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monitta
3 years ago
10

Prove or disprove that the circle with equation x^2-4x+y^2=-3 intersects the y axis

Mathematics
1 answer:
wel3 years ago
7 0
The general equation given is x^2 - 4x + y^2 = -3. Transform this to an equation of a circle of the form x^2 + y^2 = r^2.

Use completing the square method:

x^2 - 4x + 4 + y^2 = -3 + 4
(x - 2)^2 + y^2 = 1

the center of the circle is (2,0) and r = 1

To check if it intersects the y axis, find the value of the x-intercept. 
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m_a_m_a [10]

Answer:

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8 0
3 years ago
Your schools talent show will feature 12 solo acts and ensemble 2 acts. The show will last 90 min. The 6 solo performers judged
kicyunya [14]
A.  12*x + 2*y = 90
       6*x + 2*y = 60

To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.

B.  Here we can multiply second equation with negative 1 and add it to first equation.
6x = 30
x = 5

now we replace x in any of 2 equations to get y.
30+2y = 60
2y = 30
y=15

Solo acts are 5 minutes long and ensemble acts are 15 minutes long
3 0
3 years ago
How do I solve 3x+17 greater than or equal to (you can’t do the sign on a phone but it would be _>) 5
Kobotan [32]
<h3><u>The value of x is greater than or equal to -4.</u></h3>

(3x + 17) ≥ 5

Subtract 17 from both sides.

3x ≥ -12

Divide both sides by 3.

x  ≥ -4


5 0
3 years ago
What does 3 (2x - 4) = 8x 14 equal?
jeka57 [31]
6x - 12 = 8x + 14
2x = - 26
x = - 13
5 0
3 years ago
The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times t
alexdok [17]
Let the three numbers be x, y and z respectively, then
x + y + z = 62 . . . (1)
y = x - 4 . . . (2)
z = 4x . . . (3)

The above three expressions could be used to represent the numbers.

Solving the three equations, putting (2) and (3) into (1) gives
x + x - 4 + 4x = 62
6x - 4 = 62
6x = 62 + 4 = 66
x = 66/6 = 11
x = 11.
y = 11 - 4 = 7
z = 4(11) = 44

x = 11, y = 7, z = 44.
3 0
3 years ago
Read 2 more answers
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