Answer:
C.) sin(11pi/6)
Step-by-step explanation:
construct triangle with a side perpendicular to x-axis
y=(-1)sin(pi/6)
y=sin(-pi/6)
y=sin((-pi/6)+2pi)
y=sin(11pi/6)
Answer: -2x - 4
Step-by-step explanation: This is because it has a variable in it, making it an algebraic expression.
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>
1 yard is 36 inches
so 5 yards are 180 inches
1 hour is 60 minutes
so in 60 minutes she paints 180 inches
or in 1 minute she paints 3 inches
Step-by-step explanation:
since in a triangle each side must be shorter than the sum of the other 2 sides (otherwise the end points cannot connect, and there is no triangle), the necessary inequality condition must be
side < 1 + 2 = 3
so,
side < 3
for a lower limit let's go through the cases
1 < 2 + side (is always true)
2 < 1 + side
1 < side (side must be larger than 1)
and again
side < 1 + 2 = 3
side < 3
so the full restriction for the third side is
1 < side < 3