By squaring all sides of triangle ABC, we have:

PA² = PB² = PC²

From PA² = PB², we have:

(x - 3)² + (y - (-1))² = (x - (-3))² + (y - (-11))²

(x - 3)² + (y + 1)² = (x + 3)² + (y + 11)²

x² - 6x + 9 + y² + 2y + 1 = x² + 6x + 9 + y² + 22y + 121

-12x - 20y = 120

-3x - 5y = 30    ..........equation 1.

From PB² = PC², we have:

(x - (-3))² + (y - (-11))² = (x - 3)² + (y - (-8))²

(x + 3)² + (y + 11)² = (x - 3)² + (y + 8)²

x² + 6x + 9 + y² + 22y + 121 = x² - 6x + 9 + y² + 16y + 64

12x + 6y = -57     ..........equation 2.

Solving eqn. 1 and eqn. 2 simultaneously, we have:

x = -2.5 and y = -4.5.

Therefore, the coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).

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The total area available for cars to park will be 858m².

The area of the parking lot will be:

= 78 × 19

= 1482m²

The area of aisle will be:

= 8 × 78

= 624m²

The available area will be:

= 1482m² - 624m²

= 858m².

The compact parking spaces that will fit in the lot will be:

N × 12.5 = 858

N = 858/12.5

N = 68

The non compact parking spaces that will fit in the lot will be:

N × 16.5 = 858

N = 858/16.5

N = 52

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Answer:

Step-by-step explanation:

The domain is the set of x values, and the range is the set of y values.

The solution of the system of linear equation are (1, 7)

3a + 6b = 45

2a - 2b = -12

multiply equation(ii) by 3

Therefore,

3a + 6b = 45

6a - 6b = -36

9a  = 9

a = 1

Hence,

2(1) - 2b = -12

2 - 2b = -12

-2b = -12 - 2

- 2b = - 14

b = -14 / -2

b = 7

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1) [tex]4x+5=-6x+5[/tex] (given)

2) [tex]4x=-6x[/tex] (subtraction property of equality)

3) [tex]10x=0[/tex] (addition property of equality)

4) [tex]x=0[/tex] (division property of equality)

Answer:

GIVEN THAT THE TRIANGLES ARE SIMILAR THEREFORE we can use similarity theorem.

Step-by-step explanation:

Answer: $2200

Step-by-step explanation:
20% = 0.2
2750 x 0.2 = 550
2750 - 550 = 2200

OR

2750 x (1-0.2) =
2750 x (0.8) = 2200

Answer:

£2200

Step-by-step explanation:

Formula:

20% off

so:

2750x0.20= x Price of car with 80% off

2750-x= Price of car with 20% off

Find answer:

(look in image to see my work on 2750x0.20, I used Microsoft Whiteboard)

2750x0.20=550.00

2750-550=2200

The weight of each one of the five little girls if taken separately is 242.4 lb.

The weight of each girl can be determined from the average weight of the girls.

Weight of each girl = (Total weight) / number of girls

W = (129 + 125 + 124 + 123 + 122 + 121 + 120 + 118 + 116 + 114)/5

W = 1,212/5

W = 242.4 lb

Thus, the weight of each one of the five little girls if taken separately is 242.4.

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The discount percent for the given transaction is calculated as; 6.11%

We are given;

Mark Price; M.P = 4500

Now, formula for discount amount is;

Discount amount = %Discount * M.P

Discount amount = x% * 4500 = 45x

Also;

Selling price is;

S.P = M.P - Discount Amount

S.P = 4500 - 45x

VAT = Vat% * S.P

VAT = (10%*4500) - 45x

VAT = 450 - 45x

S.P with VAT = S.P + VAT Amount = 4500 - 45x + 450 - 45x = 4950 - 90x

Thus;

4950 - 90x = 4400

Solving for x gives;

x = 6.11%

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280 adults were there in the train.

What is linear equation definition and example?

Given,

      Total children are in the train = 40

     1/8  are children in train and no of children in train ,

      ∴ 1/8 × x = 40

     x = 40 × 8 ⇒ 320

The no of  passenger in train  = 320

in total passenger, 40 are children .

So, rest adults passengers are = 320 - 40 ⇒ 280

There fore, 280 adults were there in the train.

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The amount Cindy should increase for each dimension of the scaled model will be 12 meters.

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Given that:-

The scale model will be solved as follows:-

Present volume = 2 x 4 x 6 = 48 cubic meters

Let the lengths be increased by x meters now the new volume will be:-

( 2 + x ) ( 4 + x ) ( 6 + x ) = 48 x 84

( x² + 6x + 8 ) ( 6 + x ) = 48 x 84

( x³ + 44x + 12x² - 3984 ) = 0

By solving the cubic equation we will get the value of x = 12 meters.

Therefore the amount Cindy should increase for each dimension of the scaled model will be 12 meters.

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Okay, so let's call B = the number of sandwiches Bill sells

and P = the number of sandwiches Pete sells

Since Bill sells 7 times as many sandwiches as Pete, then

B = 7P

And the difference between their sales is 414 sandwiches. Since we know that Bill sells more than Pete, then

B - P = 434

So, now we can substitute for B from the equation above B = 7P

x = bill's

y = pete's

x = 8y

B - P = 434

7P - P = 434

6P = 434

P = 72.33

Therefore, Pete sells 72.33 sandwiches

Bill sells 7 x 72.33 = 506 sandwiches.

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The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

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The tangents that exists between the two given circles are not common tangents because they are not of the same size or circumference.

A tangent can be defined as the plane line that touches a curved surface such as a circle but doesn't pass through the circle.

From the diagram given, the two circles are not of the same size, that is, they have different circumstances. This means that the point where the line meets the both circles are not the same.

Therefore, the tangents that exists between the two given circles are not common tangents.

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The confidence interval comes out to be (0.685,0.735).

Calculating the Confidence Level and Other Terms

The confidence level can be calculated as follows,

z = [tex]\frac{36}{40} * 100%[/tex]%  

z = 90 %

The margin error is given as, E= 0.025

The p value in this case is 0.71

Calculating the Confidence Interval

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

Confidence interval can be obtained by using the following formula,

(p-E, p+E) = (0.71-0.025, 0.71+0.025).

Therefore, the confidence interval is (0.685, 0.735).

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Total time for whole journey would be 3 hours.

The total trip is divided into three intervals :-

Hence to find the total time of the trip we need time taken in each interval and just add them up.

The final expression would be :-

Total time taken = Time taken by bus + Time taken by train +

                                Time taken to change between them

Given:-

Thus Total time for whole journey would be 3 hours.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Area of shaded region = 34 cm²

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Area of shaded region = Area of bigger rectangle - Area of smaller rectangle.

Area (big) :

[tex] \qquad❖ \: \sf \:13 \times 6[/tex]

[tex] \qquad❖ \: \sf \:78 \: \:c m {}^{2} [/tex]

Area (small) :

[tex] \qquad❖ \: \sf \:11 \times 4[/tex]

[tex] \qquad❖ \: \sf \:44 \: \: cm {}^{2} [/tex]

Area of shaded region :

[tex] \qquad❖ \: \sf \:78 - 44[/tex]

[tex] \qquad❖ \: \sf \:34 \: \: cm {}^{2} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Area of shaded region = 34 cm²

It will require 2 tablespoons of salt for just 1 tablespoon of sugar for the combination.

Word problems are a systematic approach used in mathematics for solving real-life cases by determining unknown values.

From the given information:

i.e.

11 tablespoon of sugar  + 22 teaspoon of salt = 1 recipe

Then it will require 2 tablespoons of salt for just 1 tablespoon of sugar.

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To find x = [tex]\frac{1}{2} (AB+CD)[/tex]

[tex]x=\frac{1}{2} (46+25)\\\ x=\frac{1}{2} (71)\\ x =35.5[/tex]

Hope it helps!

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

[tex]6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136[/tex]

As the first differences are not the same, calculate the second differences:

[tex]14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is:  3n²

Compare 3n² with the given sequence:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}[/tex]

The second operations are different, therefore calculate the differences between the second operations:

[tex]3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18[/tex]

As the differences are the same, we need to add 5n as the second operation:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}[/tex]

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

The additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.

From the information, Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.

In this case, the additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.

Also, the additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem is that AX and CX are congruent.

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Answer:

What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?

✔ AC and BD are perpendicular.

What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?

✔ AX and CX are congruent.

Step-by-step explanation:

right on edge

Answer:

17 sq. cm

Step-by-step explanation:

1st you split into 2 smaller shapes

Smaller shape:

A = lw

= 1(2)

= 2

Bigger Shape:

A = lw

= 3(5)

= 15

Add them together

15 + 2 = 17