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chubhunter [2.5K]
3 years ago
11

Please help me on my equation

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
5 0

Step-by-step explanation:

g(x) has clearly in its core the same function curve.

but it is

1. upside-down

2. moved up from the x-axis by 1 unit

3. moved to the right of the y-axis by 3 units

so, how do we express these 3 attributes in the functional definition ?

1. easily : by flipping the sign. g(x) = -x² is the same function type just upside-down (mirrored into the negative y space).

g(x) = -x²

2. also very easy : a function is moved up or down on the coordinate grid by adding (or subtracting) a constant.

we need to move our function up by 1 unit : we add 1.

that makes currently g(x) = -x² + 1

3. this is the trickiest part. to move a function left or right we need to make the function "think" that the input value x is not x, but it is (x ± constant).

let's ignore 1. and 2. for the moment and just focus moving the original function 3 units to the right.

that tells us that the functional result value of x in the shifted function must be the same as the functional result value in the original function for an input value that is 3 units "earlier" on the x-axis.

that would mean g(0) = f(-3), g(1) = f(-2), g(2) = f(-1), g(3) = f(0), ...

so, we see, g(x) = f(x-3) = (x-3)²

now, we combine again 1., 2. and 3., and we get

g(x) = -f(x-3) + 1 = -(x-3)² + 1

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before the recent house bonding there were 3212 houses in Fulton country now there are 3979 houses. How many houses did develope
lorasvet [3.4K]

Answer:

767 houses

Step-by-step explanation:

Initially there are 3212 houses in the city.

After the boom there are 3979 houses in the city.(due to boom there is an increase in the number of houses).

The number of houses developed by the developers is the difference between the number of houses before and after the boom.

The number of houses developed=3979-3212=767 houses

6 0
3 years ago
Please hurry i will mark brainliest
Ksivusya [100]

Answer:

Q (8,0)

R (8,9)

S (5,0)

Step-by-step explanation:

I counted how many places is each point away from the line and then I counted the same amount of places on the other side in order to find the reflected angle.

3 0
3 years ago
the second term of a geometric sequence is 18 and the fourth term is 8 find the common ratio . And find the sum of the first 6 t
777dan777 [17]

Answer:

  • ratio: 2/3
  • sum: 73 8/9

Step-by-step explanation:

The general term of a geometric sequence is ...

  an = a1·r^(n-1)

You have the 2nd and 4th terms, so ...

  a2 = a1·r^(2-1) = a1·r

  a4 = a1·r^(4-1) = a1·r^3

We can find r from the ratio ...

  a4/a2 = (a1·r^3)/(a1·r) = r^2 = 8/18 = 4/9

Then r is ...

  r = √(4/9) = 2/3 . . . . the common ratio

The first term is ...

  a2 = 18 = a1·(2/3)

  a1 = (3/2)·18 = 27

__

The sum of the first 6 terms is ...

  Sn = a1·(r^n -1)/(r -1)

  S6 = 27·((2/3)^6 -1)/(2/3 -1)

  S6 = 27·(64/729-1)/(2/3-1) = (27)(665)/243 = 73 8/9

The sum of the first 6 terms is 73 8/9.

_____

<em>Check on the sum</em>

The first 6 terms are ...

  27, 18, 12, 8, 5 1/3, 3 5/9

Their sum is 73 8/9, as above.

8 0
3 years ago
Help me if you can please
Luden [163]

Answer:

the question is not visible

8 0
2 years ago
Here is a balanced hanger diagram
suter [353]

Based on the mass of the circle and the triangle, we can find the mass of the square to be<u> 3.33 grams</u>

<h3>Mass of each side of hanger </h3>

Assuming the mass of the square is x, the equation for the first side is:

= (3 x mass of circle) + (2 x mass of triangle) + (6 x mass of square)

= ( 3 x 2) + ( 2 x 4) + ( 6 × x)

= 6 + 8 + 6x

Mass of other side:

=  (2 x mass of circle) + (5 x mass of triangle) + (3 x mass of square)

= ( 2 x 2) + ( 5 x 4) + ( 3 × x)

= 4 + 20 + 3x

<h3>Mass of square </h3>

As both sides are equal, equate both formulas to find x:

6 + 8 + 6x = 4 + 20 + 3x

6x - 3x = 24 - 14

3x = 10

x = 10/3

x = 3.33 grams

In conclusion, each square is 3.33 grams.

Find out more on problems requiring equating at brainly.com/question/20213883.

8 0
3 years ago
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