A triangle has points R(-2,0) ,S(2,8) and T (8,2) as shown in the group. M is the midpoint of RT . What is the length of SM

Mathematics

1 answer:

wlad13 [49]4 years ago

5 0

The midpoint is calculated by averaging the coordinates of its endpoints:

$M = \left(\dfrac{-2+8}{2},\dfrac{0+2}{2}\right)=(3,1)$

Now we can use the usual distance formula to get the length of SM:

$SM=\sqrt{(2-3)^2+(8-1)^2}=\sqrt{1+49}=\sqrt{50}$

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

Step-by-step explanation:

The equation

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and we solve it the following way:

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