Which of the following are equivalent to the statement “the price decreased by 1/3”?
2 answers:
Therefore, the only statement that is equivalent to <em>"the </em><em>price decreased</em><em> by </em><em>"</em> is:
<u>F. The price is now </u><u>66, 2/3% </u><u>of what it was before</u>
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Given that the original price of something decreased by 1/3, it means:
the original price is reduced by one-third.
- One-third is not equal to half of the price.
- 1/3 is less than 1/2.
- 1/3 of the original price would be
33.3% less of the original price.
- This means that the new price would be: <em><u>100 - 33 = 66% of the </u></em><em><u>original price.</u></em> This shows a reduction in price. The price would drop.
- 1/3 is more than a quarter (1/4).
<em>Any option showing or suggesting an increase is definitely the wrong answer.</em>
Therefore, the only statement that is equivalent to <em>"the </em><em>price decreased</em><em> by </em><em>" </em>are:
<u><em>F. The price is now </em></u><u><em>66, 2/3% </em></u><u><em>of what it was before</em></u>
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Answer:
M = (8,9)
Step-by-step explanation:
Notice that the points (0,15), and (20,0) form with the origin of coordinates (0,0), a right angle triangle (please see attached image). This triangle has twon perpendicular sides of length 15 and 20 respectively. Therefore, we can find the length of the segment that joins points A (0,15) and B (20,0) by finding the length of the hypotenuse in a right angle triangle (with the Pythagorean Theorem):
Now, to get a 2:3 proportion on Segment AB which is of length 25, we need to divide it in five equal parts (see the picture on the right of the attached image), and place point M at two of these divisions from point A (0,15) and along segment AB.
In order to find the appropriate location in (x,y) coordinates, we consider a smaller triangle (pictured in orange in the image) that is similar to the first larger triangle (pictured in blue). Notice that if the length of AB is 25, each of its five equal divisions would be of length "5", and therefore two of them will render a length of "10" (which is the hypotenuse of this smaller right angle triangle.
Now, in order to find the sides of this smaller triangle (which can give us the clues on the horizontal and vertical coordinates of point M), we can use proportions.
To find the length "x" of the horizontal side , we do:
To find the length "y" of the vertical side , we do:
Then, the coordinate "x" of point M will be "8", while we can calculate the y position of point M subtracting "6" from 15 (the length of the vertical side in the original triangle). This gives us the coordinates (8,9) for point M as marked in orange in the picture.
