Answer:
l = 0.13x+1025
Step-by-step explanation:
Let the monthly sales be x
Monthly income = $1025 + 13% of monthly sales
Monthly income = $1025 + 0.13x
Since l represent the monthly income
l = 1025+0.13x
Rearrange
l = 0.13x + 1025
Hence the linear equation representing the statement is l = 0.13x+1025
Answer:
is equivalent to the inequality
Step-by-step explanation:
Given inequality :
We are supposed to find Which of the following is equivalent to the inequality
Multiply both sides by 10
is equivalent to the inequality
So, Option B is true
B)
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).
recall, slope = rise/run, and that a fraction is undefined when the denominator is 0, meaning this slope has a run = 0.
to make it short, when the slope is undefined, is a flag that we simply have a vertical line. Check the picture below.
Answer:
A). 1/2x + 4
Step-by-step explanation:
The slope is positive since the slant is towards the right and the slope is 1/2 since using rise/run shown that it is 1/2.