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Anvisha [2.4K]
3 years ago
7

Three copies of a triangle were rotated and positioned as shown.

Mathematics
1 answer:
lara31 [8.8K]3 years ago
4 0
<span>The question aks us to determine which statement is always true about the angles in the figure. If angle A and B form a right angle, then C must be also a right angle, which is not correct. Also if A and C form a right angle, then angle B must be a right angle. So answers A and C are false. Also thet we know that the sum of the interior angles of the triangle is 180 degrees. A + B + C = 180 deg. ( or a straight angle ). Answer: B. Angle A, angle B, and angle C, form a straight angle. </span>
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For the given central angle, determine the distance traveled along the unit circle from the point (1,0). 57
aliina [53]

Answer: (a)- 0.99\ \text{units}

Step-by-step explanation:

Given

Central angle is 57^{\circ}

The radius of the unit circle is 1\ \text{unit}

Arc length is given by

\Rightarrow l=\dfrac{\theta}{360^{\circ}}\times 2\pi r

Put the values

\Rightarrow l=\dfrac{57}{360}\times 2\pi \cdot1\\\\\Rightarrow l=0.99\ \text{units}

6 0
3 years ago
The prophecy states that if you go to the link in the picture this comment will make sense
likoan [24]

Answer:

no way

Step-by-step explanation:

4 0
3 years ago
Determine formula of the nth term 2, 6, 12 20 30,42​
nalin [4]

Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

so that \{b_n\} = \{4, 6, 8, 10, 12, \ldots\}.

Let \{c_n\} be the sequence of differences of \{b_n\},

c_n = b_{n+1} - b_n

and we see that this is a constant sequence, \{c_n\} = \{2, 2, 2, 2, \ldots\}. In other words, \{b_n\} is an arithmetic sequence with common difference between terms of 2. That is,

2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2

and we can solve for b_n in terms of b_1=4:

b_{n+1} = b_n + 2

b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2

b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2

and so on down to

b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)

We solve for a_n in the same way.

2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)

Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}

6 0
2 years ago
In a population of 10,000 geese the growth rate is 4% per year. What is the total increase in population over 4 years? Round you
omeli [17]

Answer:

Step-by-step explanation:

10000*4%= 400 Geese year1

10400*4%=416 Geese  year 2

10816*4%= 432.64 Geese year 3

11,248.64*4%= 449.95 Geese. year 4

11248.64+449.95= 11698.59

11698.59-10000=1698.59

Increased by 1699 Geese.

3 0
3 years ago
Read 2 more answers
Which of the following equations correctly shows the relationship between the values of x and the values of y?
Firdavs [7]
Every time the x goes up 1 the y goes up by 3
6 0
3 years ago
Read 2 more answers
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