I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
<span>625(5xy)^-3/ (5x)^2 y^7
625
= -------------------- / 25x^2y^7
125 x^3y^3
= 5/x^3y^3 / </span>25x^2y^7
= 5/x^3y^3 * (1/ 25x^2y^7)
= 1 / 5x^5y^10
answer
1
-----------------
5x^5y^10
Answer:
i. LM || NO (converse alternate interior angle theorem)
ii. <1 ≅ <2 (alternate interior angle theorem)
Step-by-step explanation:
Two or more lines are said to be parallel if they do not meet when extended, even till infinity.
Alternate angles are said to be equal in measure.
Given that;
<1 ≅ < 3,
Since <2 ≅ <3 (alternate interior angle theorem)
Then,
<1 ≅ <2 (transitive property)
Also,
<1 ≅ <2 (alternate interior angle theorem)
Therefore since <1 ≅ <2, thus;
LM || NO (converse alternate interior angle theorem)
I believe that 30.5 as a fraction is 30 and 1 half but don't take my word
Answer: The answer is (B) 2x + 3(3x – 5) = 51
.
Step-by-step explanation: We are given three options and we are to select which choice shows the result of substituting 3x – 5 into the second equation for y.
So, y = 3x - 5.
Since the standard form of a linear equation i two variables is ax + by = c, so the second equation as given in the options must be of the form 2x + 3y = 51.
If we substitute y = 3x - 5, then this equation becomes
2x + 3(3x - 5) = 51.
Thus, (B) 2x + 3(3x – 5) = 51 is the correct option.
