Answer:
She invested $30,000 at 9%
Step-by-step explanation:
Let the amount invested per percentage be $x and $y respectively
Total investment is 40,000
This means that;
x + y = 40,000 ••••••••••(i)
Now for her income;
9/100 * x = 9x/100
for the 12% = 12/100 * y = 12y/100
Now;
9x/100 + 12y/100 = 3,900
9x + 12y = 390000 •••••••••(ii)
we solve both simultaneously
From i, y = 40,000-x
Substitute this into ii
9x + 12(40,000-x) = 390,000
9x + 480,000-12x = 390,000
3x = 480,000-390,0000
3x = 90,000
x = 90,000/3
x = $30,000
Here the difference between two consecutive x terms =14-18=-4
And we have to use the following formula
f(x) = a + (x-1)d
Substituting the values of first term, a common deifference,d, we will get
f(x) = 18+(x-1)(-4)
f(x) = 18 -4x+4
f(x) = 22-4x
So the required model for the given table is f(x) = 22-4x .
Answer:
1) B=-12
2) 189.69
Step-by-step explanation:
Explanation 1: To find B, we have to replace the given points in the equation, that is , x=2 and y=1
![3x+By+6=0\\3.2+B.1+6=0](https://tex.z-dn.net/?f=3x%2BBy%2B6%3D0%5C%5C3.2%2BB.1%2B6%3D0)
Then we solve for B.
![6+B+6=0\\B+12=0\\B=-12\\](https://tex.z-dn.net/?f=6%2BB%2B6%3D0%5C%5CB%2B12%3D0%5C%5CB%3D-12%5C%5C)
Hence , B=-12
explanation 2: you have the following equation for the number of liters 3% milk:
![0.03+0.1(200)-x=0.05(200)](https://tex.z-dn.net/?f=0.03%2B0.1%28200%29-x%3D0.05%28200%29)
Solve the previous equation for x:
![0.03x+20-x=10](https://tex.z-dn.net/?f=0.03x%2B20-x%3D10)
![0.03-x=10-20\\-0.97x=-10\\x=10.31](https://tex.z-dn.net/?f=0.03-x%3D10-20%5C%5C-0.97x%3D-10%5C%5Cx%3D10.31)
Hence , there are 10.31 liters of 3% milk
Add the numbers of liters 10% butterfat is :
![200-10.31=189.69 liters](https://tex.z-dn.net/?f=200-10.31%3D189.69%20%20liters)
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