Circle K has a radius of 8 inches. Diameter AKC is drawn and point F is located on the circle such that
FC = 6. Which of the following is closest to the length of FA?

(1) 5.3
(2) 8.7
(3) 12.4
(4) 14.8

The length of EC shown in the diagram is 66.2.

"To understand the calculation, check below."

ΔBE - ΔAE = ΔAB

ΔAB = 180°- 117°

ΔAB = 63°

Δ[tex]BE-[/tex] Δ[tex]AB-[/tex] Δ[tex]BC[/tex] = Δ[tex]CD[/tex] (Congruent angles)

Δ[tex]CD= 180 - 63 - 15[/tex]

Δ[tex]CD=102[/tex]

[tex]EC = 102 + 63[/tex]

[tex]EC=165[/tex]

[tex]L = 165[/tex] • [tex]2\pi23/360[/tex]

[tex]L = 66.2[/tex]

Therefore, EC = 66.2

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Answer:

see explanation

Step-by-step explanation:

given that x and y are proportional relationships , then

y = kx ← k is the constant of proportionality

divide both sides by x

[tex]\frac{y}{x}[/tex] = k

using corresponding values of x and y from each table to find k

first table

k = [tex]\frac{10}{1}[/tex] = 10

second table

k = [tex]\frac{20}{4}[/tex] = 5

third table

k = [tex]\frac{15}{2}[/tex]

fourth table

k = [tex]\frac{4}{1}[/tex] = 4

This is not really a random sample. The athletes are heavily biased toward loving sports. Likely they'll pick their favorite sport to be the one they are currently playing.

Example: if basketball players are asked their favorite sport, they likely might pick basketball.

A much better approach is to randomly select names from a hat, use computer software, or a random number table. This will produce a more random sample to help better represent the population.

Based on the exchange rate and Victor's budget, hector can see the sumo tournament and have about $322 left over.

Conversion rate of US dollars to Japanese yen = 1 : 94.153

Ratio of dollar to Yuan

1 : 94.153 = x : 5,488

1/94.153 = x / 5,488

1 × 5,488 = 94.153x

5,488 = 94.153x

x = 5,488 / 94.153

x = 58.2881055303601

Approximately,

x = $58

Amount left with Victor = Total money with Victor - amount spent

= $380 - $58

= $322

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Answer:

Answer:

360

Step-by-step explanation:

from the survey:

32/80 - 0.4 love math

0.4*900

= 360

Answer:

  40

Step-by-step explanation:

The sum of exterior angles of a convex polygon is 360°. This relation lets you write an equation for x.

__

Clockwise from the bottom, the sum of exterior angles is ...

  90° +(x +35)° +(x +15)° +(2x -20)° +(2x)° = 360°

  120° +6x° = 360° . . . . . . . simplify

  6x = 240 . . . . . . . . . . divide by °, subtract 120

  x = 40 . . . . . . . . . . divide by 6

The value of x is 40.

Answer:

x = 40°

Explanation:

The shape is a pentagon. Any polygon's exterior angles sum up to 360°.

Now, they all sum up to 360° :

⇒ (x + 35) + (x + 15) + (2x - 20) + 2x + 90 = 360°

⇒ x + x + 2x + 2x + 35 + 15 -20 + 90 = 360°

⇒ 6x + 120° = 360°

⇒ 6x = 360° - 120°

⇒ 6x = 240°

⇒ x = 240°/6

⇒ x = 40°

The system of inequalities have no solutions, option D is correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that the graph shows the solutions to the inequalities y> 3x + 14 and y< 3x + 2.

We have to find the  system of inequalities have solutions has solutions or not

As we observe the graphs  y> 3x + 14 and y< 3x + 2 of these inequalities the shade of both lines are not overlapped.

So the two inequalities does not have solution

Hence, the system of inequalities have no solutions, opton D is correct.

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Answer:

d. 5408 Birr.

Step-by-step explanation:

24 months  = 2 years.

Amount after 2 years = 5000(1 + 0.04)^2

= 5408.

Answer:

It's a right triangle ..

Step-by-step explanation:

By using Pythagoras theorem , we can know that it's a right angled triangle or not ..

so , H² = P² + B²

=> 34² = 16² + 30²

=> 1,156 = 256 + 900

=> 1,156 = 1,156

Hence , it's a right triangle

Answer:

answer C.

Step-by-step explanation:

the base of the triangle is 4 units.the other leg is sqrt5.

the last leg is 4 +9 = 13 so it is sqrt 13.

add them all up together and you get 4+sqrt 13 + sqrt 5 which is C.

hey I will guess you are above oklahoma because it is raining(bottom right) and your temp starts with 6

Using the distance formula, each side of the park is 13 units long

The vertices of the park are given as:

(26.5, 12), (38.5, 7), (26.5, 2), (13.5, 2), (1.5, 7), and (13.5, 12).

The length of each side is calculated using the following distance formula:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

Using any consecutive points, we have:

[tex]d = \sqrt{(13.5 - 1.5)^2 + (12 -7)^2} = 13[/tex]

Hence, each side of the park is 13 units long

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Answer:

8 times larger than original

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex]πr³

when r = 2 , then

V = [tex]\frac{4}{3}[/tex]π × 2³ = [tex]\frac{4}{3}[/tex]π × 8

when r is doubled , that is r = 4 , then

V = [tex]\frac{4}{3}[/tex]π × 4³ = [tex]\frac{4}{3}[/tex]π × 64

64 is 8 times larger than 8

then new sphere is 8 times larger than original sphere

Answer:

8 times

Step-by-step explanation:

Answer:

y=x^2+6

Step-by-step explanation: Look at the vertex (0,6). We know the equation is quadratic so we know x^2. We know in the slope-interpect form equation the y-intercept is the term after the slope. The same applies in this equation. So that means the y intercept is 6 because y is 6 in the coordinate (0,6). We know the slope x^2. We need to plug that into the slope-intercept form equation.

The equation will be y=x^2+6.

Answer:

[tex]y = x^2 + 6[/tex]

Step-by-step explanation:

Vertex form for a parabola is [tex]y = a(x-h)^2 + k[/tex] where the vertex is [tex](h,k)[/tex]. Now for a vertex of (0,6), we can simply plug those values in for h and k: [tex]y = x^2 + 6[/tex].

Hope this helps!! :)

Answer:

(2,2)

Step-by-step explanation:

coordinates are written as (x,y)

where x represents the x value of the coordinate and y represents the y value of the coordinate.

If we look at the graph we can tell that "b" has an x value of 2 and a y value of 2

Therefore we can say that "b" is positioned at (2,2)

Answer:

C. (2, 2)

Step-by-step explanation:

A coordinate is used to identify a point on a graph. A coordinate is written in the form of (x, y), where x is the x-value and y is the y-value.

The x-value is the number of units left or right from the origin (0, 0), and it gets negative by going left and positive by going right.

The y-value is the number of units up or down from the origin (0, 0), and it gets negative by going down and positive by going up.

For example, the coordinates (1, -2) indicate that the x-value goes to the right one unit and the y-value goes down two units.

Here, we are asked to find the coordinate of B:

Therefore, the correct answer is C. (2, 2)

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Answer:

Step-by-step explanation:

Use the nth tern equation of the AP

We have

Find the value of d

Correct choice is a)

Now

Answer:

x=32

Step-by-step explanation:

The measure of the angle B is 30 degree after applying the sin law of triangle.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have a triangle shown in the picture:

We can apply the sin law of the triangle to find the angle B

[tex]\rm \dfrac{28}{sin91} =\dfrac{14}{sinB}[/tex]

SinB = 0.499

B  = 29.99 ≈ 30 degree

Thus, the measure of the angle B is 30 degree after applying the sin law of triangle.

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Answer: 71/28 or 2 15/28

Step-by-step explanation:

Turn both fractions into improper fractions.

5 1/4 = 21/4

2 5/7 = 19/7   multiply the denominator with the whole then add the     numerator, same denominator.

21/4 - 19/7 = ?  find common denominator to subtract

4 x 7 = 28  common denominator

Divide the new denominator by previous denominators then multiply by each respective numerator. 28 divided by 4 is 7 multiplied by 21 is 147, the same happens with 19/7.

147/28 - 76/28 = 71/28 or 2 15/28

Answer:

EK = 8

Step-by-step explanation:

Intersecting Chords Formula:  a • b = c • d

BK * KD = EK * KC

4 * 10 = (x+1) * (x-2)

40 = x^2 +x-2x-2

40 = x^2 -x -2

0 = x^2 - x-2-40

0 = x^2 -x -42

Factor

0 = (x-7) (x+6)

Using the zero product property

x-7 = 0   x+6 =0

x=7        x=-6

X is not negative

x=7

EK = x+1

EK = 7+1

EK = 8

The circumference of the wire is 4x and the area of the circle is 4x^2/π

The length of the wire is given as;

Length = 4x

This represents the circumference.

Hence, the circumference of the wire is 4x

In (a), we have:

Circumference = 4x

Calculate the radius using:

2πr = 4x

Divide through by 2π

r = 2x/π

The area is:

Area = πr^2

This gives

Area = π(2x/π)^2

Evaluate

Area = 4x^2/π

Hence, the area of the circle is 4x^2/π

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Answer:

he would use 1/16 of a liter or 2.11 oz

Step-by-step explanation:

so i took 1/4 and divided up into 4 which is 1/16 and then i took 1/4 liter and divded that up into 4 to get 2.11 oz

The scale factor will be 1.5. The corresponding angles are congruent because the size is changed not the angles.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Adnan wants a larger garden.

He draws the triangle ΔPQR to show his original garden.

He wants to enlarge a garden, so he uses a dilation to form the image of the triangle ΔPQ'R'.

He uses vertex P as the center of the dilation.

The ratio of the corresponding sides will be given as

PQ'/PQ = Q'R'/QR = R'P/RP = 1.5

The scale factor will be 1.5.

The corresponding angles are congruent because the size is changed not the angles.

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The number -1.28 is rational if it is an integer or decimal, so yes it is.

Answer:

we have 1.28 with bar above 28 signifying that the number can also be written as 1.28282828 The mixed number is then equal to,

1 and 28/99 or 1 and 28 over 99

Therefore, the answer to this item is the second choice.

Step-by-step explanation:

My brother helped me with this one

The probability of selecting the human characters will be equal to 3 / 7.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that:-

The probability will be calculated as:-

Probability = 3 / (3+4)

Probability = 3 / 7

Therefore the probability of selecting the human characters will be equal to 3 / 7.

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Part A: She needs to collect different types of data to form her classmates. It will help her to find which student spends the most time playing musical instruments.

Part B: Yes, it is a statistical question.

Zoe needs two main data from each of her classmates.

1. Name of her classmates.

2. Which student spends how much time playing musical instruments.

After that, she can make a graph or a chart in order to understand which student spends more time playing musical instruments.

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The two equation that represents the information is x + y = 150

y = 3x

let

the number of rock music = x

the number of alternative music = y

Therefore,

x + y = 150

y = 3x

The two equation that represent the information are as follows:

x + y = 150

y = 3x

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Answer:

x = 0  ;  x = 1

Step-by-step explanation:

[tex]\sqrt{x^{12}} =x[/tex]

[tex]\Longleftrightarrow \sqrt{x^{6\times 2}} =x[/tex]

[tex]\Longleftrightarrow \sqrt{\left( x^{6}\right)^{2} } =x[/tex]

[tex]\Longleftrightarrow |x^{6}|=x[/tex]

[tex]\Longleftrightarrow x^{6}=x\ \ \ ;\ |x^{6}|=x^{6}[/tex]

[tex]\Longleftrightarrow x^{6}-x=0[/tex]

[tex]\Longleftrightarrow x(x^{5}-1)=0[/tex]

[tex]\Longleftrightarrow x=0 \ \ or\ \ (x^{5}-1)=0[/tex]

[tex]\Longleftrightarrow x=0\ \ or\ \ x^{5}=1[/tex]

[tex]\Longleftrightarrow x=0\ \ or\ \ x=1[/tex]