Answer:
2/3
Step-by-step explanation:
<h2>
Answer:</h2>
<u></u>
<h2>
Step-by-step explanation:</h2>
In the question,
We have to find out the circumcentre of the circle passing through the triangle with the vertices (a₁, b₁), (a₂, b₂) and (a₃, c₃).
So,
The circle is passing through these points the equation of the circle is given by,
On putting the points in the circle we get,
So,
On solving these equation using, <u>Matrix method we can get the required equation of the circle,</u>
<u></u>
<em><u>This is the required answer.</u></em>
Multiply both sides of the second equation by 100 to get rid of the decimals:
0.05<em>n</em> + 0.10<em>d</em> = 1.50
==> 5<em>n</em> + 10<em>d</em> = 150
Multiply both sides of the first equation by -5:
<em>n</em> + <em>d</em> = 21
==> -5<em>n</em> - 5<em>d</em> = -105
Add the two equations together:
(5<em>n</em> + 10<em>d</em>) + (-5<em>n</em> - 5<em>d</em>) = 150 + (-105)
Notice that the terms containing <em>n</em> get eliminated and we can solve for <em>d</em> :
(5<em>n</em> - 5<em>n</em>) + (10<em>d</em> - 5<em>d</em>) = 150 - 105
5<em>d</em> = 45
<em>d</em> = 45/5 = 9
Plug this into either original equation to solve for <em>n</em>. Doing this with the first equation is easiest:
<em>n</em> + 9 = 21
<em>n</em> = 21 - 9 = 12
So Donna used 12 nickels and 9 dimes.
Answer:
p=0 or p=4
Step-by-step explanation:
first simplify the equation
p^3-4p^2=0
p(p^2-4p)=0
p(p-4)(p-0)=0( factorise p^2-4p)
p=0 p=0. p-4=0,p=4
therefore,p=0 or p=4