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Katarina [22]
3 years ago
10

Given that the 3rd term in an arithmetic sequence is -2 and the 7th term is -10, tell me what the 1st term in the sequence is. E

xplain how you know.
Mathematics
1 answer:
Elenna [48]3 years ago
5 0

Answer:

2

Step-by-step explanation:

a₃ = -2

a₇ = -10

The nth term of an arithmetic sequence is:

a = a₁ + d (n − 1)

Therefore:

-2 = a₁ + d (3 − 1) = a₁ + 2d

-10 = a₁ + d (7 − 1) = a₁ + 6d

Subtract the equations:

8 = -4d

d = -2

Plug into either equation to find the first term.

-2 = a₁ + 2(-2)

a₁ = 2

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The area of a rectangular parking lot is represented by A = 6x^2 − 19x − 7 If x represents 15 m, what are the length and width o
Mekhanik [1.2K]

Answer:

The length and width of the parking lot are \frac{46}{3} meters and \frac{23}{2} meters, respectively.

Step-by-step explanation:

The surface formula (A) for the rectangular parking lot is represented by:

A = w\cdot l

Where:

w - Width of the rectangle, measured in meters.

l - Length of the rectangle, measured in meters.

Since, surface formula is a second-order polynomial, in which each binomial is associated with width and length. If A = 6\cdot x^{2}-19\cdot x -7, the factorized form is:

A = \left(x-\frac{7}{2}\,m \right)\cdot \left(x+\frac{1}{3}\,m \right)

Now, let consider that w = \left(x-\frac{7}{2}\,m \right) and l = \left(x+\frac{1}{3}\,m \right), if x = 15\,m, the length and width of the parking lot are, respectively:

w =\left(15\,m-\frac{7}{2}\,m \right)

w = \frac{23}{2}\,m

l =\left(15\,m+\frac{1}{3}\,m \right)

l = \frac{46}{3}\,m

The length and width of the parking lot are \frac{46}{3} meters and \frac{23}{2} meters, respectively.

5 0
3 years ago
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See the attachment for the intermediate steps.

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