Easy question it is due in 10 minutes!!!!

Mathematics

1 answer:

seraphim [82]3 years ago

5 0

A; the coordinates in that point make M equidistant from H and F.

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A metallurgist needs to make 12.4 lb. of an 10) alloy containing 50% gold. He is going to melt and combine one metal that is 60%

sergeinik [125]

Now, let's say, we add "x" lbs of the 60% gold alloy, so.. how much gold is in it? well, is just 60%, so (60/100) * x, or 0.6x.

likewise, if we use "y" lbs of the 40% alloy, how much gold is in it? well, 40% of y, or (40/100) * y, or 0.4y.

now, whatever "x" and "y" are, their sum must be 12.4 lbs.

we also know that the gold amount in each added up, must equal that of the 50% resulting alloy.

$\bf \begin{array}{lccclll}
&\stackrel{lbs}{amount}&\stackrel{gold~\%}{quantity}&\stackrel{gold}{quantity}\\
&------&------&------\\
\textit{60\% alloy}&x&0.6&0.6x\\
\textit{40\% alloy}&y&0.4&0.4y\\
------&------&------&------\\
\textit{50\% alloy}&12.4&0.50&6.2
\end{array}$

$\bf \begin{cases}
x+y=12.4\implies \boxed{y}=12.4-x\\
0.6x+0.4y=6.2\\
-------------\\
0.6x+0.4\left( \boxed{12.4-x} \right)=6.2
\end{cases}
\\\\\\
0.6x-0.4x+4.96=6.2\implies 0.2x=1.24\implies x=\cfrac{1.24}{0.2}
\\\\\\
x=\stackrel{lbs}{6.2}$

how much of the 40% alloy? well, y = 12.4 - x.

5 0

3 years ago

I forgot how to do it help!?

Fantom [35]

Replace x with -3 and add

y = -x+1

y = -( x ) + 1

y = -( -3 ) + 1 .... replace x with -3

y = 3 + 1 ... two negatives cancel to make a positive

y = 4

So the number 4 goes right next to -3. This means the point (x,y) = (-3,4) is on the line. This is shown as point A on the attached image below.

------------------------

Repeat for x = -1

y = -x + 1

y = -( x ) + 1

y = -( -1) + 1 ... replace x with -1

y = 1 + 1

y = 2

So the point (-1,2) is also on the line. This is shown as point B.

-------------------------

Repeat for x = 0

y = -x + 1

y = -0 + 1 ... replace x with 0

y = 1

So (0,1) is on the line. This is point C.

-------------------------

Finally, plug in x = 4

y = -x + 1

y = -4 + 1 ... replace x with 4

y = -3

So (4,-3) is on the line, shown as point D.

-------------------------

After you have at least 2 points plotted on the coordinate grid, you would draw a straight line through those points. Note how points A,B, C, & D are all on the same straight line. The slope of this line is -1 meaning you go down 1 unit each time you move to the right 1 unit. The y intercept is 1, which is where the blue line crosses the y axis.