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liraira [26]
3 years ago
9

A scientist has two solutions, which she has labeled Solution A 60% and Solution B 75% Each contains salt. She knows that Soluti

on A is salt and Solution B is salt. She wants to obtain ounces of a mixture that is salt. How many ounces of each solution should she use
Mathematics
1 answer:
OverLord2011 [107]3 years ago
6 0

Answer:

The answer is "180".

Step-by-step explanation:

Please find the complete question in the attached file.

Let's

x = ounces solution of A

y = ounces solution of B

x + y = 180        \\\\y = 180 - x\\\\0.60x + 0.85y = 0.75(180)\\\\0.60x + 0.85y = 135\\\\

Multiply both sides of the equation by 100 to remove the decimal points.

60x + 85y = 13500\\\\60x + 85(180 - x) = 13500\\\\60x + 15300 - 85x = 13500\\\\-25x = -1800\\\\x = 72\ \ ounces\\\\y = 180 - 72 \\\\y = 108 \ \ ounces\\\\

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Step-by-step explanation:

b is per the identity of angles on parallel lines when intersected by one inclined line the same as the 40° angle.

so,

b = 40°

due to the parallel nature of the 2 lines there is a symmetry effect for such shapes inscribed a circle. the upper and the lower triangle must be similar. and when applying a vertical line through the central crossing point, everything to the left is mirrored by everything on the right.

so, angle c must be equal to angle b.

c = 40°

and as the sum of all angles in a triangle is always 180°, d is then

d = 180 - 40 - 40 = 100°

the interior angle of the arc angle a is the supplementary angle of d (together they are 180°), because together with d they cover the full down side of the top-left to bottom-right line.

interior angle to a = 180 - 100 = 80°

due to the symmetry again, the arc angle opposite to a is the same as a.

as we know, the interior angle to a pair of opposing arc angles is the mean value of the 2 angles.

so, we have

(a + a)/2 = 80

2a/2 = 80

a = 80°

there might (and actually should) be some more direct approaches for "a" out of the other pieces of information, but that was the most straight one right out of my mind, and I don't spend time on finding additional shortcuts, when I have already a working approach.

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1 year ago
a rectangle has an area of 102 cm2. the length of the rectangle is 17 cm. what is the perimeter of the rectangle?
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