Can someone help me on my question please answer hurry
The roots of this equation would be -1/3 and -3.
They are congruent to each other. Any two polygons with the scale factor of 1 will be congruent.
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.
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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.
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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
Answer:
A is (10,0)
B is (3, 3).
Step-by-step explanation:
First we calculate the coordinates of the point A.
Here, y = 0 so we have:
7(0) - 3x + 30 = 0
-3x + 30 = 0
x = -30/-3 = 10.
So A has coordinates (10,0).
Next we find the coordinates of the points where the line passes through the y axis. Here x = 0:
7x - 3(0) = 30
x = 30/7.
So the point is (0, 30/7).
Let the point B have coordinates (x1, y1)
Now x1 = y1 (given).
If we draw a line from B perpendicular to the x axis ( its length will be = y1) then we have 2 similar triangles.
So as corresponding sides are in the same ratio:
y1/ (30/7) = (10-x1) / 10
But as x1 = y1:
x1/ (30/7) = (10-x1) / 10
7 x1 / 30 = (10-x1) / 10
70 x1 = 30(10 - x1)
70x1 = 300 - 30 x1
100 x1 = 300
x1 = 3
So the coordinates of B are (3,3)
Checking the solution to the equation:
LHS = 3 / 30/7 = 3*7 / 30 = 21/30 = 7/10.
RHS = (10 -3 ) / 10 = 7/10.