Answer:
$2,459.21
Step-by-step explanation:
(see attached for reference)
recall that the formula for compound interest is:
A = P [ 1 + (r/n)^ (nt) ]
where,
A = Final amount ( we are asked to find this)
P = principal amount = given as $2,340
r = Annual Interest Rate = given as 5% = 0.05
n = number of times compounded in a year = 4 (compounded quarterly)
t= time = 1 year
Substituting the values into the equation,
A = P [ 1 + (r/n)^ (nt) ]
A = 2,340 [ 1 + (0.05/4)^ (4·1) ]
A = $2,459.21
To find the quotient, divide 396 by 12.
396/12= 33
Answer:
We have 40% antifreeze and 70% antifreeze and we need to make 240 liters of 64% antifreeze.
We set up 2 equations where "f" is the 40 % and "s" is the 70%
A) f + s = 240
B) .40f + .70s = (.64 * 240) (or 153.6)
To solve both equations we multiply A) by -.40
A) -.40 f - .40 s = -96.00 then we add this to B)
B) .40f + .70s = 153.60
.30s = 57.6
s = 192
f = 48
48 liters of 40% = 19.20 liters of antifreeze
192 liters of 70% = 134.40 liters of antifreeze
That equals 153.60 liters of antifreeze in a TOTAL liquid amount of 240 liters.
Double Check
153.60 / 240 = 64% antifreeze.
Step-by-step explanation:
11. 6 + 5 * 2 + (-3)
6 + 10 - 3
16 - 3
13 <==
12. 67 + 84 - 12 * 4 / 16
67 + 84 - 48/16
67 + 84 - 3
148 <==
13. -5 * -6 - 25/5 - 2
30 - 5 - 2
23 <==
14. 18 - (9 + 3) + 2^3
18 - 12 + 8
14 <==
15. -24 / -6 * 2
4 * 2
8 <==
16. 8 [ (26 + 10) - 4(3 + 2)]
8 [ (36 - 4(5)]
8 [ 36 - 20 ]
8 [ 16 ]
128 <==
17. 6 * 3 / 9 * 2 + 1
18/9 * 2 + 1
2 * 2 + 1
4 + 1
5 <==
18. (9 - -4)(-8 - -7)
(9 + 4)(-8 + 7)
13 * -1
-13 <==
QUESTION 1
We want to solve,
We factor the denominator of the fraction on the right hand side to get,
This implies
We multiply through by LCM of
We expand to get,
We group like terms and equate everything to zero,
We split the middle term,
We factor to get,
But
is not in the domain of the given equation.
It is an extraneous solution.
is the only solution.
QUESTION 2
We add x to both sides,
We square both sides,
We expand to get,
This implies,
We solve this quadratic equation by factorization,
But
is an extraneous solution