A dog's leash is 4 m long and is attached to the corner of a 2 m × 2 m square doghouse at C, as shown. The dog is attached to the other end of the leash, at D. What is the area outside of the doghouse in which the dog can play? (A) 14π m^2 (B) 16π m^2 (C) 20π m^2 (D) 15π m^2 (E) 24π m^2

Answers

Answer 1

The area outside of the doghouse in which the dog can play is 16π m².

Thus, option (B) is correct.

Given:

The leash is 4 m long.

The doghouse is a 2 m × 2 m square.

First, the area of a square is given by side length squared

So, the area of the doghouse is:

Area of the doghouse = side length² = 2²

                                                             = 4 m².

Next, the area of the circle with a radius of 4 m.

The area of a circle is given by the formula A = πr²,

So, Area of the circle = π(4²) = 16π m².

Therefore, the area is 16π m².

Thus, option (B) is correct.

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Related Questions

PLEASE ASAP PLEASE I need this plewse

Answers

The answer is 182.3537

Answer:

182.353745

Step-by-step explanation:

[tex]\frac{0.482 x61.2^2}{\sqrt{98.01} }[/tex]

Exponent First!

61.2^2 = 61.2 × 61.2 = 3745.44

Next, start multiplying it by 0.482

3745.44 × 0.482 = 1,805.30208

Then Solve for the Square root of 98.01

[tex]\sqrt{98.01}=9.9[/tex]    

Finally, divide 1,805.30208 by 9.9    

1,805.30208 ÷ 9.9 = 182.353745

The question is in the picture :)

Answers

The correct name for a side of the angle is C!

Answer:

C. ED

Step-by-step explanation:

Solve this system of equations using the ELIMINATION method.

3x - 2y = 1

2x + 2y = 4

Answers

hope this helps please like and mark as brainliest

Answer:

x = 1

y = 1

Step-by-step explanation:

3x - 2y = 1

2x + 2y = 4

3x - 2y + 2x + 2y = 1 + 4

3x + 2x = 5

5x = 5

5x ÷ 5 = 5 ÷ 5

x = 1

2x + 2y = 4

2(1) + 2y = 4

2 + 2y = 4

2 - 2 + 2y = 4 - 2

2y = 2

2y ÷ 2 = 2 ÷ 2

y = 1

Check:

3x - 2y = 1

3(1) - 2(1) = 1

3 - 2 = 1

x and y being 1 works for the first equation.

2x + 2y = 4

2(1) + 2(1) = 4

2 + 2 = 4

x and y being one works for both equations.

Find the measure of CD⎯⎯⎯⎯⎯⎯⎯⎯.

A. 8
B. 6
C. 5
D. 7

Answers

Answer:

Using the property of intersecting secant:-

[tex](DE)(CE)=(FE)(LE)[/tex]

[tex](4)(x-1+14)=(5)(x-4+5)[/tex]

[tex]4(x+3)=(5x+1)[/tex]

[tex]4x+12=5x+5[/tex]

[tex]4x+-5x=5-12[/tex]

[tex]-x=-7[/tex]

[tex]x=7[/tex]

[tex]So, CD=x-1=7-1=6[/tex]

[tex]so,~your ~answer ~is ~B) ~6[/tex]

----------------------------hope it helps...have a great day!!

By intersecting secants theorem, the measure of CD is 6 units.

What is intersecting secants theorem?

The theorem states that when two secants intersect at an exterior point, the product of the one whole secant segment and its external segment is equal to the product of the other whole secant segment and its external segment.

For the given situation,

The diagram shows the circle with the two secants intersecting at the exterior point.

By intersecting secants theorem,

[tex](CE)(DE)=(LE)(FE)[/tex] -------- (1)

Here, CE = CD + DE

⇒ [tex]CE = (x-1)+4[/tex]

DE = 4

LE = LF + FE

⇒ [tex]LE = (x-4)+5[/tex]

FE = 5

On substituting the above values in 1,

⇒ [tex](x-1+4)(4)=(x-4+5)(5)[/tex]

⇒ [tex](x+3)(4)=(x+1)(5)[/tex]

⇒ [tex]4x+12=5x+5[/tex]

⇒ [tex]5x-4x=12-5[/tex]

⇒ [tex]x=7[/tex]

Thus CD = [tex]x-1[/tex]

⇒ [tex]7-1=6[/tex]

Hence we can conclude that by intersecting secants theorem, the measure of CD is 6 units.

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The question is in the pic.

Answers

Answer:

$100

$120 in and $20 out

Step-by-step explanation:

Answer:

the answer is $100

because if the bank is loosing 2% they are having to pay $20 bc 0.02 x 1,000= 20, and they are earning 12% they getting 120 bc 0.12 x 1,000 = 120, and 120-20= $100. you have to subtract the $20 because that is what the bank is paying, so it's losing money

In total, 28 chickens and pigs were on a farm. In total, there are 90 feet. How many chickens? How many pigs?

Answers

Answer:

17pigs and 11 chicken  

Step-by-step explanation:

7.) Evaluate the expression.
12 - 3V 25

Answers

Answer:

-3

Step-by-step explanation:

[tex]\sqrt{25}[/tex] is equal to 5, so we can sub it in the equation.

This gives 12-3×5 or 12-15.

This solves to -3.

**This content involves simplifying surds, which you may wish to revise. I'm always happy to help!

Translate this sentence into an equation. 46 is the sum of 21 and Mabel's savings.

Answers

You have to add 21 by M to get the answer that you are looking for

find the value of x in the equation 4x-2=2x+10​

Answers

Answer:

x = 6

Step-by-step explanation:

Given

4x - 2 = 2x + 10 ( subtract 2x from both sides )

2x - 2 = 10 ( add 2 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

What is the factored form of 6n4 – 2413 + 18n?
ово
Bn(n° +4nº +31)
Bn(-° +30
6n(n°-4n2+3)
o Bn(n° +4n? +3)
O

Answers

the third option
6n(n3-4n2+3)

Option C is correct, 6n(n³-4n²+3) is the  factored form of expression 6n⁴ – 24n³ + 18n

What is Expression?

An expression is combination of variables, numbers and operators.

The given expression is 6n⁴ – 24n³ + 18n.

Six times of n power four minus twenty four times of n cube plus eighteen times of n.

6n⁴ – 24n³ + 18n.

Now we have to find the factored form of 6n⁴ – 24n³ + 18n.

Take 6n as common

6n(n³-4n²+3)

Hence, Option C is correct, 6n(n³-4n²+3) is the factored form of expression 6n⁴ – 24n³ + 18n

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PLS HELP ME SOLVE THIS
2a × 3

Answers

Answer:

The answer will be 2a×3=6a

the answer is 2a•3= 6a

What is the range for this set of data? 7, 15, 12Mrs. Juarez graded ten English papers and recorded the scores. 92, 95, 100, 62, 88, 90, 100, 96, 89, 98 Which statements are true? Check all that apply.

Answers

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Please find the complete question in the attached file.

Arrange the value into the ascending order:

[tex]62, 88, 89, 90, 92, 95, 96, 98, 100, 100[/tex]

Calculating the Range:

[tex]= Greatest - Lowest\\\\= 100 - 62\\\\ = 38[/tex]

Outlier =  This might be the value "far" from other data values= 62

The range of scores would be, sans outlier,

 [tex]88, 89, 90, 92, 95, 96, 98, 100, 100[/tex]

Calculating the range without outlier [tex]= 100 - 88 = 12[/tex]

Inter Quartile Range [tex]= Q_3 - Q_1[/tex]

[tex]IQR = 98 - 89 = 11[/tex]

Calculating the IQR without outlier [tex]= 99 - 89.5 = 9.5[/tex]

Therefore,

Option a is "True".

Option b is "True".

Option c is "True".

Option d is "False".

Option e is "False".

Option f is "True".

Can you help me solve in any algebraic method ?

Answers

Answer:

Step-by-step explanation:

x²+(8+3)x +24=0x²+8x+3x+24=0x(x+8)+3(x+8)=0(x+8)(x+3)=0if,(x+8)=0 then,x+8=0x=-8,,if x+3=0 then,x=0-3x= -3,,
X^2+8x+3x+24=0
X(x+8)+3(x+8)=0
-> (x+8)x(x+3)=0
->{ x= -8
{ x=-3

(2x - 3)(4 - 3x) find the product of binomials

Answers

Answer:

6x²+17x-12

Step-by-step explanation:

(2x-3)(4-3x)

8x-6x²-12+9x

Reorder.

6x²+9x+8x-12

Combine like terms.

6x²+17x-12

---

hope it helps

The groundskeeper filled the first sandbox with sand to a height of 6 inches. What is the volume,
in cubic feet, of the sand that was used to fill the first sandbox to a height of 6 inches? Show or explain
how you got your answer
Enter your answer and your work or explanation in the space provided

Answers

Answer:

you didnt provide the other 2 measurements, its length x width x height for volume

Need help with some math

Answers

Answer:

A

Step-by-step explanation:

Desnity: mass/volume

3/20= .15

Find (4.0×105)÷(5.89×102) by using a calculator. Give your answer in scientific notation and round to two decimal places.

Answers

Answer: [tex]7\times 10^{-1}[/tex]

Step-by-step explanation:

Given

[tex](4.0\times 105)\div (5.89\times 102)[/tex]

First solve the brackets part in calculator, we obtain

[tex]\Rightarrow 420\div 600.78\\\\\Rightarrow \dfrac{420}{600.78}=0.69909\approx 0.70\\\\\Rightarrow 7\times 10^{-1}[/tex]

Belinda gets 1 3/4 h for lunch. She spends 1/3 of her lunch walking for exercise. How much time does Belinda spend walking ?

This unit is operations and fractions how would I solve this?​

Answers

35 minutes. 1 3/4 hour would be converted to 105 minutes. And then one third of that is 35. So 35 minutes is your answer.

Answer:

7/12 h

Step-by-step explanation:

1/3 of 1 3/4  =  1/3 of 7/4 = 1/3 x 7/4  =  7/12 h

What are the measures of Angles a, b, and c? Show your work and explain your answers.
400
a
650

Answers

Answer:

Step-by-step explanation:

angle a=40 degree (being vertically angles)

angle a + 90 +angle b=180 degree (being sum of interior angles of a triangle)

40 +90 +angle b=180

130 + angle b=180

angle b=180-130

angle b =50 degree

vrtically opposite of angle b

vertically opposite of angle b + missing angle=65 degree (sum of two intrior opposite angle is equal to the exterion anle formed)

40 degree + missing angle=65

missing angle=65-40

missing angle=25 degree

angle c+ vertically opposite of angle b + missing angle=180 degree (being sum of interior angles of a triangle)

angle c +50 +25 =180

angle c+75=180

angle c=180-75

angle c=105 degree

help me please ASAP

Answers

Answer:

A.

Step-by-step explanation:

Vertical shifts are represented by - or +, and they are not within the parenthesis. Since the function is being shifted down by 2 units, the correct answer is A.

Question and choices are in the photo please explain the answer

Answers

Answer:

[tex]\text{A) }68\:\mathrm{cm}[/tex]

Step-by-step explanation:

The perimeter of a polygon is equal to the sum of all the sides of the polygon. Quadrilateral PTOS consists of sides TP, SP, TO, and SO.

Since TO and SO are both radii of the circle, they must be equal. Thus, since TO is given as 10 cm, SO will also be 10 cm.

To find TP and SP, we can use the Pythagorean Theorem. Since they are tangents, they intersect the circle at a [tex]90^{\circ}[/tex], creating right triangles [tex]\triangle TOP[/tex] and [tex]\triangle SOP[/tex].

The Pythagorean Theorem states that the following is true for any right triangle:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or the longest side, of the triangle

Thus, we have:

[tex]10^2+TP^2=26^2,\\TP^2=26^2-10^2,\\TP^2=\sqrt{576},\\TP=24[/tex]

Since both TP and SP are tangents of the circle and extend to the same point P, they will be equal.

What we know:

[tex]TP=SP=24[/tex][tex]TO=SO=10[/tex]

Thus, the perimeter of the quadrilateral PTOS is equal to [tex]24+24+10+10=\boxed{\text{A) }68\:\mathrm{cm}}[/tex]

Answer:

the other one should get a brainliest.

I'm just answering to make it technically possible.

You are riding in a hot air balloon on Valentine’s Day withyour sweetheart. As you get ready to set your balloon downyou notice that while your balloon is 500 ft above ground, your friends balloon is 800 ft above ground. The plan is for both balloons to descend straight down. Your balloon willland right at the edge of the lake below, but it appears thatyour friends will be pretty far away. You can see a reflectionof their balloon right in the middle (direct center) of the 1200 ft wide lake below.How far away from the lake will your friends touch down?

(Don't mind my scribbles maybe they will help, maybe not)

Answers

Answer:

Try 750 ft?

Step-by-step explanation:

Proportion:

800/500 = 1,200/x

Solve:

1,200 / 800 = 1.5

1.5 * 500 = 750

Hope this helped!

Please mark as brainliest!

marcus purchased a sail boat for $56,900. he anticipates each year the boat will decrease in value by 8.1% from the previous year.


enter numbers in the boxes to write an exponential function that models the value in dollars of the boat x years after Marcus's purchase.

Answers

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Purchase price= $56,900

Decrease in value= 8.1% per year from the previous year

To calculate the value of the sailboat after x number of years, we need to use the following formula:

Future value= purchase price / (1 + decrease in value)^x

For 10 years:

FV= 56,900 / (1.081^10)

FV= $26,112.91

Can someone please help me ASAP!!

Answers

I DONT SPEAK ENGLISH, I'M BRAZILLIAN

Answer:

brainllest if right

b

Step-by-step explanation:

are the triangle similar
1-yes
2-no

Answers

1 (yes)
Step by Step Explanation:
This is because the interior angle of any triangle adds up to 180 degrees. If two angles of the triangles are equal in the same angle, such as angles GOT and NUF are both 97. Additionally it can be pictured that if the triangle TOG were to be flipped 180 degrees, it would resemble triangle FUN

Answer:

yes the triangle are similar

Determine whether the triangles are congruent. Explain your reasoning .
SAS (Side, Angle, Side) or ASA (Angle, Side, Angle)

Answers

Answer:

Step-by-step explanation:

The two triangle are congruent for the rule SAS

QP congruent to TU

angle P and angle T are both right

side PR is in common

1. If two lines are parallel, then the slopes of the lines would be...
A. opposite
B. Reciprocals
C. Equal
D. Opposite Reciprocals
E. Binomials
F. Quadratic

2. If two lines are perpendicular, then the slopes of the lines would be...
A. Opposite
B. Reciprocals
C. Equal
D. Opposite Reciprocals
E. Binomials
F. Quadratic

Answers

1. Slope of the lines would be equal

Find the 98th term of the arithmetic sequence -10, -8, -6, ...

Answers

First term = a= -10

common difference=d= -8+10 = 2

n= 98

the 98th term = a+(n-1)d = -10+ (98-1)2

= -10+(97)2 = -10 +194

=184

98th term of the given arithmetic sequence is 184.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

The given arithmetic sequence is -10, -8, -6,......

Here, a=-10, d=-8-(-10) = 2

So, aₙ=-10+(n-1)×2

aₙ=-10+2n-2

aₙ=2n-12

a₉₈=2×98-12

a₉₈=184

Therefore, 98th term of the given arithmetic sequence is 184.

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PLZ HELP LIMITED TIME

Answers

Answer:

32

Step-by-step explanation:

Durante 8 días el precio de una acción de una compañía X cae 720 pesos, en el noveno día sube 45 pesos y el decimo día cae 120 pesos, ¿Escriba y calcule el valor de las acciones al terminar el decimo día?

Answers

Answer:

Tras 10 días la acción habrá caído $795.

Step-by-step explanation:

Dado que durante 8 días el precio de una acción de una compañía X cae 720 pesos, en el noveno día sube 45 pesos y el decimo día cae 120 pesos, `para determinar el valor de las acciones al terminar el decimo día se debe realizar el siguiente cálculo:

X - 720 + 45 - 120 = Valor

X - 840 + 45 = Valor

X - 795 = Valor

Por lo tanto, tras 10 días la acción habrá caído $795.

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