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The circle described by the equation <img src="https://tex.z-dn.net/?f=%28x-3%29%5E%7B2%7D%20%2B%28y%2B4%29%5E%7B2%7D%3D9" id="T

ElenaW [278]

Answer:

The point at which center of the image circle located is (-2, -3) so second option is correct.

Step-by-step explanation:

Given equation of circle is:

$(x-3)^{2} + (y+4)^{2} = 9$ (i)

The general equation of circle is mentioned below,

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

Here 'r' represents the radius of the circle and (h,k) shown the center of the circle.

By comparing equation (i) and equation (ii), we get

r^2 = 9

r = 3

$(x-3)^{2} = (x-h)^{2}$

$(x-3) = (x-h)$

$h = 3$

$(y+4)^{2} = (y-k)^{2}$

$(y+4) = (y-k)$

$k = -4$

So the center of given circle is (h,k) = (3,-4)

Also, the circle is translated 5 units left, that is towards the -x-axis. Therefore h = 3 - 5 = -2

Also, the circle is translated 1 unit up, that is towards the +y-axis. Therefore k = -4 + 1 = -3

Hence, the point at which center of the image circle located is (-2, -3) so second option is correct.

6 0

3 years ago

Read 2 more answers

−4.8f+6.4=−8.48 What does f stand for?

Nataly [62]

Answer:F is a unknown number

Step-by-step explanation:Isolate the variable

3 0

3 years ago

What's 0.7 multiplied by 9 Estimate Tell me estimation and answer in comments

kirill [66]

Estimate:6
Answer:6.3

8 0

3 years ago

Read 2 more answers

Solve the equation -13/4 -x= 1/2x -1

ale4655 [162]

Answer:

x = 2 or 1/4

Step-by-step explanation:

-13/4 -x= 1/2x -1

Collect like terms

-13/4+1=1/2x+x

Using LCM

(-13+4)/4=(1+2x²)/2x

9/4=(1+2x²)/2x

Cross multiply

9(2x)=4(1+2x²)

18x=4+8x²

Turn into quadratic and solve

8x²-18x+4

Using formulae method

-b±(√b²-4ac)/2a

Where a=8, b= -18 and c=4

(-(-18)±(√(-18)²-4(8)(4))/2(8)

(18±(√324-128))/16

(18±√196)/16

(18±14)/16

(18+14)/16 or (18-14)/16

32/16 or 4/16

2 or 1/4

4 0

3 years ago

Read 2 more answers

graph the parabola y equals negative x squared + 3 to graph a parabola plot the vertex and four additional points two on each si

Nataliya [291]

You don't have the graph icon here, so we'll have to graph this parabola without it.

Your parabola is y = -x^2 + 3., which resembles y = a(x-h)^2 + k. We can tell immediately that this parabola opens down and that the vertex is (0,3).

Plot (0,3). Besides being the vertex, this point is also the max. of the function.

Now calculate four more points. Choose four arbitrary x-values, such as {-2, 1, 4, 5} and find the y value for each one. Plot the resulting four points. Draw a smooth curve thru them, remembering (again) that the vertex is at (0,3) and that the parabola opens down.

6 0

3 years ago