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Advocard [28]
3 years ago
14

If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?

Mathematics
2 answers:
astraxan [27]3 years ago
5 0

The equation of a circle with center at (a,b) and radius r is: (x-a)^2+(y-b)^2=r^2.

This circle has been translated from (0,0) to (a,b).

 

The equation of the circle in our case can be rewritten as: (x-2)^2+(y-2)^2=2^2

Moving the graph 3 units to the right is: (x-2-3)^2+(y-2)^2=2^2.

Moving the graph 1 unit down is: (x-2-3)^2+(y-2-1)^2=2^2.

This gives the equation: (x-5)^2+(y-3)^2=2^2

<span>So, the center of the circle is: (5,3)</span>

dsp733 years ago
4 0

Answer:  The new co-ordinates of the center are (5, -2).

Step-by-step explanation:  The given equation of a circle is

x^2-4x+y^2+2y=4~~~~~~~~~~~~~~~~~~~~~~~~(i)

We are to find the center of the above circle if the circle (i) is translated 3 units to the right and 1 unit down.

The standard equation of a circle with radius r units and center at (h, k) is given by

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

From equation (i), we have

x^2-4x+y^2+2y=4\\\\\Rightarrow (x^2-4x+4)+(y^2+2y+1)-4-1=4\\\\\Rightarrow (x-2)^2+(y+1)^2=9\\\\\Rightarrow (x-2)^2+(y+1)^2=3^2.

Comparing the above equation with the standard equation of a circle, we get

center, (h, k) = (2, -1) and radius, r = 3 units.

If the circle is translated 3 units to the right and 1 unit down, then the co-ordinates of the new center will be

(h', k') = (h+3, k-1) = (2+3, -1-1) = (5, -2).

Thus, the new co-ordinates of the center are (5, -2).

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If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x)
Sergeeva-Olga [200]

Answer:

(f+g)(x)=f(x)+g(x)

=(-3x-5)+(4x-2)

= -3x-5+4x-2. collect like term

= -3x+4x-5-2

= x-7. the final answer

8 0
2 years ago
P(Girl Sophomore) :<br> =[?]
marusya05 [52]

Probability helps us to know the chances of an event occurring. The probability being a Sophomore given she is a girl is 1/3.

<h3>What is Probability?</h3>

Probability helps us to know the chances of an event occurring.

\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}

The probability of being a girl and Sophomore is 9/37. While the probability of being a girl is 27/37. Therefore, the probability being a Sophomore given she is a girl is,

P(Girl l Sophomores) = P(Girl and Sophomore)/ P(Girl)

                                  = (9/37) / (27/37)

                                  = 9 / 27

                                  = 1/3

Hence, the probability being a Sophomore given she is a girl is 1/3.

Learn more about Probability:

brainly.com/question/795909

#SPJ1

3 0
1 year ago
Read 2 more answers
Marla filled up her car's gas tank and then went on a trip. After she drove 329 miles, she filled her tank with 14 gallons of ga
romanna [79]

Answer:

23 1/2 miles per gallon

Step-by-step explanation:

We start with dividing 329 miles with 14 gallons because it asks to find the number of miles on each gallon of gas -

          Miles

-----------------------------     =

Each gallon of gas

329 ÷ 14 = 23 1/2 miles per gallon

6 0
3 years ago
two angles are consecutive exterior to one another. if the angles are in ratio 11:7. Then find the supplement of the larger angl
Gwar [14]

If the ratio of two consecutive exterior angles are 11:7, the supplement of the larger angle will be <u>70 degrees</u>.

The larger angle and the smaller angle are supplementary to each other since they are consecutive exterior to one another.

  • <em><u>Thus</u></em>:

If the larger angle is x, therefore:

Ratio of Larger angle to smaller angle = 11:7

  • <em>Therefore</em>:

11x + 7x = 180 degrees

  • Solve for x

18x = 180

  • Divide both sides by 18

x = 10

Larger angle = 11x = 11(10) = 110 degrees

Smaller angle = 7x = 7(10) = 70 degrees

The supplement of the larger angle, 110 degrees, is <u>70 degrees.</u>

In summary, if the ratio of two consecutive exterior angles are 11:7, the supplement of the larger angle will be <u>70 degrees</u>.

Learn more here:

https://brainly.in/question/1502890

6 0
3 years ago
If the purchase price for a house is $218,500, what is the monthly payment if you put 3.5% down for a 30 year loan with a
sashaice [31]

Answer:

218,500 - (3.5% down payment) =

210,852.50

30 years = 360 months

rate 6.5%

Use the loan payment formula (REALLY complex - see attached).

rate = 6.5/1,200 = 0.005416667

monthly payment = (rate + [rate / (((1 + rate)^months) -1)] * principal

monthly payment = (0.005416667 + [0.005416667 / (((1.005416667)^360)-1)] * principal

monthly payment = (0.005416667 + [0.005416667 / (((1.005416667)^360)-1)] * principal

monthly payment = 0.005416667 + [(0.005416667 / 6.9917988084 -1)] *  210,852.50

monthly payment = 0.005416667 + [(0.005416667 / 5.9917988084)] *  210,852.50

monthly payment = 0.005416667 + [(0.005416667 / 5.9917988084)] *  210,852.50

monthly payment = (0.005416667 + 0.0009040135) * 210,852.50

monthly payment = 0.0063206805 * 210,852.50

monthly payment = 1,332.73

Answer is a.

3 0
2 years ago
Read 2 more answers
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