the first solution is 20% acid, and say we'll be using "x" liters, so how many liters of just acid are in it? well 20% of "x" or namely 0.2x. Likewise for the 60% acid solution, if we had "y" liters of it, the amount of only acid in it is 0.6y.

$\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{liters of }}{amount}\\ \cline{2-4}&\\ \textit{1st solution}&x&0.20&0.2x\\ \textit{2nd solution}&y&0.60&0.6y\\ \cline{2-4}&\\ mixture&100&0.44&44 \end{array}~\hfill \begin{cases} x+y=100\\\\ 0.2x+0.6y=44 \end{cases}$

$x+y=100\implies y=100-x~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.2x+0.6(100-x)=44} \\\\\\ 0.2x+60-0.6x=44\implies -0.4x+60=44\implies -0.4x=-16 \\\\\\ x=\cfrac{-16}{-0.4}\implies \boxed{x=40}~\hfill \boxed{\stackrel{100-40}{y=60}}$

7 0

1 year ago

Assume each figure shown has the same orientation. Which figure is the image of square LMNP after a translation of

umka21 [38]

Figure 4 is the image of the square LMNP after the translation.

<u>Step-by-step explanation:</u>

Let us see the coordinates of the pre image LMNP as,

L (-3,1)

M(-1,1)

N(-1,-1)

P(-3,-1)

after translation of (x,y) → (x+5, y -3) the coordinates of the image obtained as,

L'(2,-2)

M'(4,-2)

N'(4,-4)

P'(2,-4) which matches the image 4.

8 0

3 years ago

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The consequent of a ratio is 36. If the ratio is 4:9 find its antecedent. ​

The consequent of a ratio is 36. If the ratio is 4:9 find its antecedent.