Answer:
(
2
x
−
6
)
2
+
4
(
2
x
−
6
)
+
3
=
0
Simplify the left side.
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(
2
x
−
6
)
2
+
8
x
−
21
=
0
Use the quadratic formula to find the solutions.
−
b
±
√
b
2
−
4
(
a
c
)
2
a
Substitute the values
a
=
4
,
b
=
−
16
, and
c
=
15
into the quadratic formula and solve for
x
.
16
±
√
(
−
16
)
2
−
4
⋅
(
4
⋅
15
)
2
⋅
4
Simplify.
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x
=
4
±
1
2
The final answer is the combination of both solutions.
x
=
5
2
,
3
2
Step-by-step explanation:
Answer for Area:
6,518.75 square meters
Explanation for Area:
First, you would multiply the length and the width of the car park to find its area (75 x 100 =7500). Now, find the area of the arena. Since you are given the diameter, divide it by 2 to get the radius (25). Now multiply π by 25^2. This should give you 1962.5. Then, since only half of the arena is in the car park, divide the area of the arena by 2. Now you have 981.25. Now, subtract this from the area of the car park (7500). Your answer should now be 6,518.75.
Answer for Fence:
295 meters
Explanation for Fence:
Add up all the sides. There are two sides with 100 meters and 2 sides with 75 meters. But, because you arent supposed to include the space where the arena is. only add 25. This gets you 300. Now, subtract 5 meters for a gate. 295 is your final answer.
y = 7 which you subtract from 2x which means 2 times x so you use all of those as the value of 2 to see what the answer would be after you multiply it by 2
What exactly are you looking for?
To find equivalent inequalities you have to work the inequality given.
The first step is transpose on of sides to have an expression in one side and zero in the other side:
x - 6 x + 7
--------- ≥ --------
x + 5 x + 3
=>
x - 6 x + 7
--------- - -------- ≥ 0
x + 5 x + 3
=>
(x - 6) (x + 3) - (x + 7) (x + 5)
--------------------------------------- ≥ 0
(x + 5) (x + 3)
=>
x^2 - 3x - 18 - x^2 - 12x - 35
--------------------------------------- ≥ 0
(x + 5) (x + 3)
15x + 53
- ------------------- ≥ 0
(x + 5) (x + 3)
That is an equivalent inequality. Sure you can arrange it to find many other equivalent inequalities. That is why you should include the list of choices. Anyway from this point it should be pretty straigth to arrange the terms until making the equivalent as per the options.