32 times 4 is 128, if I am not mistaken
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>
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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>
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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>
I am not sure if what I am about to explain is correct but I hope it is somewhere along the correct path
To solve the problem use the following steps below....
Step 1: Take your numbers and place them in parentheses
(4-1/6)
Step 2: Turn your whole number,4, into a fraction
6/6=1
6/6x4=24/6
Step 3: Place your new fraction back into the problem
(24/6-1/6)
Step 4: Use the operation,subtraction, and minus 1/6 from 24/6
(23/6)
24/6 minus 1/6=23/6
Step 5(is optional): Turn 23/6 into a mixed fraction by dividing 23 by 6
23<span>÷6= 3 5/6
Step 6(is optional): put your answer into a final statement
(4-1/6)=23/6=3 5/6
Answer: 3 5/6
I hope this helps and I apologize in advance if any false information was given.
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<h3>
Answer: 10</h3>
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Explanation:
The two smaller triangles are proportional, which lets us set up this equation
5/n = n/15
Cross multiplying leads to
5*15 = n*n
n^2 = 75
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Apply the pythagorean theorem on the smaller triangle on top, or on the right.
a^2+b^2 = c^2
5^2+n^2 = m^2
25+75 = m^2
100 = m^2
m^2 = 100
m = sqrt(100)
m = 10
Answer:
y=11/3
Step-by-step explanation:
3y=2+9
Divide both sides by 3.
3y/3 = (2+9)/3
y=2/3+9/3
Combine like terms.
<u>y=11/3</u>