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elixir [45]
3 years ago
5

Solve the following using the Substitution Method your work must be shown step by step: x + 2y = 2

Mathematics
1 answer:
Nat2105 [25]3 years ago
8 0

Answer:

x = - 2

y = 2

Step-by-step explanation:

y = - 2 + 4

y = 2

- 2 + 2(2) = 2

- 2 + 4 = 2

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Determine if the series is convergent or divergent 20-15+10-5....
Kazeer [188]

Answer:

Option b is correct.

The series 20-15+10-5....is Divergent

Step-by-step explanation:

Alternating series Test:

\sum_{n=1}^{\infty} (-1)^{n-1} (b_n) =b_1-b_2+b_3-........

b_n>0 satisfies:

  • b_{n+1} \leq b_n   for all n
  • \lim_{n\rightarrow \infty} b_n = 0

Then the series converges,

otherwise diverges.

Given the series: 20-15+10-5....

This is a alternating series:

\sum_{n=1}^{\infty} (-1)^{n-1} (20-5(n-1))

b_n = (20-5(n-1))

b_{n+1} = (20-5(n+1-1)) = (20-5n)

using the alternating series test;

b_{n+1} \leq b_n  for all n

\lim_{n\rightarrow \infty} b_n = \lim_{n\rightarrow \infty} (20-5(n-1)) = -\infty

⇒ the series diverges.

therefore, the given series i,e 20-15+10-5.... is divergent.

3 0
4 years ago
Solve each system.<br> y=7-3x<br> 3x+y=10
ad-work [718]

Answer: 0 = 3

Step-by-step explanation: If y = 7 - 3x, we can plug that in for y in the equation 3x + y = 10 by writing it as 3x + 7 - 3x = 10.

                                                                    - 7            - 7

                                                               --------------------------

                                                               3x - 3x        = 3

                                                                       0          = 3

4 0
3 years ago
Polygon WXYZ has vertices W(−2,−1) , X(−2,3) , Y(0,4) , and Z(0,0) . After a dilation the vertices of the image are W'(−4,−2) ,
Fiesta28 [93]

Answer:

scale factor (k) is 2

Step-by-step explanation:

Look at W and W'. W is (-2, -1), but W' says (-4, -2). 2 x 2 is 4 and 1 x 2 is 2. Both coordinates were multiplied by 2. The same goes for all the other vertices, so it would be k = 2.

8 0
2 years ago
In the Diagram, BD bisects ABC. Find x given the following.​
xenn [34]

Answer:

1. x=21.8 2. x-= -103

Step-by-step explanation:

8 0
3 years ago
Dan buys a car for £2700.
BartSMP [9]

Answer:

The car will be worth £2516.22 in 5 years

Step-by-step explanation:

The rule of depreciating is  

A=P(1-r)^{t}, where

  • <em>A</em> is the new value
  • <em>P</em> is the original value
  • <em>r</em> is the rate in decimal
  • <em>t</em> is the time in years

∵ Dan buys a car for £2700

∴ <em>P</em> = 2700

∵ It depreciates at a rate of 1.4% per year

∴ <em>r</em> = 1.4% = 1.4/100 = 0.014

∵ We need to find how much it will be worth in 5 years

∴ <em>t</em> = 5

→ Substitute all of these values in the rule above to find A

∵ A=2700(1-0.014)^{5}

→ Use your calculator to find the answer

∴ <em>A</em> = 2516.22

∴ The car will be worth £2516.22 in 5 years

7 0
3 years ago
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