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Evgesh-ka [11]
3 years ago
7

PLEASE HELP?!

Mathematics
1 answer:
Anon25 [30]3 years ago
3 0
The middle point of BC is (0,2), the midpoint of CD is (1,0)
to prove two lines are parallel, prove their slopes are the same.
slope of BD: m=rise/run=4/-2=-2 (the run is negative because to get to B from D on the grid, you have to move from right to left, then upward. If the horizontal move is from left to right, the run is positive)
slope of EG: m=rise/run=2/-1=-2 
EG and BD have the same slope, so they are parallel. 
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Given a 5 liter jar and a 3 liter jar and a unlimited supply of water, how do you measure out 4 liter exactly
andre [41]

Answer:

Given:

5 liter Jar

3 liter jar

Unlimited supply of water.

To measure out 4 liters exactly.

Steps to be carries out to measure out 4 liters of water exactly.

Water content: 3 liter jar = Empty , 5 liter jar = Empty

1) Fill the 3 liter jar completely with water.

3 liter jar = 3 liter , 5 liter jar = Empty

2) Empty the filled 3 liter jar of water by pouring it out into 5 liter jar.

Water content: 3 liter jar = Empty , 5 liter jar = 3 liter

3) Again fill the empty 3 liter jar completely.

Water content: 3 liter jar = 3 liter , 5 liter jar = 3 liter

4) Pour water from 3 liter jar into 5 liter jar until it is completely filled.

Water content: 3 liter jar = 1 liter , 5 liter jar = 5 liter

5)  Empty the 5 liter jar completely.

Water content: 3 liter jar = 1 liter , 5 liter jar = Empty

6) Empty the 3 liter jar by pouring the water into 5 liter jar.

Water content: 3 liter jar = Empty , 5 liter jar = 1 liter

7) Fill the 3 liter jar completely with water.

Water content: 3 liter jar = 3 liter , 5 liter jar = 1 liter

8) Empty the 3 liter jar by pouring it into 5 liter jar.

Water content: 3 liter jar = Empty , 5 liter jar = 4 liter

Now, we have exactly 4 liters of water in the 5 liter jar.

7 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
80% of what number is 64
Thepotemich [5.8K]
Make an equation.

80% = 0.8

'of' is multiplication

'what number' is 'x'

'is' is an equal sign

0.8 * x = 64

0.8x = 64

Divide 0.8 to both sides:

x = 80
5 0
3 years ago
For the angle 7π/4, draw and upload a representation of the angle on the unit circle in the coordinate plane. Place the angle in
melomori [17]

Answer:

2eXz2

Step-by-step explanation:

8 0
3 years ago
60 points Need help Asap
Anna [14]

Answer:

45 units ^2

Step-by-step explanation:

make sure to divide the triangle and sqaure up when finding the area of this polygon..

hope this helps!!

8 0
3 years ago
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