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Ymorist [56]
2 years ago
12

By finding the radius of each circle and the distance between their centers, show that the circles x²+y²=4 and x²-4x+y²-4y+4=0 i

ntersect. Illustrate graphically.

Mathematics
1 answer:
Contact [7]2 years ago
6 0

Answer:

The circles do intersect.

Step-by-step explanation:

A circle is of the form

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

where,

h = Point on x axis of the circle center

k = Point on y axis of the circle center

x^2+y^2=4\\\Rightarrow (x-0)^2+(y-0)^2=2^2

So, the center of the circle is at (0,0) and radius is 2 units

x^2-4x+y^2-4y+4=0\\\Rightarrow (x^2-4x)+(y^2-4y)=-4\\\Rightarrow (x-2)^2+(y-4)^2=-4\\\Rightarrow (x^2+4-4x)+(y^2+4-2y)=-4\\\Rightarrow (x-2)^2+(y-2)^2=-4+4+4\\\Rightarrow (x-2)^2+(y-2)^2=4\\\Rightarrow (x-2)^2+(y-2)^2=2^2

The circle center is at the point (2,2) and radius is 2 units.

Hence, the circles do intersect.

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Which equation has infinitely many solutions?
MrRa [10]

Answer:

-6y + 6 = -2(3y - 3)

Step-by-step explanation:

-6y + 6 = -2(3y - 3)

-6y + 6 = -6y + 6

Therefore, the equation has infinitely many solutions.

4 0
3 years ago
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Andrew buys books and videos in a store. He uses the expression 4b + 8v to find the cost of what he is buying, where b is the nu
7nadin3 [17]

Answer:

68

Step-by-step explanation:

1) Plug In (when you plug in you replace the defined variable with the number given. usually you have to find the numbers to plug in but since they're already given to you you just plug them in.) 4(3) + 8(7)=T   T= total cost

2) Multiply 4*3=12 8*7=56

3) Add 12+56=68

4) <u>T=68</u>

7 0
2 years ago
Please help thank you! will give brainliest!
VashaNatasha [74]

A'(-6, -10), B'(-3,-13), and C'(-5,-1) are the vertices of the ΔA'B'C' under the translation rule (x,y)→(x,y-3). This can be obtained by putting the ΔABC's vertices' values in (x, y-3).

 

<h3>Calculate the vertices of ΔA'B'C':</h3>

Given that,

ΔABC : A(-6,-7), B(-3,-10), C(-5,2)

(x,y)→(x,y-3)

The vertices are:

  • A(-6,-7 )⇒ (-6,-7-3) = A'(-6, -10)
  • B(-3,-10) ⇒ (-3,-10-3) = B'(-3,-13)
  • C(-5,2) ⇒ (-5,2-3) = C'(-5,-1)

Hence A'(-6, -10), B'(-3,-13), and C'(-5,-1) are the vertices of the ΔA'B'C' under the translation rule (x,y)→(x,y-3).

Learn more about translation rule:

brainly.com/question/15161224

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7 0
2 years ago
What is 4-9+(-6)?????????
Leviafan [203]

Answer:

it's -11

Step-by-step explanation:

hope this helped

4 0
2 years ago
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Einstein Office Equipment has a rental plan for office machines. A fax machine that lists for $722.98 can be rented for 22% of t
Archy [21]

Answer:

$13.68


Step-by-step explanation:

Assuming they rent for 1 year, the cost is broken down as follows:


Annual renting cost = 22% of 722.98 = \frac{22}{100}*722.98=0.22*722.98=159.06


Usage charge = 3.2% of 159.06 = \frac{3.2}{100}*159.06=0.032*159.06=5.09

Thus,

Total annual charge = Annual renting cost + Usage charge = 159.06 + 5.09 =164.15


Monthly rental charge would be 164.15 divided by 12 (12 months in 1 year):

\frac{164.15}{12}=13.68 dollars

6 0
3 years ago
Read 2 more answers
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