Answer:
6) x=9.75
10) Triangle OMN ~ Triangle ODK; SSS ~
11) SSS ~ theorem
12) SSS ~ theorem
Step-by-step explanation:
For #6, since the polygons are similar, then it must mean AD is congruent to JM and CD is congruent to LM. Now we can set up the proportion 39/20=x/5 and solve. Solving for x gets us x=9.75, so C is the correct choice
For #10, there's no information about angles whatsoever in the diagram, so B and C must be wrong. D must be wrong as well because if the triangles weren't similar, then why is OJ ~ JM and OK ~ KN? So thus, the triangles are similar by SSS.
For #11, this is sort of a no-brainer because there's no mention of angles, so D must be correct.
For #12, same concept, no mention of angles, all sides are similar to their respective sides of the different triangles, so A is correct.
X+(y+z) is equal to saying (x+y)+z
This is called the cumulative property when order doesn’t matter or doesn’t change the equation. As in 1+2 is the same as 2+1. No matter which way we get the same answer. This only works with multiplication and addition though. Hope this helps. Any questions please just ask!! Thank you so much!!
The mean decreases, think about it, if every single value in a data set was decreased by the same number, the average would also go down by the same number
The median would also go down, because the value in the middle of the data set would now be smaller than before
The mode would also decrease, because the value that showed up the most in the data set has now also been decreased
The range, however, stays the same. If the lowest value in a data set was 3 and the highest was 10 and you subtracted 2 from each value in the data set, you would have the lowest at 1 and the highest at 8. But, 10-3 still equals 8-1, so the range is unchanged
Let our basis be worth 1 dollar. A nickel's worth is $0.05. In order to come up with $1, the number of nickels should be:
Number of nickels = $1 * 1 nickel/$0.05 = 20 nickels
Thickness of 20 nickels = 20 nickels * 1.95 mm = 39 mm
Let's do the same for the quarters. Each quarter is worth $0.25.
Number of quarters = $1 * 1 quarter/$0.25 = 4 quarters
Thickness of 4 quarters = 4 quarters * 1.75 mm = 7 mm
Find the ratio of the two:
39 mm/7 mm = 5.57
Therefore, a stack of nickels is 5.57 times thicker than a stack of quarters worth one dollar.
