Mathematics, 01.07.2019 22:30 cici65360

George observes that for every increase of 1 in the value of x, there is a increase of 60 in the corresponding value of y. he claims that the relationship represented by the table is proportional. critique george's reasoning. table for x: 1, 2, 3, 4, 5 table for y: 90, 150, 210, 270, 330

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Answer from: RoyalGurl01

Hi there!

FACTS :

To see if multiple ratios are proportional, you can write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportionnal ratios. You can also write them as fractions and divide the numerator (top number) by its denominator (bottom number), and compare the decimal numbers the same way you would compare the fractions (I personnaly find this method easier because you don't need to simplify the fractions).

STEPS TO ANSWER:

x = 1 ; y = 90 → $\frac{1}{90} =$ 1 ÷ 90 = 0.01111111...

x = 2 ; y = 150 → $\frac{2}{150} =$ 2 ÷ 150 = 0.0133333...

x = 3 ; y = 210 → $\frac{3}{210} =$ 3 ÷ 210 = 0.01428571

x = 4 ; y = 270 → $\frac{4}{270} =$ 4 ÷ 270 = 0.0148148...

x = 5 ; y = 330 → $\frac{5}{330} =$ 5 ÷ 330 = 0.01515152

** You didn't really need to calculate them all because even the first two decimal numbers weren't equivalent, but I wanted to show you the whole process so I calculated them all.

⇒ If you compare all the decimals you got, you can easily see that they are not the same, which means that the ratios between the values of "x" and the values of "y" are not proportional. Therefore, George's reasoning wasn't good.

There you go! I really hope this helped, if there's anything just let me know! :)

Answer from: Quest

where is the triangle?

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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George observes that for every increase of 1 in the value of x, there is a increase of 60 in the cor...

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