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Mathematics

1 answer:

Kisachek [45]3 years ago

7 0

Step-by-step explanation:

x²-11x+32=4

x²-11x+28=0

(x-4)(x-7)=0

x=4 or x=7

_______

x²+8x-5=4

x²+8x-9=0

(x+9)(x-1)=0

x=-9 or x=1

_______

x²+x+4=5x+1

x²-4x+3=0

(x-1)(x-3)=0

x=1 or x=3

________

x²+x-24=-8x-2

x²+9x-22=0

(x+11)(x-2)=0

x=-11 or x=2

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Answer:

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Step-by-step explanation:

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A chemist has 200 mL of a 10% sucrose solution. She adds x mL of a 40% sucrose solution. The percent concentration, y, of the fi

user100 [1]

Answer:

The chemist needs to add 400mL of 40% solution.

Step-by-step explanation:

The equation

$y=\frac{0.1(200)+0.4x}{200+x} *100$

gives the percent concentration $y$ of the final mixture, when $x$ mL of the 40% solution are added.

Now we are asked, how many milliliters $x$ of the 40% solution should the chemist add to get final percent concentration $y=30$ ; this is just a matter of solving the equation

$30=\frac{0.1(200)+0.4x}{200+x} *100$

and we solve it the following way:

$30=\frac{0.1(200)+0.4x}{200+x} *100\\\\0.3 =\frac{0.1(200)+0.4x}{200+x}\\\\0.3(200+x)=0.1(200)+0.4x\\\\60+0.3x=20+0.4x\\\\40=0.1x\\\\x=\frac{40}{0.1} \\\\\boxed{x=400\:mL}$