The economy moves from point a, where it produces 100 units of x and 200 units of y, to point b, where it produces 200 units of
2 answers:
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IMPORTANT:
If you're trying to factor a quadratic in Algebra I:
There are no two integers that can solve this problem!
Your quadratic is <em>prime</em>!
If you're trying to solve a quadratic (find x):
The factoring approach will not work for the same reasons listed above.
Try using splitting the middle or the quadratic formula instead.
Here's how you would solve it from a more advanced approach.
If you don't know what this stuff is, just ignore it.
ab = -18, a + b = -9
Find a in terms of b.
a = -9-b
Substitute this for a in the first equation.
(-9-b)b = -18
-9b-b² = -18
Multiply everything by -1 to get rid of all these negative signs.
b² + 9b = 18
Bring over that 18.
b² + 9b - 18 = 0
Apply the quadratic formula.
(a = 1, b = 9, c = -18)
If you need to write two distinct numbers, just write out one with a + and one with a - in place of the plus-minus sign.
If you're trying to factor a quadratic in Algebra I:
There are no two integers that can solve this problem!
Your quadratic is <em>prime</em>!
If you're trying to solve a quadratic (find x):
The factoring approach will not work for the same reasons listed above.
Try using splitting the middle or the quadratic formula instead.
Here's how you would solve it from a more advanced approach.
If you don't know what this stuff is, just ignore it.
ab = -18, a + b = -9
Find a in terms of b.
a = -9-b
Substitute this for a in the first equation.
(-9-b)b = -18
-9b-b² = -18
Multiply everything by -1 to get rid of all these negative signs.
b² + 9b = 18
Bring over that 18.
b² + 9b - 18 = 0
Apply the quadratic formula.
(a = 1, b = 9, c = -18)
If you need to write two distinct numbers, just write out one with a + and one with a - in place of the plus-minus sign.
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Answer:
7. d. l = 6.48 cm, w = 6.48 cm
8. d. square
Step-by-step explanation:
For a given area, the perimeter can always be shortened by reducing the length of the long side and increasing the length of the short side. When you get to the point where you can't do that, then you have the minimum perimeter. You will reach that point when the sides are the same length: the rectangle is a square.
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7. In light of the above, the best dimensions are √42 ≈ 6.48 cm for length and width.
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8. In light of the above, the shape is a square.
_____
The attached graph shows the length of one side (x) and the associated perimeter. The other side is 42/x, which will also be 6.48.
