Answer:
The correct answers are x + y = 5600 and x - y = 700.
Step-by-step explanation:
Write a system of equations in x and y describing the situation. Do not solve the system.
Keiko has a total of $ 5600, which she has invested in two accounts.
Let x be the amount of money in the larger account and y be the amount of money in the smaller account.
So, Keiko has invested her $5600 in two accounts x and y.
Thus x + y = 5600.
Also, given by the problem, the larger account (x) is $ 700 greater than the smaller account (y).
Thus x - y = 700.
Thus the two system of equation in x and y describing the given situation are
x + y = 5600 and x - y = 700
Distribute the 3 to 4m and 6. this makes 12m-18=12
now add 18 to both sides.
12m=30
now divide by 12
m=30/12
profit=f(x)
so solve for f(x)=1000
1000=70n-400
add 400 to both sides
1400=70n
divide both sides by 70
20=n
20 students need to be enrolled to make a profit of 1000.00
Answer:
Numeric expressions apply operations to numbers. For example, 2(3 + 8) is a numeric expression. Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.
Step-by-step explanation:

Notice that

So as

you have

. Clearly

must converge.
The second sequence requires a bit more work.

The monotone convergence theorem will help here; if we can show that the sequence is monotonic and bounded, then

will converge.
Monotonicity is often easier to establish IMO. You can do so by induction. When

, you have

Assume

, i.e. that

. Then for

, you have

which suggests that for all

, you have

, so the sequence is increasing monotonically.
Next, based on the fact that both

and

, a reasonable guess for an upper bound may be 2. Let's convince ourselves that this is the case first by example, then by proof.
We have


and so on. We're getting an inkling that the explicit closed form for the sequence may be

, but that's not what's asked for here. At any rate, it appears reasonable that the exponent will steadily approach 1. Let's prove this.
Clearly,

. Let's assume this is the case for

, i.e. that

. Now for

, we have

and so by induction, it follows that

for all

.
Therefore the second sequence must also converge (to 2).