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4 years ago

What is the solution of 3x + y = 9 and 3x - 5y = 15

Mathematics

1 answer:

7nadin3 [17]4 years ago

7 0

Answer:

x = 10/3, y = -1

Step-by-step explanation:

3x+y = 9 (1)

3x-5y = 15 (2)

(1) - (2) [subtract (2) from (1)]

6y = -6

y = -1

Using (1),

3x + (-1) = 9

3x = 10

x = 10/3

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Find the nth term of the sequence 7,25,51,85,127

olya-2409 [2.1K]

Let a (n) denote the n-th term of the given sequence.

Check the forward differences, and denote the n-th difference by b (n). That is,

b (n) = a (n + 1) - a (n)

These so-called first differences are

b (1) = a (2) - a (1) = 25 - 7 = 18

b (2) = a (3) - a (2) = 51 - 25 = 26

b (3) = a (4) - a (3) = 85 - 51 = 34

b (4) = a (5) - a (4) = 127 - 85 = 42

Now consider this sequence of differences,

18, 26, 34, 42, …

and notice that the difference between consecutive terms in this sequence b is 8:

26 - 18 = 8

34 - 26 = 8

42 - 34 = 8

and so on. This means b is an arithmetic sequence, and in particular follows the rule

b (n) = 18 + 8 (n - 1) = 8n + 10

for n ≥ 1.

So we have

a (n + 1) - a (n) = 8n + 10

or, replacing n + 1 with n,

a (n) = a (n - 1) + 8 (n - 1) + 10

a (n) = a (n - 1) + 8n + 2

We can solve for a (n) by iteratively substituting:

a (n) = [a (n - 2) + 8 (n - 1) + 2] + 8n + 2

a (n) = a (n - 2) + 8 (n + (n - 1)) + 2×2

a (n) = [a (n - 3) + 8 (n - 2) + 2] + 8 (n + (n - 1)) + 2×2

a (n) = a (n - 3) + 8 (n + (n - 1) + (n - 2)) + 3×2

and so on. The pattern should be clear; we end up with

a (n) = a (1) + 8 (n + (n - 1) + … + 3 + 2) + (n - 1)×2

The middle group is the sum,

$\displaystyle 8\sum_{k=2}^nk=8\sum_{k=1}^nk-8=\frac{8n(n+1)}2-8=4n^2+4n-8$

so that

a (n) = a (1) + (4n ² + 4n - 8) + 2 (n - 1)

a (n) = 4n ² + 6n - 3

4 0

3 years ago

if one person walked 1.2miles and the other walked 0.8 miles and they made 120.00 how much money did each one make

alexdok [17]

The one who walked 1.2 miles would have made $72 and the one who walked 0.8 miles would have made $48.

7 0

3 years ago

Solve for x I'm not sure of the way I answered it so can anyone help plz

Helga [31]

Answer:

x = √76

Step-by-step explanation:

in upper triangle :

7² - 3² =40 so the third side of the upper triangle is : √40

in the biggest triangle :

(3+3)² + 40 = 76 so the another side of the biggest triangle is : √76

4 0

3 years ago

Choose the expression that best represents the product of the width and the height

nexus9112 [7]

The length of a rectangle is 12 inches more than its width. What is the width of the rectangle if the perimeter is 42 inches?

x best represents .

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3 years ago

Mark made 7 withdrawals of $75 each from her bank account. What was the overall change in her account?

MA_775_DIABLO [31]

Firstly im confused because Mark is usually a male's name. However, what you want to do is multiply 75 by 7 and your answer is $525.00 Study hard and get good grades! Train daily and become a champion!

3 0

3 years ago