Sarah mixes 2/3 cup of low fat milk and 1/2 cup of skim milk and the mixture has 111 calories. She knows that if she mixes one c
up of low fat milk and one cup of skim milk that the mixture will have 188 calories. How many calories are in one cup of low fat milk and how many calories are in
one cup of skim milk?
A 102 calories in a cup of low fat milk and 86 calories in a cup of skim milk
B 102 calories in a cup of low fat milk and 40 calories in a cup of skim milk
C 86 calories in a cup of low fat milk and 102 calories in a cup of skim milk
D 40 calories in a cup of low fat milk and 102 calories in a cup of skim milk
one cup of skim milk?
A 102 calories in a cup of low fat milk and 86 calories in a cup of skim milk
B 102 calories in a cup of low fat milk and 40 calories in a cup of skim milk
C 86 calories in a cup of low fat milk and 102 calories in a cup of skim milk
D 40 calories in a cup of low fat milk and 102 calories in a cup of skim milk
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.