I guess the chef is making the mixture for the sheriff... Let <em>x</em> be the amount of dressing with 5% vinegar that is required, and <em>y</em> the amount of 15% vinegar dressing (both amounts in mL).
The sheriff wants 390 mL of the mixed dressing, so that
<em>x</em> + <em>y</em> = 390
<em>x</em> mL of the 5% dressing contains 0.05<em>x</em> mL of vinegar, while <em>y</em> mL of the 15% dressing contains 0.15<em>y</em> mL of vinegar. The resulting mixture should have a concentration of 9% vinegar, so that it contains 0.09 (390 mL) = 35.1 mL of vinegar. This means
0.05<em>x</em> + 0.15<em>y</em> = 35.1
Solve for <em>x</em> and <em>y</em> :
<em>y</em> = 390 - <em>x</em>
0.05<em>x</em> + 0.15 (390 - <em>x</em>) = 35.1
0.05<em>x</em> + 58.5 - 0.15<em>x</em> = 35.1
23.4 = 0.10<em>x</em>
<em>x</em> = 234
<em>y</em> = 156
Answer:
15 feet
Step-by-step explanation:
Given that,
The cat is 12feet above the ground, and Peter has to put the base of his ladder 9 feet away from the tree because of mud.
If we consider a right-angled triangle, in which the height is 12 feet, base is 9 feet.
We need to find how long does the ladder need to be in order to reach the cat i.e. the hypotenuse of the triangle.
We can use the Pythagoras theorem to find it.
![H^2=h^2+b^2\\\\H^2=12^2+9^2\\\\H^2=144+81\\\\H=\sqrt{225} \\\\H=15\ \text{feet}](https://tex.z-dn.net/?f=H%5E2%3Dh%5E2%2Bb%5E2%5C%5C%5C%5CH%5E2%3D12%5E2%2B9%5E2%5C%5C%5C%5CH%5E2%3D144%2B81%5C%5C%5C%5CH%3D%5Csqrt%7B225%7D%20%5C%5C%5C%5CH%3D15%5C%20%5Ctext%7Bfeet%7D)
So, the ladder must be at a distance of 15 feet in order to reach the cat.
This is algebra. 4 times whatever is in the parentheses (8x-8) has to be equal to -192. If you do the math, x= -7
Anwser would be 18/14 simplified to 9/7