Geometry, trigonometry, functions, factorization, probabilities, similar triangles, Thales theorem, affine function, ratio, greatest common divisor
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Step-by-step solutions to various math exercises involving geometry, trigonometry, functions, and probability.
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[...] The function f is an affine function and not a linear function, it does not therefore translate a situation of proportionality. Exercise Each packet must contain the same number of strawberry-flavored candies but 770 is not divisible by 13. The candy maker cannot therefore make 13 packets of candies. The common prime factors of 770 and 546 are 2 and 7. The greatest common divisor of 770 and 546 is therefore 2*7 = 14. The maximum number of packets that can be made is 14. [...]
[...] The triangles ABC and EBD therefore have two equal angles, and if two triangles have two equal angles, then they are similar. The triangles ABC and EBD are therefore similar. Two triangles are similar if and only if the lengths of their sides are proportional, then AB/BD = CB/BE. In addition, the points D and E are aligned in the same order. Therefore, by the converse of Thales' theorem, the lines and are parallel. We know that: So: The length of BE is approximately 11.4cm. [...]
[...] Exercise The white, black, and milk chocolates are in the ratio meaning there is one white chocolate for two black chocolates, and two black chocolates for three milk chocolates. There is also one white chocolate for three milk chocolates. Let x be the number of white chocolates in the box. Then, we will have 2x black chocolates and 3x milk chocolates. We solve the following equation: There are 8 white chocolates in the box. There are 16 black chocolates in the box. There are 24 milk chocolates in the box. [...]
