To find the root, replace y with 0
X^2-12x+35=0
A=1 B=-12 C=35
B^2-4ac=(-12)^2 -4(1)(35)
=144 -140
=4
x=(-b+/- square root of b^2 -4ac) /over/ (2a)
Plug in the numbers
x=-(-12) sqr (-12)^2 4(1)(35) / (2)(1)
X=12 +/-sqr 4 / 2
Positive outcome
x=12 + sqr 4 / 2
x=12+2/2
x=7 <— this one
Negative outcome
x=12-2i/2
x=6-i
Vertex: (6,-1)
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:
-2/3
Step-by-step explanation:
The slope of a line can be represented as 
where (x1, y1) and (x2, y2) are points on the line. We can substitute the points given, (-3, 5) and (6, -1), to calculate the slope:
Answer:
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Step-by-step explanation:
2/3 = 8/12. So the answer is 4/12
