Answer:
First type of fruit drinks: 48 pints
Second type of fruit drinks: 32 pints
Step-by-step explanation:
Let's call A the amount of first type of fruit drinks. 55% pure fruit juice
Let's call B the amount of second type of fruit drinks. 80% pure fruit juice
The resulting mixture should have 65% pure fruit juice and 80 pints.
Then we know that the total amount of mixture will be:
![A + B = 80](https://tex.z-dn.net/?f=A%20%2B%20B%20%3D%2080)
Then the total amount of pure fruit juice in the mixture will be:
![0.55A + 0.8B = 0.65 * 80](https://tex.z-dn.net/?f=0.55A%20%2B%200.8B%20%3D%200.65%20%2A%2080)
![0.55A + 0.8B = 52](https://tex.z-dn.net/?f=0.55A%20%2B%200.8B%20%3D%2052)
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:
![-0.8A -0.8B = -0.8*80](https://tex.z-dn.net/?f=-0.8A%20-0.8B%20%3D%20-0.8%2A80)
![-0.8A -0.8B = -64](https://tex.z-dn.net/?f=-0.8A%20-0.8B%20%3D%20-64)
![-0.8A -0.8B = -64](https://tex.z-dn.net/?f=-0.8A%20-0.8B%20%3D%20-64)
+
![0.55A + 0.8B = 52](https://tex.z-dn.net/?f=0.55A%20%2B%200.8B%20%3D%2052)
--------------------------------------
![-0.25A = -12](https://tex.z-dn.net/?f=-0.25A%20%3D%20-12)
![A = \frac{-12}{-0.25}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B-12%7D%7B-0.25%7D)
![A = 48\ pints](https://tex.z-dn.net/?f=A%20%3D%2048%5C%20pints)
We substitute the value of A into one of the two equations and solve for B.
![48 + B = 80](https://tex.z-dn.net/?f=48%20%2B%20B%20%3D%2080)
![B = 32\ pints](https://tex.z-dn.net/?f=B%20%3D%2032%5C%20pints)
Answer:
3(2+15)= 3(2) + 3(15)
Step-by-step explanation:
Answer:
$132,000 X .0085 = $1,122 / 360 = $3.1166 X 164 = $511.13
One mill is one dollar per $1,000 dollars of assessed value.
In our case 8.5 mills equivalent to 0.0085.
So to get the assessed value for one day
we will get
$132,000 X .0085 = $1,122 / 360 = $3.1166
Now we have the value for one day,
For June 14, we will calculate the days from January 1st to date
total days are 164. i.e. 5*30+14 = 164
Finally, the seller owes
$3.1166 * 164 = 511.13
Answer:
![\large\boxed{B.\ 4x^2-41x+105}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BB.%5C%204x%5E2-41x%2B105%7D)
Step-by-step explanation:
![f(x)=4x-\sqrt{x}\\\\g(x)=(x-5)^2\\\\f(g(x))\to\text{put}\ x=(x-5)^2\ \text{to}\ f(x):\\\\f(g(x))=f\bigg((x-5)^2\bigg)=4(x-5)^2-\sqrt{(x-5)^2}\\\\\text{use}\\(a-b)^2=a^2-2ab+b^2\\\sqrt{x^2}=|x|\\\\f(g(x)=4(x^2-2(x)(5)+5^2)-|x-5|\\\\x>5,\ \text{therefore}\ x-5>0\to|x-5|=x-5\\\\f(g(x))=4(x^2-10x+25)-(x-5)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\f(g(x))=(4)(x^2)+(4)(-10x)+(4)(25)-x-(-5)\\\\f(g(x))=4x^2-40x+100-x+5\\\\\text{combine like terms}\\\\f(g(x))=4x^2+(-40x-x)+(100+5)\\\\f(g(x))=4x^2-41x+105](https://tex.z-dn.net/?f=f%28x%29%3D4x-%5Csqrt%7Bx%7D%5C%5C%5C%5Cg%28x%29%3D%28x-5%29%5E2%5C%5C%5C%5Cf%28g%28x%29%29%5Cto%5Ctext%7Bput%7D%5C%20x%3D%28x-5%29%5E2%5C%20%5Ctext%7Bto%7D%5C%20f%28x%29%3A%5C%5C%5C%5Cf%28g%28x%29%29%3Df%5Cbigg%28%28x-5%29%5E2%5Cbigg%29%3D4%28x-5%29%5E2-%5Csqrt%7B%28x-5%29%5E2%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%5C%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2%5C%5C%5Csqrt%7Bx%5E2%7D%3D%7Cx%7C%5C%5C%5C%5Cf%28g%28x%29%3D4%28x%5E2-2%28x%29%285%29%2B5%5E2%29-%7Cx-5%7C%5C%5C%5C%5Cx%3E5%2C%5C%20%5Ctext%7Btherefore%7D%5C%20x-5%3E0%5Cto%7Cx-5%7C%3Dx-5%5C%5C%5C%5Cf%28g%28x%29%29%3D4%28x%5E2-10x%2B25%29-%28x-5%29%5C%5C%5C%5C%5Ctext%7Buse%20the%20distributive%20property%3A%7D%5C%20a%28b%2Bc%29%3Dab%2Bac%5C%5C%5C%5Cf%28g%28x%29%29%3D%284%29%28x%5E2%29%2B%284%29%28-10x%29%2B%284%29%2825%29-x-%28-5%29%5C%5C%5C%5Cf%28g%28x%29%29%3D4x%5E2-40x%2B100-x%2B5%5C%5C%5C%5C%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%5C%5Cf%28g%28x%29%29%3D4x%5E2%2B%28-40x-x%29%2B%28100%2B5%29%5C%5C%5C%5Cf%28g%28x%29%29%3D4x%5E2-41x%2B105)