Answer:
my best answer for this is B. False.
I calculated as fast as i can.
The answer is actually 1, and not 0, and here's why.
Write 3^36 into (3^3)^12. Note that the exponents 3 and 12 multiply to 36
Now focus on 3^3 which turns into 27. The last digit here is 7. It turns out that this is the only thing that matters when it comes to finding the final answer.
So instead of 27^12, we can look at 7^12
Break 7^12 into (7^3)^4, then note how 7^3 = 343. Again the units digit is all we care about. So instead of 343^4, we just look at 3^4
3^4 = 81 and the units digit here is 1 which is the final answer.
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Here's an alternative approach using modular arithmetic. This is the set of tools that helps us find remainders. If we work with mod 10, then we can find the units digit of any complicated expression such as 3^36
3^36 = (3^3)^12 (mod 10)
3^36 = 27^12 (mod 10)
3^36 = 7^12 (mod 10)
3^36 = (7^3)^4 (mod 10)
3^36 = 343^4 (mod 10)
3^36 = 3^4 (mod 10)
3^36 = 81 (mod 10)
3^36 = 1 (mod 10)
We effectively follow the same steps as mentioned above, but we're using a more formal set of steps to show.
y=3x-2 y=-2x+8
3x-2=-2x+8 (plus 2 each side)
3x=-2x+6 (plus 2x each side)
5x=6 (divide by 5 each side)
x=1.2
Plug x back into an equation
y=3(1.2)-2
y=3.6-2
y=1.6
Answer: (1.2, 1.6)
Answer:
D. Y+5=-(1/2)*(x+3)
Step-by-step explanation:
Perpendicular Lines are those with the following condition:
y=a*x+b (1)
y=c*x+d (2)
Where 'a' and 'c' are the respective slope
If These two lines are perpendicular, then
a=- 1/c
Equation (1) for our case is written as y=2x-8, meaning that a=2 and b = -8
Using those principles we have that the slope for our needed line ('c') has to be -(1/2).
Now we most use the given point to find the remaining term of the equation (d) so, evaluate (-3,-5) in eq (2) to have this:
-5=(-1/2)*(-3)+d
resulting that d=-5-(3/2)
Eq (2) is written now as the following: y= (-1/2)*x - (5+3/2)
Rearranging terms, we have the following:
y+5=(-1/2)*x-(3/2)
where you can obtain a more pretty expression:
y+5=(-1/2)*(x+3)
All you have to do is plug in the number of cavities you have into the equation.
so with 50 + 100n = answer
it will be 50 +100(2) = answer
100*2 = 200
50 + 200 = <u>250</u>
the answer is 250