Answer:
three yards for blue felt and five yards for green
Step-by-step explanation:
divide each by three
Answer: a) k >4.08
b) k = 4.08
c) k<4.08
Step-by-step explanation:
Since we have given that
![f(x)=-3x^2+7x-k](https://tex.z-dn.net/?f=f%28x%29%3D-3x%5E2%2B7x-k)
a) For what values of k will the function have no zeros?
It mean it has no real zeroes i.e. Discriminant < 0
As we know that
![D=b^2-4ac](https://tex.z-dn.net/?f=D%3Db%5E2-4ac)
Here, a =-3
b = 7
c = -k
So, it becomes,
![D](https://tex.z-dn.net/?f=D%3C0%5C%5C%5C%5Cb%5E2-4ac%3C0%5C%5C%5C%5C7%5E2-4%5Ctimes%20-3%5Ctimes%20-k%3C0%5C%5C%5C%5C49-12k%3C0%5C%5C%5C%5C-12k%3C-49%5C%5C%5C%5Ck%3E%5Cdfrac%7B49%7D%7B12%7D%5C%5C%5C%5Ck%3E4.08)
b) For what values of k will the function have one zero?
It means it has one real root i.e equal roots.
So, in this case, D = 0
So, it becomes,
![D=b^2-4ac=0\\\\D=7^2-4\times -3\times -k=0\\\\49-12k=0\\\\49=12k\\\\k=\dfrac{49}{12}\\\\k=4.08](https://tex.z-dn.net/?f=D%3Db%5E2-4ac%3D0%5C%5C%5C%5CD%3D7%5E2-4%5Ctimes%20-3%5Ctimes%20-k%3D0%5C%5C%5C%5C49-12k%3D0%5C%5C%5C%5C49%3D12k%5C%5C%5C%5Ck%3D%5Cdfrac%7B49%7D%7B12%7D%5C%5C%5C%5Ck%3D4.08)
c) For what values of k will the function have two zeros?
It means it has two real roots.
In this case, D>0
So, it becomes,
![D=7^2-4\times -3\times -k>0\\\\49-12k>0\\\\-12k>-49\\\\12k](https://tex.z-dn.net/?f=D%3D7%5E2-4%5Ctimes%20-3%5Ctimes%20-k%3E0%5C%5C%5C%5C49-12k%3E0%5C%5C%5C%5C-12k%3E-49%5C%5C%5C%5C12k%3C49%5C%5C%5C%5Ck%3C4.08)
Hence, a) k >4.08
b) k = 4.08
c) k<4.08
Decreased as getting more for less/same amount makes it so the worth of euro has went down
<span>A) 5x + 7y = 3
B) 2x + 3y = 1
Multiplying Equation B by -2.5
</span><span>B) -5x -7.5y = -2.5 Then adding this to Equation A)
A) 5x + 7y = 3</span>
-.5y = .5
y = -1
Since
<span>2x + 3y = 1 then
2x -3 = 1
then x = 2
</span>
Answer:
Dan would be left over with $43 a week.
Step-by-step explanation:
= 40%
= 50%
Rent: $430 - 40% = $172
Food: $430 - 50% = $215
$215 + $172 = $387
$430 - $387 = $43