Y = 3x − 8. What is the slope of the equation?
C. 3
Answers are
Choice A) function is W(n) = 4n+4
Choice C) input values for the function are natural numbers
Choice G) figure 8 has 36 white tiles
There are only three correct answers
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Explanation:
Figure 1 has 1 red tile and 8 white tiles (9 total)
Figure 2 has 4 red tiles and 12 white tiles (16 total)
Figure 3 has 9 red tiles and 16 white tiles (25 total)
Figure 4 has 16 red tiles and 20 white tiles (36 total)
Things to notice
* The pattern counts for the red tiles are perfect squares (1, 4, 9, 16)
* The total number of tiles are also perfect squares (9, 16, 25, 36)
* The number of white tiles can be counted, but its much easier to use the formula W = T - R
W = number of white tiles
T = total number of tiles
R = number of red tiles
* The pattern for the white tile counts is 8,12,16,20 so we basically add on 4 each time. The formula is W(n) = 4n+4. Plug in n = 1 and it leads to W(n) = 8 as expected. Plug in n = 2 and it leads to W = 12 etc.
The input n is the number of the figure which is a natural number. Natural numbers are {1, 2, 3, 4, ...} which are counting numbers. The function is NOT continuous. We can't plug in n = 1.5 for instance. The input does not represent the number of white tiles as that is the output.
If we plugged in n = 6, then we get
W(n) = 4n+4
W(6) = 4*6+4
W(6) = 30
so figure 6 will have 30 white tiles (not 10)
Do the same for n = 8
W(n) = 4n+4
W(8) = 4*8+4
W(8) = 36
figure 8 has 36 white tiles
<span>First find the area of two sides (Length*Height)*2 sides, 60. Then find the area of adjacent sides (Width*Height)*2 sides, 43.2. And then find the area of ends (Length*Width)*2 ends, 72. Lastly add the three areas together to find the surface area, 175.2.</span>
