Polygon B is a scaled copy of Polygon A using a scale factor of 5.
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
We have the function:
And we want to find x=d for which the minimum/maximum value will occur.
Notice that our function is a quadratic in factored form.
Remember that the minimum/maximum value always occurs at the vertex point.
And remember that the x-coordinate of the vertex is the axis of symmetry.
Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.
Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.
Our factors are <em>(x-2) </em>and <em>(x-1)</em>.
Therefore, our roots/zeros are <em>x=1, 2</em>.
So, the average of them are:
Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.
Alternative Method:
Of course, we can also expand to confirm our answer. So:
The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.
And the formula for the vertex is:
So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:
Confirming our answer.
ANSWER
The swimming pool can hold 1,000,000 cubic feet of water.
EXPLANATION
The capacity of water the pool holds is the volume of water in the swimming pool.
The swimming pool is rectangular, therefore its volume can be calculated using the formula,
where l=1000ft is the length, w=100ft is the width and h=10ft is the height of the pool.
We substitute all these values into the formula to get:
The swimming pool can hold 1,000,000 cubic feet of water.