Mathematics College

The center is (4,5) and a point on the circle is (0,8)

Answers

Answer 1
The equation of a circle is (x - h)² + (y - k)² = radius² where (h, k) is the the center. So we plug in our given information.

(x - 4)² + (y - 5)² = radius². To find the radius, we do the distance formula from the center of the circle to the point on the circle itself. 

Distance formula is:

Distance = √((Y2 - Y1)² + (X2 - X1)²). Again, plug in given information. 

√((8 - 5)² + (0 - 4)²)
√((3)² + (- 4)²)
√(9 + 16)
√25 = 5

Your radius is 5. 

So now we complete the equation:

(x - 4)² + (y - 5)² = 5²

Your final answer:

(x - 4)² + (y - 5)² = 25

Related Questions

12+5v=2v-9 please show step by step!

Answers

12 + 5v = 2v - 9
Subtract 12 from both sides.

5v = 2v - 21
Subtract 2v from both sides.

3v = -21
Divide both sides by 3.

v = -7

To get it, combine like terms and restrain the variable. Segregating both sides by 3 gives the solution to the equation as v = -7.

How to solve the expression

To solve the condition 12 + 5v = 2v - 9, take after these steps:

Step 1: Segregate the variable terms on one side of the condition and the steady terms on the other side.

Subtract 2v from both sides to move the variable term to the cleared outside:

12 + 5v - 2v = 2v - 9 - 2v

Alter both sides of the condition:

12 + 3v = -9

Step 2: Separate the variable term by moving the reliable term to the other side.

Subtract 12 from both sides to move the dependable term to the proper side:

12 + 3v - 12 = -9 - 12

Unwind both sides of the condition:

3v = -21

Step 3: Light up for v by confining both sides of the condition by the coefficient of v, which is 3.

Portion by 3 to clarify for v:

v = -21 / 3

Streamline the division:

v = -7

The solution to the equation is v = -7.

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the width of a rectangle is shown below:

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The difference between the y-coordinates is 7 units. If the area is to be 42 square units, the missing coordinates must be 42/7 = 6 units to the right of those shown.
B = A +(6, 0) = (-4, 4) +(6, 0) = (-2, 4)

D = C +(6, 0) = (-4, -3) +(6, 0) = (-2, -3)

The appropriate choice is the last one, ...
  (-2, 4) and (-2, -3)

hello can you please help me posted picture of question

Answers

B. Seven as your answer
:)
For this question we need to make a Venn Diagram as shown below.

Start from the inner most circle.

5 patrons like all 3 drinks. 
8 patrons like Latte and Espresso. From these 8, 5 like all 3 drinks, so the patrons which only like Latte and Espresso will be 3.

Fill all the regions this way and you will get a diagram similar to the one given below. 

Count all the numbers inside the circles. These add up to 47. This means 47 patrons like the drinks.

Total number of patrons was 50. So there are 7 such patrons which do not like any of these drinks.

So, the correct answer is option B


what is the domain and range of
y=-2(x-3)(x+4)

Answers

The domain of any polynomial is "all real numbers."

The vertex of this function is (-0.5, 24.5), so the range of y=-2(x-3)(x+4) is
  -∞ < y ≤ 24.5

I have two bags. bag 1 contains 1010 blue marbles, while bag 2 contains 1515 blue marbles. i pick one of the bags at random, and throw 66 red marbles in it. then i shake the bag and choose 55 marbles (without replacement) at random from the bag. if there are exactly 22 red marbles among the 55 chosen marbles, what is the probability that i have chosen bag 1

Answers

55 blue or red marbles,

55-22 = 33 blue marbles

bag1+bag2= 2525

bag1=.4 

33/55=.6  blue marbles

bag 2=.6

so it is 40% that U choose bag 1 















One serving of Mike’s crackers has 150 calories and a mass of 30 grams. How many calories are in 6 grams of the crackers?

Answers

The amount of calories that are in 6 grams of crackers is 30 grams.

What is the amount of calories in the crackers?

Division is the mathematical operation that is used to determine the quotient of a number.  It is the process of grouping a number into equal parts using another number.

Calories in 6 grams = (150 / 30) x 6 = 30 grams

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Final answer:

To find the calories in 6 grams of Mike's crackers, divide the total calories by the total mass of one serving to get the unit rate (5 calories/gram) and then multiply by the mass in question (6 grams) to obtain 30 calories.

Explanation:

The question asks how many calories are in 6 grams of Mike's crackers, given that one serving of 30 grams has 150 calories. To find the calories in 6 grams of the crackers, we can use unit rate and proportions.

Step-by-Step Calculation

First, determine the calories per gram of the crackers by dividing the total calories by the total mass (in grams) of one serving. This gives us the unit rate: 150 calories / 30 grams = 5 calories per gram.

Next, since we're asked about the calories in 6 grams, we multiply the calories per gram (unit rate) by the mass: 5 calories/gram × 6 grams = 30 calories.

Therefore, there are 30 calories in 6 grams of Mike's crackers. This calculation illustrates the utility of understanding proportions and unit rates in everyday applications such as determining caloric intake from portions of food.

hey can you please help me posted picture of question

Answers

The inverse of 7x ix x/7

The composition of the function and its inverse must be zero. So the composition of 7x with x/7 is:

[tex](F( F^{-1}x)) \\ \\ =F( \frac{x}{7}) \\ \\ = 7(\frac{x}{7}) \\ \\ = x [/tex]

Thus, 7x and x/7 are inverse of each other.

So the answer to this question is option B

Marcus baked a loaf of banana bread for a party. He cut the loaf into equal size pieces. At the end of the party, there 6 pieces left. Explain how you can find the number of pieces in the whole loaf if Marcus told you that 1/3 of the loaf was left.

Answers

Marcus is left with 6 pieces and 1/3 of the loaf. so  by the problem if x is the whole loaf 1x/3 =6 x =18 . The total pieces of loaves  were 18

please help me with this if you can

Answers

The worst error will be where the prediction is farthest away from the actual value. Since the actual value corresponds to predictions in the 2nd column, the prediction at the far right (22.8) is the farthest away. The greatest error is ...
(22.8 -22.3)/22.3 * 100% ≈ 2.2%

Which graph best represents the equation -4x + 5y = 10?

Answers

Do you have a photo to show the separate graphs?

Answer: these are the graphs and i need the answer

Step-by-step explanation:

When subtracted, what is the simplified form of (5 − 3i) − (4 + 6i)? Write the answer in standard form, a + bi, where a and b are real numbers.

Answers

(5 - 3i) - (4 + 6i)      Remove the brackets. Be careful with those on the right.
5 - 3i - 4 - 6i            Did you notice how the second set worked. That - sign affected both terms inside the brackets. Now collect your like terms.

5 - 4 - 3i - 6i   The - 3i and - 6i  act like money. You are three dollars in the hold and you spend another 6. Where does that put you ?
1 - 9i              You are now 9 dollars in the whole.


in the plane figure shown below. if the degree measures of the angle are as shown, then x+y=

Answers

we know that

the sum of the internal angles in the figure shown is 360 degrees
so
360°=100°+60+70°+y+80°+x
360°=(x+y)+310°
(x+y)=360°-310°-----> 50°

the answer is
x+y is 50°

what is the area of a square with a radius of 9 cm

Answers

the answer would be 254.34
squares don’t have radius’, circles do. If you mean the length of one side is 9, then the area would be 81cm squared.

If you mean the area of a circle with a 9cm radius, then it would be 254.34 cm squared.

As viewed from above, a swimming pool has the shape of the ellipse x24900+y22500=1, where x and y are measured in feet. the cross sections perpendicular to the x-axis are squares. find the total volume of the pool. v = cubic feet

Answers

4900>2500, the major axis of the ellipse is along x-axis
a=sqrt(4900)=70
b=sqrt2500=50

The squares are parallel to the y-axis, thus their sides extend in the y-axis direction, hence the length of the sides are:
y=+/-50sqrt(1-x^2/4900))
The area of the square 
=y^2=[2500-2500(x^2/4900)

Thus, the volume will be sum along the x-axis from one of the ends of the ellipse to the other. by definition, the limits are (-a to a)=(-70 to 70)
But since the ellipse is symmetrical we can go from (0 to 70) and double the integral.
thus
V=2*int(0 to 70)[2500-2500(x^2/4900)]dx
=int(0 to 70)[5000-(50/49)x^2]dx
=[5000x-50/147x^3] (0 to 70)
=233,333 1/3 ft^3

if you flip a coin four times what is the probability of flipping tails four times

Answers

There are 16 possible outcomes.
Out of all 16 outcomes, there is only one way to get the result T T T T.
Therefore, the probability is 1/16 or 0.0625




all I drink 3/4 of a 16 fluid ounce bottle of juice how many fluid ounces of juice are left in the bottle

Answers

4 fluid ounces. 16 * 1/4 is 4
STEP 1:
multiply 16 oz. by 3/4 to find how many ounces are 3/4 of the bottle

=16 * 3/4
=(16*3)/4
=48/4
=12 ounces


STEP 2:
subtract step 1 answer from the whole 16 oz. to find number of ounces left

=16 - 12
=4 ounces left


CHECK:
multiply the whole 16 oz. by the fraction that would be left (4/4 - 3/4= 1/4). There are several ways to check this problem; this is just one way.

=16 * 1/4
=(16*1)/4
=16/4
=4


ANSWER: 4 ounces would be left

Hope this helps! :)

hey can you please help me posted picture of question

Answers

The correct answer is the option B.To solve this problem you must apply the proccedure shown below:

 1. You have the following expression:

 (11-7i)-(16-11i)

 2. If you want to substract both terms, you  need to substract the real numbers and the complex numbers. Then, you obtain:

 11-7i-16+11i
 (11-16)+(-7+11)

 3. Then, you obtain the following result:

 -5+4i

 4. Therefore, as you can see, the correct answer is the second option (option B), which is:

 B. -5+4i
Correct answer is option B.

Solution is shown below:

To add or subtract two complex numbers, the real part is added or subtracted from real part and the complex part is added to or subtracted from complex part as shown below:

(11 - 7i) - (16 - 11i)

= 11 - 7i - 16 + 11i

= -5 + 4i

So, the answer to this question is option B

A listing of all possible outcomes of an experiment and their corresponding probability of occurrence is called

Answers

A listing of all possible outcomes of an experiment and their corresponding probability of occurrence is called Probability distribution

The listing of all possible outcomes for an experiment is known as a probability distribution.

The following information is related to the probability distribution is:

It is the table or an equation that is connected with each and every result of the statistical experiment along with the probability of occurrence.Also, it is the list of all possible experiment results.

Therefore we can conclude that the listing of all possible outcomes for an experiment is known as a probability distribution.

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PLZ HELP ASAP CIRCLES

Answers

The center of the circle is at (-1, 1). The radius is determined by the distance from the center to the highlighted point (6, -4). The distance = sqrt[(6+1)^2 + (-4-1)^2] = sqrt[49 + 25] = sqrt(74)
Therefore, the equation of the circle is:
(x + 1)^2 + (y - 1)^2 = 74

The amount of money that a student at harvard university carries on his/her person is normally distributed with a mean of $25 and a standard deviation of $15. what is the probability that a randomly selected sample of 25 harvard university students will have an average amount of less than $22 on his/her person?

Answers

Mean, m = $25
Standard deviation, s = $15
Sample size, n = 25 students
X <$22

Now,
Z = [(X - m)*Sqrt (n)]/s = [(22-25)*Sqrt(25)]/15 = -1

From Z tables,
P(X) = P(Z = -1) = 0.1587 = 15.87%

Therefore, probability that the selected sample has an average of less than $22 is 15.87%.

Each square is one square meter

Answers

36 square meters i believe

is this correct if not help me

Answers

So far, so good.

You have properly counted squares and circles.

Factor completely 56a2b3 − 35ab.
7ab(8ab2 − 5)
7a(8b2 − 5ab)
Prime
7a(8ab3 − 5b)

Answers

A. 

Both numbers have a factor of 7ab. Pull that out by dividing. 

Answer:

7 ab ( 8 ab² - 5 ) .

Step-by-step explanation:

Given  : 56 a²b³ − 35 ab.

To find : Factor completely.

Solution : We have given 56 a²b³ − 35 ab.

Taking 7ab common form both terms .

7 ab ( 8 ab² - 5 ) .

Therefore, 7 ab ( 8 ab² - 5 ) .

Find the midpoint of the segment with the given endpoints. P(–2, 1) and Q(–3, 2)

Answers

Answer:

  (-5/2, 3/2)

Step-by-step explanation:

The midpoint is the average of the coordinates of the endpoints:

  (P +Q)/2 = ((-2, 1) +(-3, 2))/2 = (-2-3, 1+2)/2 = (-5/2, 3/2)

with an 18% discount, George was able to save 13.23 what was the original price

Answers

The original price is 74! Hope this helps!

18% = $13.23

1% = $13.25 ÷ 18 = $0.7361

100% = $0.7361 x 100 = $73.61

Answer: $73.61

How do you evaluate this equation: a number decreased by the difference of m and 7? Please help and quick!!

Answers

Let n be the number. 

A number decreased by the difference of m and 7 can be translated into mathematical expression as

     [tex]n-\left(m-7\right)[/tex]

if 12 1/2% of a sum of money is $40 what is the total sum of money?

Answers

12 1/2% = 12.5%

12.5% = $40

1% = 40 ÷ 12.5 = $3.20

100% = $3.20 x 100 = $320

Answer: $320

The total sum of money will be $320.

Let the total sum of money be represented by x.

Based on the information given, the equation to solve the question will be:

12 1/2% × x = 40

0.125x = 40

Divide by 0.125

x = 40/0.125.

x = 320

Therefore, the total sum of money will be $320.

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each of 5 boys ate 2/3 of a pizza. what is the total amount of pizza the boys ate?

Answers

3 1/3 pizzas.

Turn 5 into a fraction. 5/1

Multiply the two fractions. 5/1 × 2/3 = 10/3

Simplify this to 3 1/3 pizzas.

Hope this helps!

We have that for the Question "each of 5 boys ate 2/3 of a pizza. what is the total amount of pizza the boys ate?" it can be said that each boy ate

Pt=3.333pizza

From the question we are told

each of 5 boys ate 2/3 of a pizza. what is the total amount of pizza the boys ate?

total amount of pizza the boys ate

Generally the equation for the total amount of pizza the boys ate  is mathematically given as

Pt=N*Ratio

Therefore

Pt=5*2/3

Pt=3.333pizza

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Under what circumstances is a t statistic used instead of a z score for a hypothesis test

Answers

If you know the population standard deviation sigma, then you'd use the z score. Otherwise, you would use a t statistic. However, if n is large enough (usually n > 30), then you can approximate the T distribution with the normal Z distribution. Some stats textbooks will allow the use of a z score if n > 30. Though it will depend on your specific book and/or your teacher. 

HURRY PLEASE ITS TIMED
In the year 2000, Franklintown had a population of 30,000 people. Its population had decreased by 3% each year since then. Part A: Can this situation be modeled by an exponential decay function, an exponential growth function, or neither? Explain. Part B: If the population continues to decrease at the same rate, what would you expect the approximate population to be in 2016? Show your work.

Answers

Part A:
 For this case we have a function of the form:
 y = A * (b) ^ t
 Where,
 A: initial amount
 b: decrease rate
 t: time
 Substituting values we have:
 y = 30000 * (0.97) ^ t
 Answer:
 this situation can be modeled by an exponential decay function.

 Part B:

 We have the following function:
 y = 30000 * (0.97) ^ t
 For the year 2016 we have to:
 t = 16
 Substituting values:
 y = 30000 * (0.97) ^ 16
 y = 18427.6096
 Rounding:
 y = 18428
 Answer:
 The approximate population for 2016 is:
 y = 18428
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