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>
The arc measure of AD in degrees is 43 degrees.
<u>Step-by-step explanation</u>:
- The angle measure of the straight line is 180°.
- ∠APD + ∠DPC + ∠CPB = 180°
⇒ (7x+1)° + 90° + (9x-7)° = 180°
⇒ 16x + 84° = 180°
⇒ 16x = 96°
⇒ x = 96/16
x = 6
Substitute x=6 for angle ∠APD = (7x+1)°
∠APD = 7(6)+1 = 43°
The arc measure of AD in degrees = 43 degrees.
Answer:
B 12x+11
Step-by-step explanation:
4x + 8x + 7 + 4
Combine like terms
12x +11
Answer:
x=99792212
Step-by-step explanation:
get the x alone by subtracting 6787 from both sides
6787-6787+x=99798999-6787
x=99792212
Hope this helps!
Answer:
B.60
Step-by-step explanation:
He expects to take 2 months to complete the ride. What is the minimum number of miles that he must plan to ride each day to complete his ride in 60 days?
It's 60 miles per day to get to Los Angeles to Washington D.C
Hope it helped you brainiest plz and thank you!!!!!!!!!!!