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Sonbull [250]
3 years ago
10

If E=[-1,0,1,2,3,4] and F=[3,4,5,6,7,8] what is E U F?

Mathematics
1 answer:
KatRina [158]3 years ago
7 0

E=\{-1,\ 0,\ 1,\ 2,\ 3,\ 4\}\\\\F=\{3,\ 4,\ 5,\ 6,\ 7,\ 8\}\\\\E\ \cup\ F=\{-1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8\}

All elements from set E and from the set F. The same elements are only once.

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An = a1 + (n - 1)d
yarga [219]

Answer:

The car will travel 1980 meters in 15 minutes.

Hence, option 'D' is true.

Step-by-step explanation:

Given that a car travels 300 meters in the first minute, so

  • a₁ = 300

Each minute after, the car travels 120 meters. , so the sequence becomes

a₁, a₂, a₃, a₄, a₅, ...

300, 420, 540, 660, 780, ...

An arithmetic sequence has a constant difference 'd' and is defined by  

a_n=a_1+\left(n-1\right)d

computing the differences of all the adjacent terms

20-300=120,\:\quad \:540-420=120,\:\quad \:660-540=120,\:\quad \:780-660=120

The difference between all the adjacent terms is the same and equal to d=120

now, we have

  • a₁ = 300
  • d = 120

so substituting a₁ = 300 and d = 120 in the nth term of the sequence

a_n=a_1+\left(n-1\right)d

a_n=120\left(n-1\right)+300

a_n=120n+180

Thus, the nth term of the sequence is:

a_n=120n+180

<u>Determining the distance the car travels in 15 minutes</u>

As we have already determined the nth term of the sequence such as

a_n=120n+180

now substituting n = 15

a_{15}=120\left(15\right)+180

a_{15}=1800+180

a_{15}=1980

Therefore, the car will travel 1980 meters in 15 minutes.

Hence, option 'D' is true.

6 0
3 years ago
A 48 inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece
Y_Kistochka [10]

Complete question :

A 48 inch board in to be cut into three pieces so that the second piece is twice as long as the first, and the third piece in 3 times as long as the first. If x represents the length of the first, find the lengths of all three

Answer:

Length of first piece = x = 8

Length of second = 2x = 8*2 = 16

Length of third = 3x = 8 * 3 = 24

Step-by-step explanation:

Let :

Length of first piece = x

Length of second = 2x

Length of third = 3x

The total lengtb of board = 48 inches

Hence,

First + second + third = 48

x + 2x + 3x = 48

6x = 48

x = 48 / 6

x = 8

Length of first piece = x = 8

Length of second = 2x = 8*2 = 16

Length of third = 3x = 8 * 3 = 24

6 0
4 years ago
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