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
Answer:
The slope is 1/-11.
Step-by-step explanation:
Slope (m) =
ΔY
/ΔX
=
1
/-11 = -0.090909090909091
Answer:
<em>The estimated sales were $260 million</em>
Step-by-step explanation:
Assume the endpoints of a segment are (x1,y1) and (x2,y2).
The midpoint (xm,ym) is calculated as follows:


The sales ov Cars, Inc. were (2008,240 million) and (2010,280 million). We need to use the midpoint to estimate the sales in 2009:


The estimated sales were $260 million
Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function
such that
.- If there exists a function
such that
, then
is surjective
Let us start by the first implication.
Our hypothesis is that the function
is surjective. From this we know that for every
there exist, at least, one
such that
.
Now, define the sets
. Notice that the set
is the pre-image of the element
. Also, from the fact that
is a function we deduce that
, and because
the sets
are no empty.
From each set
choose only one element
, and notice that
.
So, we can define the function
as
. It is no difficult to conclude that
. With this we have that
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function
such that
.
Take an element
, then
. Now, write
and notice that
. Also, with this we have that
.
So, for every element
we have found that an element
(recall that
) such that
, which is equivalent to the fact that
is surjective. Therefore, the prove is complete.
Answer:
LN = 66 cm
Step-by-step explanation:
The 3 parallel lines divide the 2 sides they intersect in proportion, that is
=
, substitute values
=
( cross- multiply )
15LM = 315 ( divide both sides by 15 )
LM = 21
Hence
LN = LM + MN = 21 + 45 = 66 cm