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Leni [432]
3 years ago
6

Find the value of each variable

Mathematics
1 answer:
shepuryov [24]3 years ago
3 0
The value of the variable d is 10.
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How much pure water must be mixed with 10 liters of a 25% acid solution to reduce it to a 10% acid solution?
elena-s [515]

Suppose you add x liters of pure water to the 10 L of 25% acid solution. The new solution's volume is x + 10 L. Each L of pure water contributes no acid, while the starting solution contains 2.5 L of acid. So in the new solution, you end up with a concentration of (2.5 L)/(x + 10 L), and you want this concentration to be 10%. So we have

\dfrac{2.5}{x+10}=0.1\implies25=x+10\implies x=15

and so you would need to add 15 L of pure water to get the desired concentration of acid.

8 0
4 years ago
4(5m+3x)+2x<br> write an equivalent expression.
zloy xaker [14]

Answer:

20+14x

Step-by-step explanation:

3 0
3 years ago
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Point Eis on line segment DF. Given DE = 8 and EF= 2, determine the length<br> DF.
julia-pushkina [17]

Step-by-step explanation:

if that's what you mean

6 0
3 years ago
an aircraft carrier leads port heading due west at 28 knots. A helicopter is 175 nautical miles from the carrier at an angle of
emmainna [20.7K]
Let’s say it takes time t hours for the interception.
In that time the carrier travels 28t nm west and the helicopter 130t nm.
Now we use the sine rule to find the angle x which lies between the distance 175 and 130t.
sin(x)/28t=sin35/130t. So sin(x)=28sin35/130=14sin35/65=0.1235 and x=7.0964 degrees.
Therefore the helicopter should use a bearing of 35+7.0964=42.0964 degrees north of east or 47.9 degrees east of north approx.
8 0
3 years ago
Which equation is equivalent to √x^2+81 = x+10
jeka57 [31]

Keywords:

<em>equation, operations, equivalent, binomial, square root </em>

For this case we have an equation in which we must apply operations to rewrite it in an equivalent way. We must start by raising both sides of the equation to the square. Thus, we eliminate the square root of the left side of equality and finally solve the binomial of the right side of equality.

So we have:

\sqrt {x ^ 2 + 81} = x + 10\\(\sqrt {x ^ 2 + 81}) ^ 2 = (x + 10) ^ 2\\x ^ 2 + 81 = (x + 10) ^ 2

By definition:(a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2

x ^ 2 + 81 = x ^ 2 + 2 (x) (10) + (10) ^ 2\\x ^ 2 + 81 = x ^ 2 + 20x +100

Thus, x ^ 2 + 81 = x ^ 2 + 20x +100 is equivalent to \sqrt {x ^ 2 + 81} = x + 10

Answer:

x ^ 2 + 81 = x ^ 2 + 20x +100

Option D

4 0
3 years ago
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