Answer:
Step-by-step explanation:
Rewrite
100
x
2
100
x
2
as
(
10
x
)
2
(
10
x
)
2
.
(
10
x
)
2
+
60
x
+
9
(
10
x
)
2
+
60
x
+
9
Rewrite
9
9
as
3
2
3
2
.
(
10
x
)
2
+
60
x
+
3
2
(
10
x
)
2
+
60
x
+
3
2
Check the middle term by multiplying
2
a
b
2
a
b
and compare this result with the middle term in the original expression.
2
a
b
=
2
⋅
(
10
x
)
⋅
3
2
a
b
=
2
⋅
(
10
x
)
⋅
3
Simplify.
2
a
b
=
60
x
2
a
b
=
60
x
Factor using the perfect square trinomial rule
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
, where
a
=
10
x
a
=
10
x
and
b
=
3
b
=
3
.
(
10
x
+
3
)
2
6+5=11+5=16+5=21
3+6=9+6=15+6=21
It will take Marco and Sophie 3 hours to get the same amount of money. The amount of money they will have will be $21.
Answer:
The final depth of Melissa is 14 meters below the surface
Step-by-step explanation:
In this kind of problems, involving directions, etc, usually one position is the positive direction and the other position is the negative direction.
In our problem, we suppose that the surface is the positivo zero, above the surface is the positive position(positive depth) and below the surface is the negative directions(negative depth).
The problem states that Melissa is 29 meters below the surface. So, her initial position is 29 meters in the negative direction, so it is equal to -29.
Then, the problem states that Melissa rises upward 15 meters. Upward is the positive direction, so she moved to the positive direction. It means that we are going to do -29+15 = -14 meters.
It means that the final depth of Melissa is 14 meters below the surface
