1. Maria has 8 cups of a fruit punch that consists of 25% orange juice and 75% apple juice. She wants to make a drink that is 40% orange juice. How many cups of orange juice should Maria add to th mixture?
A: ?
Determine whether the trinomial is a perfect-square. If so, factor. If not, explain.
2. 16x^2 - 24x - 9
A: ?
(I think this trinomial may be a perfect-square, but my textbook says otherwise.)
cups of orange juice --- x
cups of apple --------- 8-x
.25x + .75(8-x) = 4.(8)
25x + 75(8-x) = 40(8)
I will let you finish it
2.
For your type of perfect-square trinomial the first and last terms would have to be positive.
---- the -9 takes this one out of the category.
It is not a perfect square.
Argggghhh
Duplicate question
Didn't see that Steve had already answered it
1. To solve this problem, we will use the concept of mixing solutions or ingredients together.
Let's begin by figuring out the total amount of orange juice in Maria's fruit punch. We know that the fruit punch consists of 25% orange juice. So, we can determine that 25% of the total volume of the fruit punch is orange juice.
Let 'x' be the number of cups of orange juice Maria needs to add to the mixture.
The total volume of the fruit punch after mixing should be the sum of the original 8 cups and the additional 'x' cups of orange juice. Therefore, the total volume of the fruit punch is 8 + x cups.
Now, let's calculate the amount of orange juice in the mixture. Since 25% of the fruit punch is orange juice, we can set up the following equation:
0.25 * (8 + x) = 0.40 * (8 + x)
Here, 0.25 represents the 25% orange juice concentration, and 0.40 represents the desired 40% orange juice concentration.
Simplifying the equation, we get:
2 + 0.25x = 3.2 + 0.40x
By isolating 'x' on one side of the equation, we can solve for it:
0.15x = 1.2
Divide both sides by 0.15:
x = 8
Therefore, Maria should add 8 cups of orange juice to the mixture.
2. To determine if the trinomial 16x^2 - 24x - 9 is a perfect square, we can use the middle term coefficient rule.
The trinomial is in the form ax^2 + bx + c, where a = 16, b = -24, and c = -9.
To check if it is a perfect square, we compare the square of half of the middle term coefficient with the last term.
Half of the middle term coefficient is (-24/2) = -12.
The square of -12 is 144.
Since the last term of the trinomial is -9, which is not equal to 144, the trinomial 16x^2 - 24x - 9 is not a perfect square.
Therefore, the trinomial cannot be factored using the perfect square rule.