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The standard form of the equation is (x – 1)² + y² = 3 is not true, as we just showed that the standard form of the equation is \((x - 1)^2 + y^2 = 9\).

What is circle ?

A circle is a two-dimensional geometric shape consisting of all points that are the same distance from a given point called the center. The distance from the center to any point on the circle is called the radius. The diameter of a circle is the distance across the circle through the center.

The formula for the circumference of a circle is C = 2πr, where r is the radius and π (pi) is a mathematical constant approximately equal to 3.14159. The circumference is the distance around the circle.

The formula for the area of a circle is \(A = \pi r^2\) where r is the radius. The area is the amount of space inside the circle.

According to the question:
To determine which statements are true, we can use the general equation of a circle in standard form:

\((x - h)^2 + (y - k)^2 = r^2\)

where (h,k) are the coordinates of the center of the circle and r is the radius.

Comparing this to the given equation\(x^2 + y^2 - 2x - 8 = 0,\) we can complete the square to get:

\((x - 1)^2 + y^2 = 9\)

From this, we can see that the center of the circle is (1,0) and the radius is 3.

Therefore, the statements that are true are:

The radius of the circle is 3 units.

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The statement "The center of the circle lies on the y-axis" is not true, as the center of the circle is at (1,0), which does not lie on the y-axis.

The statement "The standard form of the equation is (x – 1)² + y² = 3" is not true, as we just showed that the standard form of the equation is\((x - 1)^2 + y^2 = 9.\)


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Answer:

60 minutes

Step-by-step explanation:

It took him 30 minutes to run 5 kilometers, so doubling 5 to 10 would double 30 to 60 minutes

Answer:

9 - 6r

Step-by-step explanation:

Answer:

Formula for g(x) is \(g(x) = 3 sin(\frac{\pi }{5}x + \frac{\pi }{5} ) + 6\)

Step-by-step explanation:

Given - g is a trigonometric function of the form g(x)=a sin (bx+c)+d.  The function intersects its midline at (-1 , 6) and has a minimum point at (-3.5 , 3)

To find - Find a formula for g (x). Give an exact expression.

Proof -

Given that,

g(x)=a sin (bx+c)+d

We know that, Midline is present in between maximum and minimum

Here given that, minimum is present is 3 and midline is present at 6

So, Maximum occurs at 9.

Now,

We know that,

Standard form of sine function is - g(x) = Asin(B(x-C)) + D

Where

A = Amplitude

and Amplitude = (Maximum - minimum) / 2

                         = (9 - 3)/ 2

                         = 6/2 = 3

⇒A = 3

Now,

Period = \(\frac{2\pi }{B}\)

⇒B = (2π) / Period

      = (2π) / 10

      = π/5

⇒B = π/5

Now,

Phase Shift : C = -1 ( i.e. 1 to the left)

Vertical Shift : D = 6

So,

We get

g(x) = Asin(B(x-C)) + D

      = \(3 sin(\frac{\pi }{5}(x -(- 1))) + 6\)

⇒\(g(x) = 3 sin(\frac{\pi }{5}x + \frac{\pi }{5} ) + 6\)

∴ we get

Formula for g(x) is \(g(x) = 3 sin(\frac{\pi }{5}x + \frac{\pi }{5} ) + 6\)

Answer:

x, y

Step-by-step explanation:

Answer:

Give brainly to my previous answer then

Step-by-step explanation:

Answer:

1st one is equivalent,  2nd one is equivalent, 3rd is not

Step-by-step explanation:

Answer:

ms girll i think you multiply

Answer:

3. 147 \(ft^{3}\)  4. \(\frac{160}{3} \pi\) \(ft^{3}\)

Step-by-step explanation:

3. Volume of a square pyramid = \((base.edge.length)^{2}\) × \(\frac{height}{3}\)

Variables:

V = volume

x = base edge length

h = height

V = \(x^{2}\)  × \(\frac{h}{3}\)

x = 7 ft

h = 9 ft

Plug the values in the equation:

V = \(7^{2}\) × \(\frac{9}{3}\)

V = 49 × 3

V = 147 \(ft^{3}\)

4. Volume of cone = \(\pi r^{2} \frac{h}{3}\)

Variables:

V = volume

r = radius

h = height

V = \(\pi r^{2} \frac{h}{3}\)

r = 8ft /2 = 4 ft (radius is half of the diameter)

h = 10 ft

V =  \(\pi 4^{2} \frac{10}{3}\)

V = \(\pi\) × 16 × \(\frac{10}{3}\)

V = \(\frac{160}{3} \pi\) \(ft^{3}\)

Answer:

interchangeable parts.

Step-by-step explanation:

Eli Whitney here demonstrates interchangeable parts.He took several guns, dismantled them, put the pieces in a box, and shook it. He then randomly selected the pieces he needed, assembled on rifle, and fired it. popularized in America when Eli Whitney used them to assemble muskets in the first years of the 19th century, allowed comparatively unskilled workers to manufacture vast quantities of arms rapidly and at lower expense, and made repair and replacement of parts exponentially simpler.

Answer:

2×3+3

6+3

9

I think this is your answer

According to the 4:3 ratio, that would mean that there were 32 seniors on the team at the start of summer training.

The mix of juniors and seniors on the team is a great combination that allows the younger players to learn from those with more experience. With the seniors showing the juniors the ropes, the team will be able to reach its full potential this season.

Overall, the varsity football team is in a great position heading into the upcoming season. With a balanced roster of 48 juniors and 32 seniors, the team is sure to be a strong contender in their division. The juniors and seniors will be a great combination, and the team is sure to benefit from the leadership and guidance of the seniors.

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Answer:

2One-fifteenth

Step-by-step explanation:

\(3\frac{13}{15} - 1\frac{4}{5}\)

\(2\frac{13 - 12}{15}\)

2 \(\frac{1}{15}\)

The given pattern is derived by dividing each number by 3.

-405 ÷ 3 = -135
-135 ÷ 3 = -45
-45 ÷ 3 = -15

To find the next number in the pattern, we need to divide -15 by 3:

-15 ÷ 3 = -5

Therefore, the next number in the pattern is -5.

The pattern is formed by dividing each number by 3. By applying this pattern, we find that the next number is -5.

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The graph of the linear equation is attached

From the question, we have the following parametes that can be used in our computation:

A bowling alley charges $6 for shoe rental and $2 for each game.

This means that

Intial value = 6

Rate = 2

The function is then represented as

f(x) = Initial + Rate * x

So, we have

f(x) = 6 + 2x

See attachment fr the graph

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Answer:

x = 20

Step-by-step explanation:

To solve this problem we first observe the Pythagoras equation. If a= 16 and b=12 are the lengths of the legs of a right triangle and c=x is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.  

This relationship is represented by the formula: a*a + b*b = c*c

\(\sqrt{16^2 + 12^2}\) = x  

Answer:

pretty sure its

government

nonprofit organization

bank

Step-by-step explanation:

doing exam thingy

Answer:

hes right

Step-by-step explanation:

Answer: 10 ft

Step-by-step explanation:

diameter = 2r

diameter = 2(5)

diameter = 10 ft

Answer:

10 ft

Explanation:

When you have the radius, and you're trying to find the diameter, just multiply the radius by 2:

Diameter = Radius × 2

                = 5 × 2

                = 10 ft

Therefore, the radius is 10 ft.

Answer/Step-by-step explanation:

r are roses,

r + 6

Ben plants 6r

[RevyBreeze]

Therefore,

substitute the values of x in the equations

Therefore,

(1, 6) (-1, 1)

The labor productivity of this manufacturing process in terms of dollars per labor hour is $73.47.

To find the labor productivity of this manufacturing process in terms of dollars per labor hour, we need to calculate the total revenue from the tuxedos and divide it by the total number of labor hours.

Total revenue from tuxedos = 96 tuxedos * $225 per tuxedo

                                               = $21,600

Total number of labor hours = 7 employees * 42 hours per employee

                                               = 294 labor hours

Labor productivity = Total revenue / Total number of labor hours

                               = $21,600 / 294 labor hours

                               = $73.47 per labor hour

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Answer: (7.5, 4.5)

Step-by-step explanation:

To find the midpoint, we can just find the average of the x values and the y values.

x=(10+5)/2=15/2=7.5

y=(5+4)/2=9/2=4.5

Answer:

X= 60 Y= 50

Step-by-step explanation:

180-50-60= 70 (not marked angle)

180-50-70= 60 (angle x)

180-70-60= 50 (angle y)

Answer:

x=60

y=50

Step-by-step explanation:

I think this is right.

Answer:

$36

Step-by-step explanation:

4.5 * 8 = 36

4 * 8 = 32

1/2 of an hour would be 1/2 of 8= 4

4+32 = $36

Answer:

c) 80 cm it's really easy

The standard error for the distribution of sample means is 6.

To find the standard error for the distribution of sample means, we use the formula:

SE = σ / √n

Where SE is the standard error, σ is the standard deviation of the population, and n is the sample size.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.

A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread

Plugging in the given values, we get:

SE = 18 / √9

SE = 18 / 3

SE = 6


So, the correct answer is option b. 6.

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The measure of the side "a" by cosine law for the given triangle is 11.46 which is closest to 12 in option (B).

What is a triangle?
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle a side is opposite to angle A,b is opposite of angle B and c is the opposite of angle C.

By cosine law,

cosA = (b² + c² - a²)/(2bc)

As per the given,

ΔABC; b= 10; c = 14, and ∠A = 54°

cos54° = (10² + 14² - a²)/(2×10×14)

0.5877 = (10² + 14² - a²)/(2×10×14)

(10² + 14² - a²) = 164.579

a² = 131.4201

a = 11.46

Hence "The measure of the side "a" by cosine law for the given triangle is 11.46 which is closest to 12 in option (B)".

Since this is the incomplete question. The complete question is :

Given: ΔABC; b= 10; c = 14, and ∠A = 54°. Find the length of side a to the nearest whole number.

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The surface area of the spherical balloon is 198 cm².

The circumference of a sphere is related to its radius by the formula:

C = 2πr

Given that the circumference of the balloon is 25 cm, we can solve for the radius:

25 = 2πr

Dividing both sides by 2π, we find:

r = 25 / (2π)

To calculate the surface area of a sphere, we use the formula:

A = \(4\pi r^2\)

Substituting the value of r we found:

A = \(4\pi (25 / (2\pi ))^2\)

Simplifying the equation, we get:

\(A = 4\pi (25^2) / (4\pi^2)\)

The π in the numerator and denominator cancels out, and the equation simplifies to:

A = 625 / π

Now, we can calculate the approximate surface area rounded to the nearest centimeter:

A ≈ 625 / 3.14

A ≈ \(198.0918 cm^2\)

Rounding to the nearest centimeter, the approximate surface area of the balloon is \(198 cm^2.\)

Therefore, the answer is C. \(198 cm^2.\)

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There are 30,240 ways to line up the eight kids such that Felicia is next to exactly one of her three best friends (Bob, Cassandra, or Hubert).

To find the number of ways to line up the eight kids such that Felicia is next to exactly one of her three best friends (Bob, Cassandra, or Hubert), we can break down the problem into several cases.

Case 1: Felicia is next to Bob

In this case, we treat Felicia and Bob as a single entity. So, we have a total of seven entities to arrange: Felicia and Bob, Cassandra, Hubert, and the remaining four kids. The number of ways to arrange these entities is 7!. However, within Felicia and Bob, they can be arranged in 2! ways. Therefore, the total number of arrangements in this case is 7! × 2!.

Case 2: Felicia is next to Cassandra

Similar to Case 1, Felicia and Cassandra are treated as a single entity. We have a total of seven entities to arrange: Felicia and Cassandra, Bob, Hubert, and the remaining four kids. The number of ways to arrange these entities is 7!, and within Felicia and Cassandra, they can be arranged in 2! ways. Hence, the total number of arrangements in this case is 7! × 2!.

Case 3: Felicia is next to Hubert

Again, Felicia and Hubert are treated as a single entity. We have a total of seven entities to arrange: Felicia and Hubert, Bob, Cassandra, and the remaining four kids. The number of ways to arrange these entities is 7!, and within Felicia and Hubert, they can be arranged in 2! ways. Thus, the total number of arrangements in this case is 7! × 2!.

To get the final answer, we sum up the number of arrangements from all three cases:

Total number of arrangements = (7! × 2!) + (7! × 2!) + (7! × 2!)

Simplifying further:

Total number of arrangements = 3 × (7! × 2!)

Now, let's calculate the value of 7! × 2!:

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040

2! = 2 × 1 = 2

Substituting these values:

Total number of arrangements = 3 × 5,040 × 2

Total number of arrangements = 30,240

Therefore, there are 30,240 ways to line up the eight kids such that Felicia is next to exactly one of her three best friends (Bob, Cassandra, or Hubert).

It's worth noting that this calculation assumes that the ordering of the remaining four kids is flexible and can be arranged in any way.

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The original limit represents the derivative of f(x) = \(x^4\) + 5x³ + 10x² + 5x + 5 at the point a=0, and the value of the limit is 5.

To find the function and number, we need to simplify the expression first. Using the binomial formula, we can expand \((1+h)^5\) as follows:
\((1+h)^5\) = 1 + 5h + 10h² + 10h³ + \(5h^4\) + \(h^5\)
Then, we can substitute this expansion into the original expression and simplify:
lim h→0 [(1+h)^5 - 1]/h
= lim h→0 [1 + 5h + 10h² + 10h³ + \(5h^4\) + \(h^5\) - 1]/h
= lim h→0 [5h + 10h² + 10h³ + 5h^4 + h^5]/h
= lim h→0 [5 + 10h + 10h² + 5h³ + h^4]
Now, we can see that this limit represents the derivative of the function f(x) = \(x^4\) + 5x³ + 10x² + 5x + 5 at the point a=0. Taking the derivative of f(x) using the power rule, we get:
f'(x) = 4x³ + 15x² + 20x + 5
Evaluating this derivative at a=0, we get:
f'(0) = 4(0)² + 15(0)² + 20(0) + 5 = 5
Therefore, the original limit represents the derivative of f(x) = \(x^4\) + 5x³ + 10x² + 5x + 5 at point a=0, and the value of the limit is 5.

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Okay, according with the identities of parallelograms we have: AE=CE and BE=DE.

Replacing we obtain:

AE=CE

2x=x+2

2x-x=2

x=2

BE=DE

y+10=4y−8

10+8=4y-y

18=3y

y=18/3

y=6

And considering that BD=BE+DE, we got:

BD=(y+10)+(4y-8)=(6+10)+(4*6-8)=(16)+(24-8)=16+16=32

So, finally we obtain that the length of BD is 32 units.