Since the average of 6 tests is 6, and we know that the average is found by dividing the total score by the number of tests, we can just multiply the average by the number of tests to find the total score. Doing this, we get 82 * 6 which simplifies to 492.
The multiplication of 3 and -4 on a number line is shown
<h3><u>Solution:</u></h3>
The number line representation is shown below
On number line the points are at equal distances
The multiplication of 3 with -4 can be understood in the following way:-
a × b , means a jumps b times
Eg :- 3 × -4 means 3 jumps -4 times
Which basically mean we are going to move 3 number per step , and we are going to do this 4 times and –ve sign indicates we will move in negative direction
Therefore,
So, when we move from 0 , when we take first step we reach -3 , in next step we reach -6 , in next we reach -9 and in the last step we reach -12
Which is the product 3 and -4 .i.e.
x
4
−
12
x
2
=
64
x
4
-
12
x
2
=
64
Move
64
64
to the left side of the equation by subtracting it from both sides.
x
4
−
12
x
2
−
64
=
0
x
4
-
12
x
2
-
64
=
0
Rewrite
x
4
x
4
as
(
x
2
)
2
(
x
2
)
2
.
(
x
2
)
2
−
12
x
2
−
64
=
0
(
x
2
)
2
-
12
x
2
-
64
=
0
Let
u
=
x
2
u
=
x
2
. Substitute
u
u
for all occurrences of
x
2
x
2
.
u
2
−
12
u
−
64
=
0
u
2
-
12
u
-
64
=
0
Factor
u
2
−
12
u
−
64
u
2
-
12
u
-
64
using the AC method.
Tap for fewer steps...
Consider the form
x
2
+
b
x
+
c
x
2
+
b
x
+
c
. Find a pair of integers whose product is
c
c
and whose sum is
b
b
. In this case, whose product is
−
64
-
64
and whose sum is
−
12
-
12
.
−
16
,
4
-
16
,
4
Write the factored form using these integers.
(
u
−
16
)
(
u
+
4
)
=
0
(
u
-
16
)
(
u
+
4
)
=
0
Replace all occurrences of
u
u
with
x
2
x
2
.
(
x
2
−
16
)
(
x
2
+
4
)
=
0
(
x
2
-
16
)
(
x
2
+
4
)
=
0
Rewrite
16
16
as
4
2
4
2
.
(
x
2
−
4
2
)
(
x
2
+
4
)
=
0
(
x
2
-
4
2
)
(
x
2
+
4
)
=
0
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
a
2
-
b
2
=
(
a
+
b
)
(
a
-
b
)
where
a
=
x
a
=
x
and
b
=
4
b
=
4
.
(
x
+
4
)
(
x
−
4
)
(
x
2
+
4
)
=
0
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
If any individual factor on the left side of the equation is equal to
0
0
, the entire expression will be equal to
0
0
.
x
+
4
=
0
x
+
4
=
0
x
−
4
=
0
x
-
4
=
0
x
2
+
4
=
0
x
2
+
4
=
0
Set the first factor equal to
0
0
and solve.
Tap for fewer steps...
Set the first factor equal to
0
0
.
x
+
4
=
0
x
+
4
=
0
Subtract
4
4
from both sides of the equation.
x
=
−
4
x
=
-
4
Set the next factor equal to
0
0
and solve.
Tap for more steps...
x
=
4
x
=
4
Set the next factor equal to
0
0
and solve.
Tap for more steps...
x
=
2
i
,
−
2
i
x
=
2
i
,
-
2
i
The final solution is all the values that make
(
x
+
4
)
(
x
−
4
)
(
x
2
+
4
)
=
0
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
true.
x
=
−
4
,
4
,
2
i
,
−
2
i
x
=
-
4
,
4
,
2
i
,
-
2
i
x
4
−
1
2
x
2
=
6
4
x
4
-
1
2
x
2
=
6
4
Put the whole number over 1....1 is the denominator