Part A
The pattern of squares is 1, 4, 9, ... which is the set of perfect squares
and so on
The 7th figure will have 49 squares because 7^2 = 49
<h3>Answer: 49</h3>
==============================================================
Part B
Each pattern has one circle per corner (4 circles so far). In addition, there's one circle per unit side to form the perimeter.
- Pattern 1 has 4+4(1) = 8 circles
- Pattern 2 has 4+4(2) = 12 circles
- Pattern 3 has 4+4(3) = 16 circles
The nth term will have 4+4n circles. The first '4' is the number of circles at the corners. The 4n is the circles along the perimeter. If you wanted, 4+4n factors to 4(1+n).
Plug in n = 20 to find the 20th figure has 4+4n = 4+4(20) = 84 circles
<h3>Answer: 84</h3>
==============================================================
Part C
- Pattern 1 has 1 square + 8 circles = 9 items total
- Pattern 2 has 4 squares + 12 circles = 16 items total
- Pattern 3 has 9 squares + 16 circles = 25 items total
This seems to suggest if the pattern number is odd, then we need an odd number of tiles (square + circular).
Let n be the pattern number. Pattern n needs n^2 square tiles and 4+4n = 4n+4 circular tiles. Overall, n^2+4n+4 tiles are needed.
It turns out that if n is odd, then n^2+4n+4 is always odd. The proof is shown below.
Side note: n^2+4n+4 factors to (n+2)^2
<h3>Answer: B) will always be odd</h3>
Answer:
-2.90625
Step-by-step explanation:
Given the polynomial function
P(x) = x^5-x^4+x^3-3
If c = 1/2
At x = c
P(1/2) = (1/2)^5-(1/2)^4+(1/2)^3-3
P(1/2) = 1/32 - 1/16 + 1/8 - 3
P(1/2) = 1-2+4-96/32
P(1/2) = -93/32
P(1/2) = -2.90625
Hence P(c) is -2.90625
Answer:
I believe the answer would be 4
Step-by-step explanation:
I'm going to use (a) to represent the side length in my explanation. side length is equivalent to the square root of the surface area over 6. The 6 is coming from there being 6 faces on a cube. So to solve this equation, you would first write it out. a=96/6. Next you would divide 96/6, giving you 16. and then lastly, you would find the square root of 16, which is 4. giving you a final answer of 4.
Hope this helps, and you understand it more!
9514 1404 393
Answer:
$44.49
Step-by-step explanation:
The total cost before tax will be ...
$49.96 +49.96 + 0.50(49.96) = $124.90
With tax added, the cost is ...
$124.90 × 1.071 = $133.77
Then the average cost per shirt for the 3 shirts is ...
$133.77/3 = $44.59
The mean cost of a shirt is $44.59.