A circle is inscribed in a regular hexagon with side length 12 units. Find the value of x.

Answers

Answer 1

The image of the inscribed circle is missing so i have attached it.

Answer:

x = 35

None of the given options are correct.

Thus, Option D is the answer.

Step-by-step explanation:

From the attached image, we can see that there are two lines projecting out of the centre of the circle with one having it's endpoint touching the edge of the hexagon while the other is perpendicular to the centre of a side of the hexagon and labeled x has it's endpoint touching both the circumference and the hexagon side.

Since line labeled x projects from the centre of the circle to the circumference, we can say that the radius is x.

The triangle formed is a right angled triangle with the other part touching only the hexagon as the hypotenuse.

We see the remaining part between the circle and the hexagon of this hypotenuse line given as 2.

Thus, hypotenuse = x + 2

This is because from the centre to the circumference is x as earlier discussed and this hypotenuse line crosses the circumference of the circle before touching the edge of the hexagon.

Using pythagoras theorem, we can find x:

x² + 12² = (x + 2)²

x² + 144 = x² + 4x + 4

x² will cancel out to give;

4x + 4 = 144

4x = 144 - 4

4x = 140

x = 140/4

x = 35

A Circle Is Inscribed In A Regular Hexagon With Side Length 12 Units. Find The Value Of X.

Related Questions

252 = 42 x 6
Which statement does the equation represent? Answer options with 4 options
A. 42 is 6 more than 252.
B. 252 is 42 more than 6.
C. 42 is 6 times as many as 252.
D. 252 is 42 times as many as 6.

Answers

Answer:

C. 42 is 6 times as many as 252

Step-by-step explanation:

because 42×6 = 252

Conceded goals: 0,1,2,3,4 Frequency:2,8,4,10,6 What is the mean number of goals conceded

Answers

Answer:

2.333

Step-by-step explanation:

Given that:

Conceded goals: 0,1,2,3,4

Frequency:2,8,4,10,6

Mean(m) = Σ(fx) / Σf

Σfx = (0*2) + (1*8) + (2*4) + (3*10) + (4*6) = 70

Σf = (2 + 8 + 4 + 10 + 6) = 30

Hence,

Mean = 70 / 30

Mean = 2.333

A young sumo wrestler goes on a special diet to gain weight.
The variable www models the wrestler's weight (in kilograms) after the wrestler has been on a special diet for ttt months.
w=80+5.4tw=80+5.4tw, equals, 80, plus, 5, point, 4, t
How much weight does the wrestler gain every 222 months?
kilograms

Answers

Answer:

10.8 kg

Step-by-step explanation:

w = 80 + 5.4t

At time 0, when he starts the diet, his initial weight is

w = 80 + 5.4(0)

w = 80

80 kg.

After 2 months, t = 2. His weight is

w = 80 + 5.4t

w = 80 + 5.4(2)

w = 80 + 10.8

w = 90.8

90.8 kg.

His gain in 2 months was 90.8 kg - 80 kg = 10.8 kg

Answer: 10.8 kg

The wrestler gains 10.8 kg every 2 months.

What is an equation?

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

We have been given an equation that models the wrestler's weight (in kilograms) after the wrestler has been on a special diet for t months.

w = 80 + 5.4t

We need to find his weight after 2 months.

At time t = 0, when he starts the diet, the wrestler's initial weight would be,

⇒ w = 80 + 5.4(0)

⇒ w = 80 kg

After 2 months, t = 2 the wrestler's weight  weight would be,

⇒ w = 80 + 5.4(2)

⇒ w = 80 + 10.8

⇒ w = 90.8 kg

We need to find the weight gain in 2 months.

90.8 - 80 = 10.8 kg

Therefore, the wrestler gains 10.8 kg every 2 months.

Learn more about an equation here:

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which expression is equivalent to 4 - (-7)​

Answers

Answer:

4 + 7

(also 11)

Step-by-step explanation:

Answer:

7+4 or 11

Step-by-step explanation:

7+4 since 4-(-7) makes a mega plus.

PLEASE ANSWER FAST WILL GIVE YOU BRAINLEST LOL
You are testing two scales for accuracy by weighing two different objects.
Use the drop-down menus to complete the statements about the scales' accuracy.

Answers

Answer:

This is because the object on the 1st scale weighs (more) than the object on second scale, each pound of error results in a (lesser) percent error. The first scale was (10) pounds off the second scale,was (3) pounds off, so 1st scale was (10)% off 2nd scale was (12)% off.

Answer:

Because the object on Scale 1 weighs more than the object on Scale 2, each pound of error results in a lesser percent error. Scale 1 was 10 pounds off and Scale 2 was 3 pounds off, so Scale 1 was 10% off and Scale 2 was 12% off.

Step-by-step explanation:

Got it right on TTM so yeah! :)

Miss Rojas has a container of Jolly Ranchers on her desk. The ratio of Red Jolly Ranchers to Green Jolly Ranchers is 3 to 7. If there are 42 green jolly ranchers in the container, what is the total amount of Jolly Ranchers in the container?

Answers

Answer:

The total amount of Jolly Ranchers in the container is 60 Jolly Ranchers

Step-by-step explanation:

We have a ratio of

Red Jolly Ranchers : Green Jolly Ranchers

3:7

Sum of the proportion = 3 + 7 = 10

Hence:

Let the total number of jolly ranchers = x

7/10 of x = 42 Green Jolly Ranchers

Hence:

7/10 × x = 42

7x /10 = 42

Cross Multiply

7x = 420

x = 420/7

x = 60 Jolly Ranchers

The total amount of Jolly Ranchers in the container is 60 Jolly Ranchers

Can the hypotenuse or a leg be a decimal? Why or why not?

Answers

Answer:

yes

because the of use the Pythagoras theorm

Alia made a scale drawing of a square park, which has a side length of 30 feet. She used the scale 3 centimeter = 5 feet. What will be the area of the scale drawing?

Answers

Answer:

324cm²

Step-by-step explanation:

Given the scale conversion;

3 centimeter = 5 feet

x = 30 feet

Cross multiply

5x = 3 * 30

5x = 90

x = 90/5

x = 18cm

Hence the side length in cm is 18cm

Area of the square = L²

Area of the square = 18²

Area of the square = 324cm²

Hence the area of the scale drawing is 324cm²

A circular spinner for a game has a radius of 5 cm. The probability of winning on one spin of this spinner is $\frac{2}{5}$. What is the area, in sq cm, of the WIN sector? Express your answer in terms of $\pi$.

Answers

The total area of a circle is pi * radius^2

The total area of the circle is pi x 5^2 = 25pi sq. cm.

2/5 of this is success, so the answer is 2/5 * 25pi = 10 pi sq. cm.

Probability
Help me with this one plzzz

Answers

Answer:

a. 5/10 = 50%

b. likelihood you'll draw a card with a B on it

I'm not sure about c.

answer all questions please.

Answers

Domain: -∞ ≥ x ≥ ∞
Range: y ≥ 0
This graph shows a function

This table shows a proportional relationship between the number of cups of lemonade and strawberry juice used for
strawberry lemonade.
Cups of
Lemonade
Cups of
Strawberry
juice
1
3
4
12
21
Enter the number of cups of lemonade used for 1 cup of strawberry juice.
cups

Answers

Answer:

number of cups of lemonade used = 1/3 cups

Step-by-step explanation:

number of cups of lemonade : strawberry juice

= 1 : 3

Enter the number of cups of lemonade used for 1 cup of strawberry juice.

Let

x = number of cups of lemonade used

number of cups of lemonade : strawberry juice

= x : 1

Equate both ratios to get x

1 : 3 = x : 1

1/3 = x / 1

Cross product

1*1 = 3 * x

1 = 3x

Divide both sides by 3

x = 1/3 cu

number of cups of lemonade used = 1/3 cups

2. Which expression is equivalent to 1/4 n – 16? ​

Answers

Answer:

1/4n - 16 =

1/4(n - 64)

Step-by-step explanation:

Two expression are said to be equivalent, if after substituting the value of variable by any constant the numerical value of both original expression and equivalent expression are same.

Determine the sign of each product and place it in the correct category​

Answers

Answer:

sorry i had too

Step-by-step explanation:

someone passed this to me) 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Identify the following division expressionS that have a quotient of 25. (MORE THAN ONE ANSWER)
(A) 125/5

(B) (100/20) + (100/5)

(C) (100/5) + (25/5)

(B) 125/25

(MULTIPLE CHOICE BRAINLIST IF RIGHT)

Answers

Answer:

a and c are correct

Step-by-step explanation:

i hoped this helped

is 49 greater than or less than 7.1​

Answers

Answer:

Greater

Step-by-step explanation:

just because

Answer:

greater

Step-by-step explanation:

49>7.1

how many ducks are left if they started with 8 and 3 ran away?

Answers

Answer:

5?xd

Step-by-step explanation:

Currently, professional men's basketball players score an average of 18.2 points per game with a standard deviation of 4.5 points. The current top-scoring professional basketball player scores an average of 36.2 points per game. In one season in the 1990s, professional basketball players averaged 13.2 points per game with a standard deviation of 3.7 points. The top-scoring professional basketball player averaged 30.1 points per game. Which player did better relative to his peers?

Answers

Answer:

The 1990s basketball player did better than the current basketball player because his z-score is higher.

Step-by-step explanation:

i just took the test

Find the focus, this looks different from the other ones I’ve done which is why I am confused

Answers

Answer:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (0,0)(0,0)

Focus: (0,32)(0,32)

Axis of Symmetry: x=0x=0

Directrix: y=−32y=-32

xy−223−11600116223xy-223-11600116223

Step-by-step explanation:

please mark me as brainliest thank you

Answer:

A

(0, 3/2)

Step-by-step explanation

select all expressions whose value is negative

Answers

Answer:

"2 + 2(-3)(7) = negative

-2(27 ÷ 9)+4= negative

(14 ÷ -2)(-6)= positive

(4 - 10) - ( 8 ÷ ( -2))= negative

Step-by-step explanation:

2 + 2(-3)(7) = -40

-2(27 ÷ 9)+4= -2

(14 ÷ -2)(-6)= 42

(4 - 10) - ( 8 ÷ ( -2))= -2"

In a school of 450 students, 110 of them are in the choir, 240 of them are in the band and 60 students are in the choir and the band.
Please help I've been trying to solve this for an hour (T-T)

Answers

There are 270 in band an 140 in choir and 40 students left

Find xy when x(-7,10) and y(3,4)

Answers

Answer:

Distance xy = 11.66 unit (Approx)

Step-by-step explanation:

Given:

x(-7,10)

y(3,4)

Find:

Distance xy

Computation:

Distance = √(x2-x1)²+(y2-y1)²

Distance xy = √(3+7)²+(4-10)²

Distance xy = √ 100 + 36

Distance xy = 11.66 unit (Approx)

Nat is thinking of a four-digit counting number. The thousands digit and the hundreds digit are the same. The sum of all 4 digits is 28. The four-digit number is an odd multiple of 5. Exactly two digits are even. What is Nat’s number?

Answers

The answer is C, 2240.

Explanation from the book makes more sense now that I've thought about it a bit more.

Let ABCD be your four digits; D has to be odd since the four-digit number is odd (5 odd digits from the sequence). A has 8 options (1 thru 9, but one of the unit is reserved for digit D); B has 8 options aswell (0 thru 9, again one digit is reserved for digit D); C has 7 options (0 thru 9; one digit accounted for D and two A and B); D has 5 options since it must be odd.

8*8*7*5 = 2240

We want to use the given information to find a 4-digit number.

We will get the number: 8,875

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

A general 4-digit number can be written as:

a*1,000 + b*100 + c*10 + d

Where a, b, c, and d are whole numbers between [0, 9].

We also know that:

"The thousands digit (a) and the hundreds digit (b) are the same"

a = b.

"The sum of all 4 digits is 28"

a + b + c + d = 28

"The 4-digit number is an odd multiple of 5"

All the multiples of 5 end with a 0 or a 5, this is an odd one, so it must end with a 5, then we know that:

d = 5

"Two of the digits are even".

Ok, now let's write the equations that we found

a = b

a + b + c + d = 28

d = 5

Because of the last statement, only two digits are even, and we have that a is equal to b, the two even numbers must be these two, then we know that:

a is even.

And from the first equation, we can rewrite the second one as:

a + a + c + d = 28

Using the third equation and replacing it here, we have:

a + a + c + 5 = 28

2*a + c = 23

Now we can try to input different values of a in the equation, and see what value of c we get:

if a = 2, then:

2*2 + c = 23

4 + c = 23

c = 23 - 4 = 19

But c can be, at max, 9, then we can discard this.

Now let's try with a larger value for a, this time a = 8.

2*8 + c = 23

16 + c = 23

c = 23 - 16 = 7

c = 7

This is correct, then we can conclude that:

a = 8b = 8c = 7d = 5

Then the 4-digit number is:

8,875

If you want to learn more, you can read:

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Drag each figure to show if it is similar to the figure shown or why it is not similar.

Answers

Answer:

1st one - not similar diff ratio

2nd- similar

3rd- not similar diff shape

4- not similar diff ratio

5- similar

6- not so sure but i would go w either not similar diff shape or similar

Step-by-step explanation:

Find X
Coordinates are: 3x, 3x+10, 2x+10

Answers

Answer:

D. 20

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Geometry

All angles in a triangle add up to 180°

Step-by-step explanation:

Step 1: Set Up Equation

3x + 3x + 10 + 2x + 10 = 180

Step 2: Solve for x

Combine like terms:                    8x + 20 = 180Isolate x term:                              8x = 160Isolate x:                                       x = 20

See the Pic for my question.

Answers

Answer:

C. 7

Step-by-step explanation:

4 * Sum (i = 1 to 3) (1/2)^(i - 1) =

= 4 * [(1/2)^0 + (1/2)^1 + (1/2)^2]

= 4 * [1 + 1/2 + 1/4]

= 4 * [7/4]

= 7

Answer:

7

Step-by-step explanation:

because I'm smart like that

Drag and drop an answer to each box to correctly complete the proof.

Given: m | n m 1 = 50 m 2 = 48°, and line s bisects ABC

Prove: m/3

49°

It is given that m | n m

1 = 50 m

2

- 48° and fine s bisects

ABC By the

m/DEF = 989 Because

angles formed by two parallel lines and a transversal are congruent

DEF

A BC

SO MZABC 98 By the

angles 4 and 5 are congruent

and m

4 is half m

ABC So the measure of in24_49 Because vertical angles

Answers

Answer:

Step-by-step explanation:

The correct question is shown in the image attached below.

Recall that: the line m is parallel to line n. In addition to that, [tex]m \angle 1 = 50^0[/tex] and [tex]m \angle 2 = 48^0[/tex], and [tex]\angle ABC[/tex] is bisected by line s.

At this moment, by the angle addition postulate, angle DEF i.e.

∠DEF [tex]= m \angle 1 + m \angle 2[/tex]

∠DEF = 50° + 48°

∠DEF = 98°

Similarly, using the rule of the alternate exterior angle ∠DEF = ∠ABC (∵ alternate exterior angles exhibit congruency).

Furthermore, By the definition of a bisector, angles 4 and 5 are congruent due to the fact that the line of a bisector splits the angle into two equal parts.

m∠4 = m∠5

98/2 = 49°

Finally;

from the diagram, angle 3 and 4 are vertical angles

Thus, m∠3 = 49 by substitution property of equality ( because vertical angles are congruent angles).

1) Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $20 for every 400 envelopes she finishes. Jason earns $10 for every 250 envelopes he finishes.

A) Create tables, draw graphs, and write equations that show the earnings, y, as functions of the number of envelopes stuffed, x, for both Anna and Jason.

B) Who makes more from stuffing the same number of envelopes? Explain how you know using the information above.

C) Anna has savings of $100 at the beginning of the summer and she saves all of her earnings from her job. Graph her savings as an equationof the number of envelopes she’s stuffed, n. How does this graph compare to her previous earnings graph? What is the meaning of the initial value and slope in each case?

D)You survey 6 other employees and findthe following data on envelopesstuffed (x) and dollars earned(y). Plot a trend lineon the graph. Find the equation of the trend line.

Answers

Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. Anna earns $20 for every 400 envelopes. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x[/tex]

The table is:

x:   200     400       600     800     1000

y:    10        20          30        40       50

ii)

Jason has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

[tex]y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x[/tex]

x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table of Anna and Jason we can see that Anna makes more stuffing than Jason for the same number of envelopes.

c) Anna has a savings of $100 initially. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100[/tex]

Therefore from the graph there is a y intercept at 100. That is the earnings starts initially is $100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value of y at x = 0)

For the first graph, the slope is 1/20 with an initial value of 0 while for the second graph the slope is 1/15 with an initial value of 100

D) The trend line pass through the points (10, 10) and (100, 40), hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}[/tex]

solve this and explain it to me please

it's weird my brother And I am fighting for this my brother says it's p but I think it's P-Q​

Answers

Answer: U - (P - P∩Q)

Where U represents the universal set.

Step-by-step explanation:

In the image, we can see that the shaded part is all the region minus the part of P that does not share elements with Q.

This part of P can be written as:

P - P∩Q

there we write:

"The elements of P, minus the elements that P share in common with Q"

Then to write the shaded area, we need to write the universal set, U, minus the thing we wrote above, this is:

U - (P - P∩Q)

What is the final amount if 1102 is increased by 2% followed by a further 1% increase? Give your answer rounded to 2 DP.

Answers

To increase by 2% you multiply to get 1102*0.02=22.04. You then add that to 1102, getting 1124.04. To then decrease it by 1% you multiply to get 1124.04*0.01=11.24. Subtract 11.24 from 1124.04 to get a final answer of 1112.8

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

The final amount of 1102 with a 2% increase followed by a 1% increase is 1135.28.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

We have,

Amount = 1102

Percentage increase = 2%

Another percentage increase = 1%

Now,

The final amount.

= 101% of 102% of 1102

This can be written as,

= 101/100 x 102/100 x 1102

= (101 x 102 x 1102) / 10000

= 1135.28

Thus,

The final amount of 1102 with a 2% increase followed by a 1% increase is 1135.28.

Learn more about percentages here:

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