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Volgvan
2 years ago
5

2x + 3y = 2 y = {x+3

Mathematics
1 answer:
FrozenT [24]2 years ago
8 0

The solution of the system is (-2,2)

Step-by-step explanation:

a solution is a system of equations intersecting.

on the graph you can see that the lines intersect at (-2,2)

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Need an answer as soon as possible.
Elza [17]
Part A

Answer: The common ratio is -2

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

Explanation: 

To get the common ratio r, we divide any term by the previous one

One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2

Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time

Side Note: each term is multiplied by -2 to get the next term

============================================================
Part B

Answer:
The rule for the sequence is 
a(n) = (-2)^(n-1)
where n starts at n = 1

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

Explanation:

Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio

The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)

============================================================
Part C

Answer: The next three terms are 16, -32, 64

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

Explanation:

We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms

-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64

showing that the next three terms are 16, -32, and 64

An alternative is to use the formula found in part B

Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier

Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier

Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier

while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
6 0
3 years ago
Twenty-three million, five hundred fifty in numerals
Anna35 [415]

Answer: 23,550,000   .......                          

5 0
3 years ago
Read 2 more answers
A museum has an aquarium in the shape of a right rectangular prism that is 22.9 meters long 7.5 meters wide and 4.6 meters high
V125BC [204]
The volume equals: Height * Width * Long
therefore the volume = 22.9*7.5*4.6 = 790 cubic meter.
7 0
3 years ago
Read 2 more answers
When I woke up it was 37° during the day the temperature increase 14° and then begin to decrease when I went to bed it was 29° h
GREYUIT [131]
Answer: The temperature decreased by 22 degrees

Explanation: 37 + 14 is equal to 51. So take 51 and subtract 29 from it since the weather decreased and you get 22 as your answer :)
3 0
3 years ago
(−2 − √3)(−2 + √3) simplified​
nata0808 [166]

Answer:

1

Step-by-step explanation:

To simplify this, we can use foil:

  • First: -2 × - 2 = 4
  • Outside: -2 × √3 = -2√3
  • Inside: -√3 × -2 = +2√3
  • Last: -√3 × √3 = -3

From this, we get 4 - 2√3 + 2√3 - 3 which can be simplified to 1

Hope this helps!

4 0
2 years ago
Read 2 more answers
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