Answer:
x = 1/3
Step-by-step explanation:
Both bases can be written as powers of 6.
36^x = (1/6)^(x-1) . . . . . . given
(6^2)^x = (6^-1)^(x -1) . . . . . bases as powers of 6
6^(2x) = 6^(-x+1) . . . . . . . . . simplify exponents
2x = -x +1 . . . . . . . . . . . . . . . .equate exponents of the same base
3x = 1 . . . . . . . add x
x = 1/3 . . . . . divide by 3
x=3 and y=−2
Step-by-step explanation:
Solve8x+5y=14for x:
8x+5y=14
8x+5y+−5y=14+−5y(Add -5y to both sides)
8x=−5y+14
8x8=−5y+148(Divide both sides by 8)
x=−58y+74
Step: Substitute−58y+74forxin−4x−5y=−2:
−4x−5y=−2
−4(−58y+74)−5y=−2
−52y−7=−2(Simplify both sides of the equation)
−52y−7+7=−2+7(Add 7 to both sides)
−52y=5
−52y−52=5−52(Divide both sides by (-5)/2)
y=−2
Step: Substitute−2foryinx=−58y+74:
x=−58y+74
x=−58(−2)+74
x=3(Simplify both sides of the equation)
Answer:
x=3 and y=−2
Answer: you would have $1772 at the end of 10 years.
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = $1200
r = 3.9% = 3.9/100 = 0.039
t = 10 years
Therefore,
A = 1200 x 2.7183^(0.039 x 10)
A = 1200 x 2.7183^(0.39)
A = $1772 to the nearest dollar
Subtract y from the fist equation to get an expression for x.
... x + y - y = 6 - y
... x = 6 - y
Assuming your multiplication symbol (×) in the second equation is supposed to be the variable x, performing the substitution gives
... 3(6-y) - y = 6 . . . . . . equation after substitution
... 18 - 4y = 6 . . . . . . . . eliminate parentheses
... 12 - 4y = 0 . . . . . . . . subtract 6
... 3 - y = 0 . . . . . . . . . . divide by 4
... 3 = y . . . . . . . . . . . . .add y
Now, we can use the above expression for x to find x
... x = 6 - y = 6 - 3
... x = 3
The solution of the system of equations is (x, y) = (3, 3).
38, I think I don't know if i am correct but a cube has 6 sides and if you roll it twice 6*6=36 and a coin has 2 sides and is tossed once so 2*1=2 so 2+36+38. I am sorry if its isn't correct.
