Area of circles

Susan designed a circular pool with a diameter of 25 meters. what is the area of the bottom of the pool? round to rhe nearest tenth.

In the given diagram, line AB is parallel to CB. i.e. AB∥CD ∠EGB = 57°

then the value of ∠EHD = 57°

In this diagram, since AB is parallel to CD, we can infer that ∠EGB and ∠EHD are corresponding angles, and corresponding angles are congruent when a pair of parallel lines are intersected by a transversal. Given that ∠EGB = 57°, we conclude that ∠EHD is also 57° based on the properties of corresponding angles. Thus, ∠EHD = 57°.

When two parallel lines are intersected by a transversal, the corresponding angles formed on either side of the transversal are congruent. In this case, we are given that line AB is parallel to line CD, which implies that ∠EGB and ∠EHD are corresponding angles.

Given: ∠EGB = 57° (Given in the diagram)

Since AB || CD, ∠EGB ≅ ∠EHD (corresponding angles are congruent).

Therefore, ∠EHD = ∠EGB = 57°.

Hence, ∠EHD is also 57° based on the properties of corresponding angles.

In mathematical terms, we use the property of corresponding angles formed by a transversal intersecting two parallel lines to establish the congruence between ∠EGB and ∠EHD. This property is a fundamental aspect of geometry dealing with angles and parallel lines.

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The question appeared to ask about the impact of dilation on a polygon's perimeter, but the scale factor was not provided. Generally, the perimeter of a dilated polygon is the original perimeter multiplied by the scale factor. Another part of the student's question involved calculating the actual diameter of a swimming pool from a scale drawing using a provided scale factor.

The student appears to have asked a question about a dilation of a polygon and its effect on the perimeter, as well as having other queries related to scale factors and how they apply to various geometric figures and real-life objects. Unfortunately, the specific scale factor for the dilation in question 5 is not provided. However, generally speaking, when a figure is dilated by a scale factor, the length of all sides is multiplied by that factor. Given that the perimeter is the sum of all side lengths, the perimeter of the dilated polygon would also be multiplied by the same scale factor. So if a polygon has a perimeter of 18 units and it is dilated by a scale factor, to find the perimeter of the dilated image we multiply the original perimeter by the scale factor. It's important to note that without knowing the exact scale factor, we cannot determine what the new perimeter would be.

For question 12, to find the actual diameter of the pool, we need to use the scale factor provided, which is 1/72. If the scale drawing shows a diameter of 1(1/2) inches, we can calculate the actual diameter using the following:

The rest of the calculations follow a similar method, using the respective scale factors and measurements to determine the actual sizes or scale sizes of objects.

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The correct option is d. [tex]30\ units[/tex]. This means that the original polygon was dilated with a scale factor of to obtain the image with a perimeter of [tex]30\ units.[/tex]

To find the perimeter of the image of a polygon after dilation with a scale factor, we need to understand how dilation affects the dimensions.

1. Perimeter of the original polygon:

Let's denote the original perimeter of the polygon as [tex]\( P \)[/tex]. According to the problem, the original perimeter is [tex]18 \ units[/tex]

[tex]\( P = 18 \) \ units[/tex]

2. Dilation with a scale factor:

Dilation with a scale factor [tex]\( k \)[/tex] multiplies all dimensions (lengths of sides) of the polygon by [tex]\( k \).[/tex]

3. Perimeter after dilation:

After dilation with a scale factor [tex]\( k \)[/tex], the perimeter [tex]\( P' \)[/tex] of the polygon's image is given by:

[tex]\( P' = k \times P \)[/tex]

Here, [tex]\( k \)[/tex] is the scale factor.

4. Calculating the perimeter of the image:

The problem states that the polygon is dilated with a scale factor of [tex]\( \sqrt{3} \)[/tex]. So, [tex]\( k = \sqrt{3} \).[/tex]

Now, calculate [tex]\( P' \)[/tex]

[tex]\( P' = \sqrt{3} \times 18 \)[/tex]

[tex]\( P' = 18 \times \sqrt{3} \)[/tex]

[tex]\( P' = 18 \times 1.732 \)[/tex]

[tex]\( P' = 31.176 \)[/tex]

None of the given options match the exact calculated perimeter [tex]\( P' = 31 \) units[/tex]. However, based on the options provided, the closest answer to our calculated value is [tex]30\ units[/tex] (option d).

angles formed by these tosses are  [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.

Step-by-step explanation:

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

[tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ [tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]

⇒ [tex]c^2 -a^2 - b^2 = -2ab (cosx)[/tex]

⇒ [tex](cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}[/tex]

⇒ [tex](cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}[/tex]

⇒ [tex](cosx) =0.18310[/tex]

⇒ [tex]cos^{-1}(cosx) = cos^{-1}(0.18310)[/tex]

⇒ [tex]x = 79.45[/tex]

The Law of Sines (or Sine Rule) is very useful for solving triangles:

[tex]\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}[/tex]

We can now find another angle using the sine rule:

⇒[tex]\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}[/tex]

⇒[tex]sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}[/tex]

⇒[tex]Y = 59.02 degrees[/tex]

So, the third angle =[tex]180 - 79.45 - 59.02 = 41.53 degrees.[/tex]

Therefore, angles formed by these tosses are  [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.

Answer: 2/8; 3/6 and 3/5

Step-by-step explanation:

3/6 = 1/2 = 0.5

3/4= 0.75

2/8= 1/4 = 0.25

To arrange in the order of least to greatest= 2/8; 3/6 and 3/5

Answer:

-0.9659258 is the exact value

Answer:

Step-by-step explanation:

The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.

The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...

  (6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60

where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.

____

The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.

The values for Mar 12 through Mar 25 are ...

  3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070

Answer: Mar 18: 125

Mar 19: 318

Mar 20: 743

Mar 25: 15,070

Step-by-step explanation:

The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.

The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...

(6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60

where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.

____

The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.

The values for Mar 12 through Mar 25 are ...

3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070

Step-by-step explanation:

.

Answer: 9/12 + 4/12 which equals 13/12 or 1 1/12

Explanation: The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator. Keep the denominators the same with the answer then add!

Answer:

Step-by-step explanation:

The Pythagorean theorem states that for a right triangle, the sum of the square for each of the sides is equal to the square of the hypotenuse.

See attached for graphic and formula

Answer:

2^6

Step-by-step explanation:

2*2*2*2*2*2

There are six 2's multiplied together so the base is 2 and the exponent is 6

2^6

Answer:

B

Step-by-step explanation:

Angles at each vertex of a rectangle is right angle

Total bill amount = $ 189

Step-by-step explanation:

Given:

The bill amount = $ 175

Coupon = 10%

Coupon amount = [tex]\frac{10 \times 175}{100}[/tex]

                            [tex]=\$ 17.5[/tex]

Bill Amount after applying the coupon = [tex]=\$ 175-\$ 17.5=\$ 157.5[/tex]

Tip = [tex]20 \% \text { of } 157.5[/tex]

   = [tex]\frac{20 \times 157.5}{100}=\$ 31.5[/tex]

So the tip amount = $ 31.5

Total bill amount after the coupon and tip = [tex]\$ 31.5+\$ 157.5=\$ 189[/tex]

So the total bill amount is $ 189.

4,000,000

because the hundred thousand place value is the digit 5 or higher, the millions rounds up!! in this case, the 3 in the millions rounds up to 4 and the rest of the digits on the right turn to 0, also remember commas!!!!!

3 887 860 rounded to the nearest million is 4 000 000.

From the given number 3 887 860, stating the place value of each digit

We have 0 ones (or unit), 6 tens, 8 hundreds, 7 thousands, 8 ten thousands, 8 hundred thousands and 3 million.

Hence, the number we are rounding is 3 (since we are asked to round to the nearest million)

To round a number, we either round up or round down.  

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down; and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Since, the number that follows the digit we are rounding is 8, then we round up. We round up by adding 1 to the digit we are rounding and turn the remaining numbers to zeros.

(3+1 = 4)

Hence, 3 887 860 rounded to the nearest million is 4 000 000.

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Answer:

no

because it should be 99

Answer:

yes

Step-by-step explanation:

Please mark brainliest, everybody keeps bullying me because i get the answers faster, then they delete my explanation to do theirs :(

Answer:

i just need points

Step-by-step explanation:

Answer: classroom numbers are 353 and 355

Step-by-step explanation:

Let x represent the first no

Then x+2 represents the second number

Turn the question to an equation= x - (x +2) =708

Therefore, 2x + 2= 708

2x= 708-2

2x= 706

x= 353 and x+2= 355

Hope you understand, please mark brainliest.

Answer:

The first number is 353, and the second is 353 + 2, or 355.

Step-by-step explanation:

Represent the first number by n and the next by n + 2.  

Then n + (n + 2) = 2n + 2 = sum of the two numbers = 708.

Subtracting 2 from both sides yields 2n = 706.  Dividing both sides of this latest result by 2 yields n = 353.

The first number is 353, and the second is 353 + 2, or 355.

Check:  do 353 and 355 sum up to 708?  YES

Answer:

I'm so sorry you don't know this. Here!

Step-by-step explanation:

You divide 1,060 with 30%

1,060 - 30% (30) = 742!

Val scored 742 points!

Final answer:

The tangent of ∠Y in ΔXYZ is the ratio of the length of side XZ to the length of side ZY, which is 65/72.

Explanation:

In ΔXYZ, we are given that ∠Z = 90°, YX = 97, XZ = 65, and ZY = 72. To find the tangent of ∠Y, we use the definition of the tangent function in a right triangle, which is the ratio of the length of the opposite side to the length of the adjacent side for the given angle.

Since ∠Z is the right angle and we are interested in a tangent of ∠Y, the opposite side to ∠Y is XZ (which measures 65), and the adjacent side to ∠Y is ZY (which measures 72).

Therefore, the tangent of ∠Y is given by the ratio:
tan(∠Y) = opposite/adjacent = XZ/ZY = 65/72.

Answer:

210

Step-by-step explanation:

126 / 3 = 42

42 x 5 = 210

therefore the train can traval 210 miles in 5 hours.

hope this helps

~angilina

CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal. ∠GAC ≅ ∠HFD by the transitive Property of Congruence.

Angles that are of the same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of the same measure,

then

[tex]m\angle A = m\angle B[/tex]

is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.

We write the congruency between them as;

[tex]\angle A \cong \angle B[/tex]

In the figure BC || DE .

Angles

CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal.

GAC and DFE are not congruent

CAF and EFH are not congruent

GAB and EFA are not congruent

∠GAC ≅ ∠AFE because they are corresponding angles of parallel lines cut by a transversal.

∠AFE ≅ ∠HFD by the Vertical Angles Theorem.

Therefore, ∠GAC ≅ ∠HFD by the transitive Property of Congruence.

∠AFD = ∠AFE

Two angles that are equal to the same angle must themselves be equal.

( By Transitive property of equality)

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Answer:

The oldest fossil is closer to the surface.

Step-by-step explanation:

Usually, the closer to the core of the Earth, the older the fossils. However, in this image, the oldest fossil is closer to the surface.

Answer:

The younger fossil is in the bottom layer, while the older fossil is in the top layer. These locations are opposite to the principle of superposition.

Step-by-step explanation:

Plato

A: the factors of 45 are the only one shaded on the hundreds chart

The shaded numbers, all are factors of 45. Therefore, option A is the correct answer.

We need to check what set of numbers is shaded on the hundred charts.

In math, a factor is a number that divides another number completely with no remainder. Factors and multiples are a part of our daily life. For example, they are used in arranging items in a box, handling money, finding patterns in numbers, solving ratios, and working with expanding or reducing fractions.

The factor of a number is always less than or equal to the given number.

From the given chart the shaded numbers are 1, 3, 5, 9, 15 and 45.

The shaded numbers, all are factors of 45. Therefore, option A is the correct answer.

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Answer:

Step-by-step explanation:

Answer

20%

Explanation

Answer:

t = 2.76

PLEASE VOTE BRAINLIEST

Step-by-step explanation:

Answer:

the fractions of all the shapes are circles can be obtained would be computed as:  

                      [tex]\frac{450}{1600}=\frac{9}{32}[/tex]        

Step-by-step explanation:

The fraction of the number of white shapes to the number of black shapes is 5/11.

Let us consider that there are:

As the fraction of the number of white circles to the number of white squares is 3:7

It means out of 10 total parts, 3/10 are white circles and 7/10 are white squares.

Calculating Number of white circles:

                                                           [tex]\frac{3}{{10}} \times 500=150[/tex]

Calculating Number of white squares:

                                                            [tex]\frac{7}{{10}} \times 500=350[/tex]

As the fraction of the number of black circles to the number of black squares is 3:8.

Calculating Number of black circles:

                                                            [tex]\frac{3}{{11}} \times 1100=300[/tex]

Calculating Number of black squares:

                                                            [tex]\frac{8}{{11}} \times 1100=800[/tex]

As

Therefore, the fractions of all the shapes are circles can be obtained would be computed as:

                            [tex]\frac{450}{1600}=\frac{9}{32}[/tex]                            

Answer:

yes, it is

hope its helpful ! :)