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3 years ago

2x+y=10------1 using substitution method

Mathematics

1 answer:

Andrei [34K]3 years ago

8 0

Why is there a bunch of dash marks and then the number one...?

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A pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10 liters o

ladessa [460]

X = amount of the 18% solution

y = amount of the 40% solution

we know the 18% solution has only 18% of alcohol, the rest is maybe water or something, now, how many liters is 18%? well, 18% of anything is just (18/100) * anything, so, 18% of x is just (18/100) *x or 0.18x, and that's how many liters are there.

likewise, how many liters are there in the 40% solution? well, (40/100) * y, or 0.4y, that many.

we know the mixture has to yield 10 liters at 20% alcohol, how many liters of only alcohol is that? well, (20/100) * 10, or 2 liters.

$\bf \begin{array}{lccclll}
&\stackrel{liters}{amount}&\stackrel{alcohol~\%}{quantity}&\stackrel{liters}{alcohol}\\
&------&------&------\\
\textit{18\% solution}&x&0.18&0.18x\\
\textit{40\% solution}&y&0.40&0.4y\\
------&------&------&------\\
mixture&10&0.20&2
\end{array}$

$\bf \begin{cases}
x+y=10\implies \boxed{y}=10-x\\
0.18x+0.4y=2\\
----------\\
0.18x+0.4\left( \boxed{10-x} \right)=2
\end{cases}
\\\\\\
0.18x-0.4x+4=2\implies -0.22x=-2
\\\\\\
x=\cfrac{-2}{-0.22}\implies x=\cfrac{100}{11}\implies x=9\frac{1}{11}$

how much of the 40% solution? well y = 10 - x

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4 years ago

write a formula that describes the value of an initial investment of $100 that loses value at a rate of 8% per year compounded c

Sati [7]

Answer:

$A = 100(.92)^{t}$

Step-by-step explanation:

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3 years ago

A rectangle has area x3 + 3x2 - 18x in.2 and width x + 6 in. What is the length in inches?

Viefleur [7K]

Answer:

HOPE THIS HELPS

Step-by-step explanation:

The area = length * Width.

We know the width = X+6 inches and Area = x^3+3x^2–18x.

This problem can be solved just by dividing the area by width and we get a quotient as X^2–3x.

So the length is x^2–3x inches.

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lutik1710 [3]

I'm pretty sure it's $42

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3 years ago

The formula V = Bh, where B represents the area of the base, can be used to find the volume of a rectangular prism. Which formul

zhenek [66]

Answer:B

V = l. w. h

Step-by-step explanation:

Volume of a rectangular prism is base area * height

The base is a rectangle, hence, the base area equals area of a rectangle which is length * width

Replacing base area (B) in the formula,

V = Bh

V= l * w * h

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4 years ago

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