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Darya [45]
3 years ago
8

If (5, 4) and (7,2) are the endpoints of a diameter of a circle, what is the equation of the circle?

Mathematics
2 answers:
STatiana [176]3 years ago
8 0

Answer:

  (x -6)^2 +(y -3)^2 = 2

Step-by-step explanation:

The midpoint (C) is the center of the circle:

  C = ((5, 4) +(7, 2))/2 = ((5+7)/2, (4+2)/2) = (6, 3)

A circle with center (h, k) that goes through point (a, b) can be written as ...

  (x -h)^2 +(y -k) ^2 = (a -h)^2 +(b -k)^2

Using the values for this problem, we get ...

  (x -6)^2 +(y -3)^2 = (5 -6)^2 +(4 -3)^2

  (x -6)^2 +(y -3)^2 = 2

liberstina [14]3 years ago
6 0

Answer:

Its A.

Step-by-step explanation:

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If you roll the six sided dice six times, are you guaranteed to get a sum of 7 once? answer
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Yes it can be guaranteed to get a sum of 7 once
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3 years ago
A certain car rental location charges a daily fee as well as a mileage charge. On one trip a businessman rented a car for the da
nikklg [1K]

Answer:

x\approx 267\ miles

Step-by-step explanation:

<u>Linear Modeling</u>

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

f(x)=mx+b

For the problem at hand, we must pick the adequate variables according to the data provided.

The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:

c = the charge for renting a car in dollars

x = the distance driven by the businessman in miles

Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:

c = mx+b

We must find the values of m and b with the data provided. Substituting the first point:

79 = 150m+b

Substituting the second point:

63.70 = 65m+b

Both equations form the following system:

\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.

Subtracting both equations:

150m-65m=79-63.70

Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:

85m=15.3

Solving:

m=15.3/85=0.18

From the first equation

79 = 150m+b

Solving for b:

b=79-150m=79-150(0.18) = 52.

The model for the problem is:

c=0.18x+52

Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100

100=0.18x+52

Solve for x:

0.18x+52=100

0.18x=100-52=48

x=48/0.18=266.67

Rounding to the closest integer:

\boxed{x\approx 267\ miles}

7 0
3 years ago
specialty T-shirts are being sold online for $30 each plus a one-time handling fee of $2.75 . The total cost is a function of th
myrzilka [38]

30(5)+2.75=152.75

The answer is D.

30t +2.75; 152.75

5 0
3 years ago
Find the future value of $3633.49 invested for 2 years at 4% compounded monthly? ​
SSSSS [86.1K]

Answer:

$290.68

Step-by-step explanation:

$3633.49 times 2 times 4% = $290.68

3 0
2 years ago
If you were to open an account that will pay you 3.5% interest with a deposit of $150 so find the following ending amount for ea
aev [14]

Answer:

FV= $160.68

Step-by-step explanation:

Giving the following information:

Initial investment= $150

Interest rate= 3.5% compounded annually

Number of periods= 2

T<u>o calculate the future value, we need to use the following formula:</u>

FV= PV*(1+i)^n

PV= present value

i= interest rate

n= number of periods

FV= 150*(1.035^2)

FV= $160.68

3 0
3 years ago
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