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anzhelika [568]
3 years ago
10

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

Mathematics
1 answer:
zepelin [54]3 years ago
8 0

Answer:

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

As we know the given points

Center = (5, -4)

and

Point on circle = (-3,2)

The distance between point on circle and center will give us the radius of circle

So,

The formula for distance is:

\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}\\Taking\ center\ as\ point\ 1\ and\ the\ other\ point\ as\ point\ 2\\d=\sqrt{(-3-5)^{2}+(2-(-4))^{2}}\\d=\sqrt{(-8)^{2}+(2+4)^{2}}\\d=\sqrt{(-8)^{2}+(6)^{2}}\\\\d=\sqrt{64+36}\\d=\sqrt{100} \\ d=10\\So\ the\ radius\ is\ 10

The standard form of equation of circle is:

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

where h and k are the coordinates of the center. So putting in the value:

(x-5)^{2}+(y-(-4))^{2}=(10)^{2}\\(x-5)^{2}+(y+4)^{2}=100

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A vehicle factory manufactures cars. The unit cost (the cost in dollars to make each car) depends on the number of cars made. If
Nataly [62]

Answer:

The function is missing in the question. The function is $ C(x) = 0.8x^2 -544x +97410 $

The answer is 4930

Step-by-step explanation:

Unit cost of a car is given as

$ C(x) = 0.8x^2 -544x +97410 $

Cost will be minimum when

x = -(-544)/ 2 x 0.8

  = 340

Therefore, minimum cost for unit car is

$ C(x) = 0.8x^2 -544x +97410 $

$ = 0.8(340)^2 -544(340) +97410 $

=  4930

4 0
3 years ago
Can someone help me please
Yakvenalex [24]

Answer:

the third one ( -7+u+8t)

Step-by-step explanation:

first you add the ts together and you get 8. Then u keep the U and cancel out the +2 nad the -2. Then you are left with your answer. have a nice day

7 0
2 years ago
Based on the information given say whether or not △ABC∼△FED. Explain your reasoning.
GalinKa [24]

Answer:

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F = x

m∠D = 2x-20°.

Now, let m∠A = m∠B = y

So, m∠C = m∠A + 30° = y+30

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B +  m∠C = 180

y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50

Therefore, m∠A = 50°, m∠B = 50° and m∠C =  m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50

Therefore,  m∠F = 50°  

m∠E = 50° and  

m∠D =  2x-20=2(50)-20=100-20=80\°

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.

5 0
3 years ago
Find the slope, Y-intercept, and equation (make sure there is no decimals if there is a decimal make it into a fraction)!
adelina 88 [10]

Answer:

Slope is 5/3

y-intercept = -3

y = 5/3x - 3

Step-by-step explanation:

To find the slope, take to coordinates and use the equation below

m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}

7-2 = 5

6-3= 3

Now you have your slope which is 5/3

Then take the slope and input it into point slope form to get your y-intercept.

y-y₁=m(x-x₁)

y-2 = 5/3(x-3)

y-2=5/3x-5

add two to both sides to get Y by itself

y = 5/3x - 3

now you have your y-intercept, which is -3

Then check your answer by inputing two different coordinates for X and Y

7 = 5/3(6)-3

7=7

12= 5/3(9)-3

12=12

6 0
2 years ago
WHAT ARE<br>THE common FACTORS of 4 and 8​
Mars2501 [29]

Hello!

Answer:

4- 8, 12, 16, 20, 24 ect keep adding 4

8- 16, 24, 32, 40, 48 ect keep adding 8

Step-by-step explanation:

both- 16, 24, 40, 48

Hope this helps have a good day! <3

Plz mark brainliest when u get the chance!

8 0
2 years ago
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