Answer: x=11
Step-by-step explanation:
Answer:
Greetings!
The answer to the first image is: 3
The second image is 4
Step-by-step explanation:
Here's how to rationalize a denominator:
1. Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
2. Make sure all radicals are simplified.
3. Simplify the fraction if it is needed.
I hope this helps you! :)
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
Answer:
42 yd²
Step-by-step explanation:
Area of a rectangle = width x length
lateral surface area is the area of the sides only
So the difference between the total surface area and the lateral surface area would be the surface area of the ceiling and floor (top and bottom).
area of floor and ceiling = 2(3.5 x 6) = 42 yd²
Or, we can calculate the total surface area and lateral surface area, then find the difference:
total surface area = 2(3.5 x 4.2) + 2(4.2 x 6) + 2(3.5 x 6) = 121.8 yd²
lateral surface area = 2(3.5 x 4.2) + 2(4.2 x 6) = 79.8 yd²
difference = 121.8 - 79.8 = 42 yd²
