420 gallons of 90% antifreeze must be mixed with 60 gallons of 10% antifreeze to get mixture that is 80% antifreeze
<em><u>Solution:</u></em>
Let "x" be the gallons of 90% antifreeze
The, final mixture would contain (x + 60) gallons
Then by given question, we can say,
"x" be the gallons of 90% antifreeze must be mixed with 60 gallons of 10% antifreeze to get 80 % of (x + 60) gallons
<em><u>Thus we frame a equation as:</u></em>
![x \times 90 \% + 60 \times 10 \% = (x + 60) \times 80 \%](https://tex.z-dn.net/?f=x%20%5Ctimes%2090%20%5C%25%20%2B%2060%20%5Ctimes%2010%20%5C%25%20%3D%20%28x%20%2B%2060%29%20%5Ctimes%2080%20%5C%25)
<em><u>Solve the above equation for "x"</u></em>
![x \times \frac{90}{100} + 60 \times \frac{10}{100} = (x + 60) \times \frac{80}{100}\\\\0.9x + 6 = (x+60) \times 0.8\\\\0.9x + 6 = 0.8x + 48\\\\\text{Combine the like terms }\\\\0.9x - 0.8x = 48 - 6\\\\0.1x = 42\\\\x = \frac{42}{0.1} = 420](https://tex.z-dn.net/?f=x%20%5Ctimes%20%5Cfrac%7B90%7D%7B100%7D%20%2B%2060%20%5Ctimes%20%5Cfrac%7B10%7D%7B100%7D%20%3D%20%28x%20%2B%2060%29%20%5Ctimes%20%5Cfrac%7B80%7D%7B100%7D%5C%5C%5C%5C0.9x%20%2B%206%20%3D%20%28x%2B60%29%20%5Ctimes%200.8%5C%5C%5C%5C0.9x%20%2B%206%20%3D%200.8x%20%2B%2048%5C%5C%5C%5C%5Ctext%7BCombine%20the%20like%20terms%20%7D%5C%5C%5C%5C0.9x%20-%200.8x%20%3D%2048%20-%206%5C%5C%5C%5C0.1x%20%3D%2042%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B42%7D%7B0.1%7D%20%3D%20420)
Thus, 420 gallons of 90% antifreeze is used
Answer:
C. Multiplication
Step-by-Step Explanation:
This problem is testing your knowledge of the Order of Operations. Here is the correct order:
Exponents (inside parenthesis)- There are no exponents for you to solve in this expression, so just ignore this step for now. (example: (4 + 2²) --> (4 + 4))
Parenthesis (from left to right)- In this case, you would solve the expressions inside the parenthesis <em>first</em> because there are no exponents.
Multiplication and Division (from left to right outside of parenthesis)- After solving the expressions inside the parenthesis, there will be one multiplication you need to solve next.
Addition and Subtraction (from left to right outside of parenthesis)- The only operation left for you to do now is addition. You can either do this in one whole step, or you can divide it into two steps. I've done it in two to keep it simple.
Here is the problem worked out in steps in case you are confused:
Step 1: Parenthesis
(-8 ÷ 4) + 5 + 4(3 - 6)
(-2) + 5 + 4(-3)
Step 2: Multiplication
-2 + 5 + 4(-3)
-2 + 5 + (-12)
Step 3: Addition
-2 + 5 + (-12)
3 + (-12)
-9
(Note: '3 + (-12)' could also be written as '3 - 12', making it a subtraction instead of an addition)
Hope this helps!
Answer:
rad17 or 4.12
Step-by-step explanation:
use pythagreom thereom
1^2+4^2=c^2
1+16=c^2
17=c^2
rad17 if your teacher wants you to simply all the way its
4.12
The coefficient of the first term.
If it's talking about the left end, then it'll be the first degree. So since it's to the third power, you'll have something that looks like x^3, which starts at the bottom left. The negative sign indicates a swapped axis. So it'll be the coefficient (which is -3). That states it'll start from the top left and go downward. The +3 is just a vertical shift.
If the 2 is an exponent, it should be marked as such.
“3x2” means 3x⋅2
“3x^2” means 3x²
3x²+8x = 0
Discriminant = 8²-4(3)(0) = 64