An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is 24pi inches. The artist plans to fill the inside of each dot with blue colored glass.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.

The two angles are 18 degrees and 72 degrees. The smaller angle is one-fourth of the larger, and they add up to 90 degrees because they are complementary.

In mathematics, complementary angles are two angles whose measures add up to 90 degrees. Based on the question, let's denote the smaller angle as x and the larger angle (its complement) as y.

Given that x is 1/4 of y, we can write the equation x = y/4.

Also, since they're complementary, their measures add to 90 degrees, giving the equation x + y = 90.

From x = y/4, it can be inferred that y = 4x. Substituting y in the second equation we get x + 4x = 90, which simplifies to 5x = 90. Dividing both sides by 5, we have x = 18.

To find y, substitute x = 18 into the equation y = 4x, giving y = 4*18 = 72. Therefore, the measures of the two angles are 18 and 72 respectively.

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Answer:

30 & 60

Step-by-step explanation:

The tutor is correct, besides the fact that the interior angles would equal 180, not 190. Typos happen.

Answer:

(1/3, -13/3)

Step-by-step explanation:

I know this is correct because I got this question right on my quiz. Exact question, word for word. Hope this helps!

Answer:

the common difference of the sequence (d) = -3

Step-by-step explanation:

Given sequence is 1st term, 2nd term, 3rd term

= 5, 2, -1

It is an arithmetic sequence.

The common difference (d) = second term - first term

d = 2 - 5

d = -3

Therefore, the common difference of the sequence (d) = -3

Hope this will helpful.

Thank you.

The answer is true. This was just on my quiz and I know its correct.

Answer:

5 2/3

Step-by-step explanation:i thought this problem was literally impossible to do and its stopped me from progressing but i finally found out the answer and here it is

To find the missing digit to make 2,72_ divisible by 6, add the digit 4.

To find the digit that makes 2,72_ divisible by 6, we need to focus on the divisibility rules for 6. In this case, a number is divisible by 6 if it is divisible by both 2 and 3. For 2, the last digit must be even, and for 3, the sum of the digits must be a multiple of 3.

Given the number 2,72_, the blank digit needs to be 4 to make the number divisible by 6. This is because when the digit 4 is added, the number becomes 2,724, which is divisible by both 2 and 3.

Answer(-3,2)

Step-by-step explanation:

Answer:

No this is not the sequence geometric.

Step-by-step explanation:

Given : 2, -4, -16, -36, ...

To find : Is the sequence geometric? If so, identify the common ratio.

Solution : We have given that 2, -4, -16, -36, ...

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Geometric Sequence like this:

{a, ar, ar², ar³, ... }

On comparing

2, -4, -16, -36, ...

{ 2 , 2 ×-2, 2×(-2)², 2×(-2)³..

So we get { 2, -4, -8, -16...

Therefore , No this is not the sequence geometric.

Since the quotient between consecutive terms is different, the sequence is not geometric, and the correct option is:

In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio.

In this problem, the sequence is: {2, -4, -16, -36, ...}

[tex]-\frac{4}{2} = -2[/tex]

[tex]\frac{-16}{-4} = 4[/tex]

Different quotients, hence not geometric, and option D is correct.

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Answer:

Step-by-step explanation:

-5(x -6) = 10x . . . . . given

-5x +30 = 10x . . . . distributive property of multiplication over addition

30 = 15x . . . . . . . . addition property of equality (5x was added to both sides)

2 = x . . . . . . . . . . . division property of equality (both sides were divided by 15)

hope this helped

Answer:

it is A  "No, this is not a direct variation."

Step-by-step explanation:

i jus took the test

Pressure and volume have an inverse relationship, known as Boyle's Law, where if pressure increases, volume decreases and vice-versa. This is represented by the mathematical equation P.V = k, where k is a constant. This is graphically represented as a hyperbola.

From the details available, it can be concluded that the relationship between pressure (P) and volume (V) is not a direct variation, but an inverse one. This relationship is also known as Boyle's Law, which states that the product of the pressure and volume for a given amount of gas at a constant temperature remains constant. Mathematically this can be written as P = k·1/V or P.V = k, where k is a constant.

This means that when the pressure increases, volume decreases and vice-versa. If you were to graphically represent this, you would get a hyperbola, not a straight line, which distinguishes it as an inverse relationship rather than a direct one.

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Answer: The steps for using a compass and straightedge to construct a square are as follows :-

1. Use a straightedge to draw line a and label a point on the line as point P.

2. Construct a line perpendicular to line a through point P.

3. Label a point on this line as point R.

4. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→.

5. Label the points of intersection as points S and T.

6. Keeping the same compass width, place the compass on point T and draw an arc in the interior of∠SPT to intersect the previously drawn arc.

7. Label the point of intersection as point Q.

8. Without changing the compass width, place the compass point on point S and draw an arc in the interior of∠SPT .

9. Use the straightedge to draw QS ,QT,SR and RT.

Here we have finished with the square RTQS.

The cost of the bench is $ 375

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of the bench be = B

Now , the equation will be

Let the cost of the table be = T

Now , the total cost of the table and bench = $ 799

Substituting the values in the equation , we get

B + T = 799   be equation (1)

And , garden table costs $49 more than the bench

So , T = 49 + B   be equation (2)

Substituting the value of T from equation (2) in equation (1) , we get

B + 49 + B = 799

2B + 49 = 799

Subtracting 49 on both sides of the equation , we get

2B = 750

Divide by 2 on both sides of the equation , we get

B = $ 375

Therefore , the value of B is $ 375

Hence , The cost of the bench is $ 375

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To write intervals where f(x) is greater than or equal to 0, solve the equation f(x) >= 0 for x. The solutions are then expressed in interval notation. For instance, x >= 3 is written as [3, infinity).

To write the interval for which f(x) is greater than or equal to 0 in interval notation, you first need to establish where the function is above or touching the x-axis. With algebraic functions, you simply solve the equation f(x) >= 0 for x to find where the function is non-negative. You then write these solutions in interval notation. For example, if your solution was x >= 3, you would write this in interval notation as [3, infinity). Also, keep in mind that round brackets ( ) are used when the number is not included in the interval while square brackets [ ] are used when the number is included.

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The number of minutes taken to fill the pool in three-fourths full is 225.

Given that,

Based on the above information, the calculation is as follows:

[tex]= (12000 \times \frac{3}{4}) \div 40[/tex]

= 225 minutes

Therefore we can conclude that the number of minutes taken to fill the pool in three-fourths full is 225.

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x = 6cm * sin(50) = 4.59

 rounded to 4.6

 Answer is C

Answer:

option C is correct    

The approximate value of x is, 4.6 cm(nearest to tenth)

Step-by-step explanation:

In the given figure; the triangle is right angle triangle:

Label the figure:

then, the triangle XYZ is right angle triangle.

Using trigonometric ratio:

The ratio of the opposite side of a right triangle to the hypotenuse is called  the sine. i.e,

[tex]Sine=\frac{opposite}{Hypotenuse}[/tex]

using sine ratio in triangle XYZ:

[tex]\sin 50^{\circ} = \frac{XY}{XZ}[/tex]

Substitute the value of XY = x cm and XZ = 6 cm in above ratio:

[tex]\sin 50^{\circ} = \frac{x}{6}[/tex] or

[tex]0.76604444247801 = \frac{x}{6}[/tex]

Simplify:

[tex]x= 4.59626665[/tex] cm

Therefore, the approximate value of x nearest to tenth is, 4.6 cm

Answer:

A. The ball is at the same height as the building between 8 and 10 seconds after it is thrown.

C. The ball reaches its maximum height about 4 seconds after it is thrown

Step-by-step explanation:

edg.

The percent error of the given problem is 1% inaccuracy.

Suppose the actual value and the estimated values after the measurement are obtained. Then we have:

Error = Actual value - Estimated value

We have been given that accepted value of a length measurement is 200 cm and the experimental value is 198 cm.

Actual value = 200

Estimated value = 198

The percent accuracy,

198/200 x 100%  

= 99%

Therefore,

Error = Actual value - Estimated value

Percent Inaccuracy: 100 - 99%

= 1% inaccuracy

Hence, the percent error of the given problem is 1% inaccuracy.

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