Answer:
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Answer:
Approximately 3.5 feet - Option B
Step-by-step explanation:
Imagine that you have this walkway around the garden, with dimensions 30 by 20 feet. This walkway has a difference of x feet between it's length, and say the dimension 30 feet. In fact it has a difference of x along both dimensions - on either ends. Therefore, the increases length and width should be 30 + 2x, and 20 + 2x, which is with respect to an increases area of 1,000 square feet.
( 30 + 2x )
( 20 + 2x ) = 1000 - Expand "( 30 + 2x )
( 20 + 2x )"
600 + 100x + 4
= 1000 - Subtract 1000 on either side, making on side = 0
4
+ 100x - 400 = 0 - Take the "quadratic equation formula"
( Quadratic Equation is as follows ) -
,
,

There can't be a negative width of the walkway, hence our solution should be ( in exact terms )
. The approximated value however is 3.5081...or approximately 3.5 feet.
Answer:
The third side must be smaller than 20 inches and greater than 4 inches

Step-by-step explanation:
Let a, b and c be the lengths of triangle's sides. Then

Use this rule in your case. So, if a=12 and b=8, then

Hence, you get

From these inequalities, you can state that

So, c must be smaller than 20 inches and greater than 4 inches.
26.270833 was not sure about the first one but the seconed one was 14
Answer:
[Vertex form]
Step-by-step explanation:
Given function:

We need to find the vertex form which is.,

where
represents the co-ordinates of vertex.
We apply completing square method to do so.
We have

First of all we make sure that the leading co-efficient is =1.
In order to make the leading co-efficient is =1, we multiply each term with -3.


Isolating
and
terms on one side.
Subtracting both sides by 15.


In order to make the right side a perfect square trinomial, we will take half of the co-efficient of
term, square it and add it both sides side.
square of half of the co-efficient of
term = 
Adding 36 to both sides.


Since
is a perfect square of
, so, we can write as:

Subtracting 21 to both sides:


Dividing both sides by -3.

[Vertex form]