Rewrite the following equation in the center-radius form of the equation of a circle. x2 + 12x + y2 - 12y = -56
A.
(x - 6)2 + (y + 6)2 = 16
B.
(x + 6)2 + (y - 7)2 = 16
C.
(x + 6)2 + (y - 6)2 = 16
D.
(x + 8)2 + (y - 5)2 = 16

Answer:

2. w = -3

4. c = -2

6. r = 7

8. n = 4

Step-by-step explanation:

It's hard to read the photo, but I'll try.

2.

\( 2^{w + 4} \times 2^{4w + 6} = 2^{2w + 1} \)

On the left side, you have a product of 2 powers with the same base.

Give the same base and add the exponents, as in the rule

\( a^m \times a^n = a^{m + n} \)

You get on the left side 2 to the sum of the exponents.

\( 2^{w + 4 + 4w + 6} = 2^{2w + 1} \)

Simplify the long exponent on the left side.

\( 2^{5w + 10} = 2^{2w + 1} \)

Now we have another rule we can use. If two powers are equal, and their bases are equal, then the exponents must be equal.

Here, 2 to the power 5w + 10 equals 2 to the power 2w + 1. Since both bases are 2 and are equal, then the exponents must be equal.

5w + 10 = 2w + 1

Subtract 2w from both sides. Subtract 10 from both sides.

3w = -9

Divide both sides by 3.

w = -3

4.

\( \dfrac{1}{5} = 5^{2c + 3} \)

We need to write the left side as a power of 5. Then we equate the exponents like we did in problem 2.

Recall the rule:

\( a^{-n} = \dfrac{1}{n} \)

Apply this rule to the left side in reverse.

\( 5^{-1} = 5^{2c + 3} \)

Now we have two powers that are equal, both having the same base, 5, so the exponents must be equal.

2c + 3 = -1

2c = -4

c = -2

6.

\( 216 = 6^{2r - 11} \)

This is the same idea as problem 4. Write the left side as a power of 6.

\( 6^3 = 6^{2r - 11} \)

\( 2r - 11 = 3 \)

\( 2r = 14 \)

\( r = 7 \)

r = 7

8.

\( 4^{n} \times 4^{2n - 9} = 64 \)

This problem is similar to problem 2.

\( 4^{n + 2n - 9} = 4^3 \)

\( 4^{3n - 9} = 4^3 \)

3n - 9 = 3

3n = 12

n = 4

Given:

The figure of circle E. \(m\angle ABD=(11x-3)^\circ,m\angle ACD=(8x+15)^\circ\).

To find:

The measure of arc AD.

Solution:

We know that the inscribed angles on the same arc are congruent and their measures are equal.

\(\angle ABD\) and \(\angle ACD\) are inscribed angles on the same arc AD. So,

\(m\angle ABD=m\angle ACD\)

\(11x-3=8x+15\)

\(11x-8x=3+15\)

\(3x=18\)

\(x=6\)

Now,

\(m\angle ABD=(11x-3)^\circ\)

\(m\angle ABD=(11(6)-3)^\circ\)

\(m\angle ABD=(66-3)^\circ\)

\(m\angle ABD=63^\circ\)

We know that the intercepted arc is always twice of the inscribed angle.

\(m(Arc(AD))=2\times m\angle ABD\)

\(m(Arc(AD))=2\times 63^\circ\)

\(m(Arc(AD))=126^\circ\)

Therefore, the measure of arc AD is 126 degrees.

4.5 hours more will it take for Naomi and Claire to have painted the same number of square feet.

Let the time taken for them to paint equal areas be x hrs.

Naomi  = 2x + 16.5

Clair  = 4x + 7.5

Naomi's area = Clair's area

This is :

2x + 16.5 = 4x + 7.5

4x - 2x = 16.5 -7.5

2x = 9

x = 4.5 hours

Therefore 4.5 hours more will it take for Naomi and Claire to have painted the same number of square feet.

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The number of hours in a week a student played basketball is \(11\frac{3}{8}\).

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.

Also given that 1/4 of the exercise of a student came from playing basketball.

Therefore, Time playing basketball is one-fourth of the total time exercised which is,

= (3 + 1/4)×(1/4).

= (13/4)×(1/4).

= (13/8).

Therefore, In a week the student played (13/8)×7.

= 91/8.

= \(11\frac{3}{8}\).

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The probability that the mean weekly wage of a randomly selected group of 16 workers from the factory will be within $3 of the population mean wage is 0.98

To solve this problem,

We can use the central limit theorem which states that the sample means from a large sample will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

First, we need to find the standard error of the mean, which is equal to the standard deviation divided by the square root of the sample size:

Standard error of the mean = 5 / sqrt(16) = 1.25

Next, we need to find the z-score for the lower and upper bounds of the sample mean:

lower z-score = (402 - 405) / 1.25 = -2.4

upper z-score = (408 - 405) / 1.25 = 2.4

We can use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores:

lower probability = 0.0082

upper probability = 0.9918

To find the probability that the sample mean is within $3 of the population mean we need to subtract the lower probability from the upper probability:

Probability = 0.9918 - 0.0082 = 0.9836

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In 30 minutes, the woman will travel 12.5 miles.

This is due to the fact that the rate (25 mph) times the time equals the distance traveled. Mathematically, this can be expressed as d = rt, where d represents the distance, r represents the rate (speed), and t represents the time. In this instance, the distance can be calculated as d = 12.5 miles by multiplying d = 25 mph by 30 minutes/60 minutes.

The distance between two points is measured in distance. The rate, or the amount of distance traveled per unit of time, is the speed at which a person or vehicle travels. The woman in the car is traveling at a rate of 25 miles per hour (mph).

In this instance, the time is. The formula d = rt can be used to determine the distance traveled by multiplying her rate by the time. Given the rate and duration of travel, this formula can be used to determine the distance traveled by any object or person.

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Answer:

a) \(p\rightarrow \neg q \wedge \neg r\)

b) \(r\vee q \iff \neg p\)

Step-by-step explanation:

Given statements:

\(p:\) It is raining

\(q:\) Sam is wearing a hat

\(r:\) It is winter

To find:

The symbolic forms for the following:

a) If it is raining then Sam is not wearing a hat, and it is not winter.

b) It is winter or Sam is wearing a hat, if and only if it is not raining.

Solution:

a) The statement followed by 'if ' is written on the left hand side and the statement followed by 'then' is written after the symbol \(\rightarrow .\)

Not of a statement \(s\) is represented as \(\neg s\).

And is represented by \(\wedge\) symbol.

Therefore, the statement in symbolic form becomes:

\(p\rightarrow \neg q \wedge \neg r\)

b) Not of a statement \(s\) is represented as \(\neg s\).

Or is represented by \(\vee\) symbol.

If and only if is represented by the symbol \(\iff.\)

Therefore, the statement in the symbolic form becomes:

\(r\vee q \iff \neg p\)

Answer:

The inverse of the function is logx/log12

The inverse of a function

Given the function expressed as:

y = 12^x

To find the inverse, switch the variables to have:

x = 12^y

Take the log of both sides

logx = y log 12

y = logx/log12

Hence the inverse of the function is logx/log12

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Step-by-step explanation:mark brainlenies

Answer:

3. 2(x - 3) = x + 4

2x - 6 = x + 4

x = 10

4. 3x = 2(x - 1)

3x = 2x - 2

x = -2

Answer:

The angles are 63 , 97

Step-by-step explanation:

Let one angle be x

As sum of two angles is 160, the other angle = 160 - x

Their difference  = 34

x - [160- x] = 34

Use distributive property to remove the brackets

x - 160 + x = 34

Add like terms

x + x - 160 = 34

2x - 160 = 34

Add 160 to both sides

2x  = 34 + 160

2x = 194

Divide both sides by 2

2x/2 = 194/2

x = 97°

One angle = 97°

Other angle = 160 - 97 = 63°

Answer:

Volume: 37.692 cm3

Step-by-step explanation:

1) 1/3 x 3.14 x 3 power of 2 x 4

2) 1.047 x 9 x 4

3) 37.692 cm3

Answer:

\(Volume ~of~cone=\pi /3r^{2} h\)

\(r=3cm\)

\(h=4 cm\)

\(volume=\pi /3\times3^{2} \times4\)

\(=12\pi =12\times3.14\)

\(=37.68~ cm^{2}\)

-----------------------

hope it helps...

have a great day!!

Answer:

The apple weighs 105 grams because it is between 100 and 110

The orange weighs 145 because both of them weigh 250 and 250-145=105

Step-by-step explanation:

Answer:

Apple: 105 grams

Orange: 145 grams

Step-by-step explanation:

The apple weighs 105, as the scale points to the tick representing 5 greater than 100.

The orange weighs 145 because the scale points to 250. We need to subtract the weight of the apple in order to isolate the weight of the orange.

250 - 105 = 145

Hope this helps.

Answer:

f(x)=12x

Step-by-step explanation:

Like and give 5 star rating

Please brainlest

Answer:

=13x-5

Step-by-step explanation:

Answer:

13x-5

Step-by-step explanation:

You would use distributive property to get 15x-9 and then the -2x+4.

Distributive property works for the numbers in the parenthesis and you multiply the 5x and the -3 by 3.

Then, you would do your basic math to get 13x-5

we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

To compute n, we can use the formula:
n = ((zα/2)^2 * 2p*(1-p*)) / (ε^2)
Where zα/2 is the z-score associated with a confidence level of 1-α, p* is the probability of success for a binomial distribution, and ε is the margin of error.
Since we are given that the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 is at least 0.80, we can set α = 0.20 to find the corresponding z-score of 1.28.
Using p* = 1/2 as an upper bound for both P1 and P2, we can calculate the margin of error as:
ε = zα/2 * sqrt((p*(1-p*)) / n)
Plugging in the values, we get:
0.05 = 1.28 * sqrt((0.25) / n)
Solving for n, we get:
n = 501.76
Therefore, we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

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Answer:

i believe C is correct :)

Answer:

The answer you got was correct.

Step-by-step explanation:

Predation means the preying of one animal on others,or more simplified,the action of attacking or plundering.

Answer:

1274

it is 1274

Step-by-step explanation:

mark as brainlest for the answer thankyou

The angular coordinate, angular velocity, and angular acceleration of the flywheel are: (a) At t = 0, θ = θ0 = 0.5 rad, ω = 0, and α = 12π²θ0 = 23.55 rad/s².

(b) At t = 0.125 s, θ = 0.267 rad, ω = 4.116 rad/s, and α = -69.08 rad/s².

The given equation for the angular displacement of the flywheel is θ=θ0e(-3πcos(4πt)). Here, θ0 = 0.5 rad. To find the angular velocity and angular acceleration, we need to differentiate θ with respect to time.

θ = θ0e(-3πcos(4πt))

ω = dθ/dt = -12π²θ0e(-3πcos(4πt))sin(4πt)

α = d²θ/dt² = -48π³θ0e(-3πcos(4πt))(cos(4πt) - 2)sin(4πt)

Substituting t = 0, we get:

(a) At t = 0, θ = θ0 = 0.5 rad, ω = dθ/dt = 0, and α = d²θ/dt² = 12π²θ0 = 23.55 rad/s².

(b) At t = 0.125 s, θ = 0.267 rad, ω = dθ/dt = 4.116 rad/s, and α = d²θ/dt² = -69.08 rad/s².

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Answer:

Geometric Sequence

Finding the sum

The sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Solution:

Geometric Series Sum Formula: S = a₁/1 - r

Given: a₁ = 3/4

          a₂ = -9/16

          a₃ = 27/64

          a₄ = -81/256

1. Find the common ratio.

      a_n = a₁r ⁿ ⁻ ¹

       a₂  = a₁r ⁿ ⁻ ¹

  -9/16 = 3/4 r ² ⁻ ¹

  -9/16 = 3/4 r

2. Divide both sides of the equation by 3/4 to find r.

   -9/16/3/4 = 3/4 r/3/4

 (-9/16)(4/3) = r

       -36/48 = r

           -3/4 = r

3. Using r = -3/4, find the sum of the infinite geometric series 3/4 -9/16 +27/64 -81/256+ ...

   S = a₁/1 – r

   S = 3/4/1 – (-3/4)

   S = 3/4/1 + ¾

   S = 3/4/4/4  + 3/4

   S = 3/4/7/4

   S = (3/4)(4/7)

   S = 12/28

   S = 3/7

4. Therefore, the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Definition:

     A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant while the sum of an infinite number of terms in a geometric sequence is called sum to infinity.

Code: 10.3.1.1

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Step-by-step explanation:

a) S'(t) = 0.09t² + 1t + 9 b) S(4) = 51.84 million dollars and S'(4) = 16.24 c) s'(14) = 54.00 means that the rate at which the company's sales are increasing 14 months from now is 54.00 million dollars per month.

(a) To find the derivative of S(t), we need to take the derivative of each term using the power rule:

S'(t) = 0.09t² + 1t + 9

(b) To find S(4), we simply substitute 4 for t in the expression for S(t):

S(4) = 0.03(4)³ + 0.5(4)² + 9(4) + 4
S(4) = 3.84 + 8 + 36 + 4
S(4) = 51.84 million dollars

To find S'(4), we substitute 4 for t in the expression for S'(t):

S'(4) = 0.09(4)² + 1(4) + 9
S'(4) = 3.24 + 4 + 9
S'(4) = 16.24

To two decimal places, S(4) = 51.84 million dollars and S'(4) = 16.24.

(c) s(14) = 352.40 means that the total sales of the company 14 months from now will be 352.40 million dollars.

s'(14) = 54.00 means that the rate at which the company's sales are increasing 14 months from now is 54.00 million dollars per month. This suggests that the company's sales are increasing at a fairly rapid rate, which could be a positive sign for the company's future growth.

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Answer: 6

Step-by-step explanation: 6 is my answer

Answer:

150-200

Step-by-step explanation:

A. passenger train 36mph

B. freight train 18mph

What is meant by speed?

Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.

Given that, A freight train departs from a train depot and let us consider it is travelling at an 'x' mph

and An hour later a passenger train departs the same train depot with a speed 'of x+18 mph.

After 2 hours the passenger train overtakes the freight train.

The total distance travelled by both trains when the passenger train overtakes the freight is equal.

Distance travelled by freight train = x*3

Distance travelled by passenger train = (x+18)*2

Now, 3x = 2x + 36

x = 18

and x + 18 = 36

Therefore, The speed of the passenger train and freight train are 36mph, and 18mph respectively

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Answer:

where is the question?...

Step-by-step explanation:

ion see the numbers

Answer:

Sorry but you have to take a picture so that I can see the question , so that I can answer it.

Step-by-step explanation:

Answer:

The point (-8, 2) is in Quadrant 2.

Step-by-step explanation:

Quadrant 1: (x, y)

Quadrant 2: (-x, y)

Quadrant 3: (-x, -y)

Quadrant 4: (x, -y)

Answer:

The point, -8,2, will be located in quadrant II.

Answer:

A) 50°, 65°, 65°

B) 45°, 50°, 85°

C) 20°, 60°, 100°

Step-by-step explanation:

To see if the angles can be used to construct triangles, you have to check if the degrees add up to 180 (Since the degrees in a triangle always have to add up to 180 degrees).

A) 50° + 65° +  65° = 180° (Good!)

B) 45° +  50° +  85°  = 180° (Good!)

C) 20° +  60° +  100° = 180° (Good!)

D) 30° +  60° +  70° = 160° (Bad!)

E) 20° +  45° +  120° = 185° (Bad!)