Answer:
Step-by-step explanation:
Move 729 to the left side of the equation by subtracting it from both sides. x 3 − 729 = 0 Factor the left side of the equation. Rewrite 729 as 9
3
. x
3
−
9
3
=
0
. Since both terms are perfect cubes, factor using the difference of cubes formula, a
3
−
b
3
=
(
a
−
b
)
(
a
2+ab+b2). Where a
=x and b=9. (x−9)(x2+x⋅9+92)=0
. Simplify. Move 9 to the left of x
. (x−9)(x2+9x+92)=0. Raise 9 to the power of 2
. (x
−9
)(
x
2
+
9
x
+81
)=0
. Set x
−9 equal to 0 and solve for x. Set the factor equal to 0. x−
9=
0. Add 9 to both sides of the equation. x=9
. Set x2+
9
x
+
81 equal to 0 and solve for x
. Set the factor equal to 0
. x2+9x+81=0. Use the quadratic formula to find the solutions. −b±√b2−4(ac) 2a. Substitute the values a=1, b=9, and c=81 into the quadratic formula and solve for x. −9±√92−4⋅ (1⋅81
) 2⋅
1 Simplify. Simplify the numerator. Raise 9 to the power of 2. x=−9±√81−4⋅(1⋅81) 2⋅1. Multiply
81
by
1
.
x
=
−
9
±
√
81
−
4
⋅
81
2
⋅
1
Multiply
−
4
by
81
.
x
=
−
9
±
√
81
−
324
2
⋅
1
Subtract
324
from
81
.
x
=
−
9
±
√
−
243
2
⋅
1
Rewrite
−
243
as
−
1
(
243
)
.
x
=
−
9
±
√
−
1
⋅
243
2
⋅
1
Rewrite
√
−
1
(
243
)
as
√
−
1
⋅
√
243
.
x
=
−
9
±
√
−
1
⋅
√
243
2
⋅
1
Rewrite
√
−
1
as
i
.
x
=
−
9
±
i
⋅
√
243
2
⋅
1
Rewrite
243
as
9
2
⋅
3
.
Tap for fewer steps...
Factor
81
out of
243
.
x
=
−
9
±
i
⋅
√
81
(
3
)
2
⋅
1
Rewrite
81
as
9
2
.
x
=
−
9
±
i
⋅
√
9
2
⋅
3
2
⋅
1
Pull terms out from under the radical.
x
=
−
9
±
i
⋅
(
9
√
3
)
2
⋅
1
Move
9
to the left of
i
.
x
=
−
9
±
9
i
√
3
2
⋅
1
Multiply
2
by
1
.
x
=
−
9
±
9
i
√
3
2
Factor
−
1
out of
−
9
±
9
i
√
3
.
x
=
−
1
9
±
9
i
√
3
2
Multiply
−
1
by
−
1
.
x
=
1
−
9
±
9
i
√
3
2
Multiply
−
9
±
9
i
√
3
by
1
.
x
=
−
9
±
9
i
√
3
2
The final answer is the combination of both solutions.
x
=
−
9
−
9
i
√
3
2
,
−
9
+
9
i
√
3
2
The solution is the result of
x
−
9
=
0
and
x
2
+
9
x
+
81
=
0
.
x
=
9
,
−
9
−
9
i
√
3
2
,
−
9
+
i
√
3
2
First we rearrange by using the definition of between.
AB=x+10, BC=x+14, AC=22
Given that AB+BC=AC, we can solve for X
(X+10)+(X+14)=22
X+10+X+14=22
2X+24=22
2X+24-24=22-24
2X=-2
2X/2=-2/2
X= -1
Answer:
$7.5 plus $65 per hour
Step-by-step explanation:
We are trying to find the minimum she can make in one day. The minimum amount of hours she can work is 1, so find y when x=1:
y=7.5x+65
y=7.5(1)+65
y=7.5+65
No, John is incorrect.
<h3>
Correct work shown:</h3>
The correct answer should be x = 7 or x = -1
Answer:
6. r=2
8.x=3
Step-by-step explanation:
6. 4r-3=5
4r-3=5 add 3 to both sides
4r=8 divide 4 by both sides
r=2
8. 5x-6=9
5x-6=9 add 6 to both sides
5x=15 divide 5 by both sides
x=3
