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4 years ago

Suppose that G(x) = F(x - 6) - 3. Which statement best compares the graph of G(x) with the graph of F(x)?

2 answers:

8 0

From the given, G(x) = F(x - 6) - 3, the graph is shifted to 6 units to the right and 3 units down. Thus, the answer is letter A. It should be noted that for horizontal shifting, negative means to the right and down for vertical shifting.

lilavasa [31]4 years ago

8 0

Answer:

Option A -The graph of G(x) is the graph of F(x) shifted 6 units to the right and 3 units down.

Step-by-step explanation:

Given : G(x)=F(x-6)-3

We can compare graph of G(x) with graph of F(x) by looking at a and b values in G(x)=F(x-a)-b

where, a=6 and b=3

For the value of a :

If some unit is subtract from the x value then the graph shifted to right by that unit.

mathematically we can write,

f(x)→ f(x-a) → f(x) shift right with a units.

Therefore, in G(x)=F(x-6)-3

F(x)→ F(x-6) → F(x) shift right with 6 units.

⇒Graph of G(x) is the graph of F(x) shifted 6 units right.

For the value of b:

If some units is subtract from the function then the graph shifted downward by that unit.

mathematically we can write,

f(x)→ f(x)-b → f(x) shift down with b units.

Therefore, in G(x)=F(x-6)-3

F(x)→ F(x)-3 → F(x) shift down with 3 units.

⇒Graph of G(x) is the graph of F(x) shifted 3 units down.

Therefore, option A is correct that the graph of G(x) is the graph of F(x) shifted 6 units to the right and 3 units down.

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What is the first step in solving the equation: 3(x+2) = 12?

yanalaym [24]

Answer:

Divide by 3 on both sides.

Step-by-step explanation:

Original Expression: 3(x+2) = 12

Divide by 3 on both sides: x+2 = 4

Subtract 2 from both sides: x=2

Let me know if this helps!

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3 years ago

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kkurt [141]

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3 years ago

Size of u.s. states the total surface area (in square miles) for each of six selected eastern states is listed here. 28,995 pa 3

KonstantinChe [14]

Standard deviation of first data set = 5879.1 Standard deviation of second data set = 14768.78 The second data set is more variable. The basic definition of standard deviation is the square root of the mean of the squares of the difference from the mean. It's a bit of a mouthful, but easy enough to do. For the first data set, first calculate the mean. (28995 + 37534 + 31361 + 27087 + 20966 + 37741) / 6 = 30614 Now calculate the square of the differences from the mean (28995 - 30614)^2 = 2621161 (37534 - 30614)^2 = 47886400 (31361 - 30614)^2 = 558009 (27087 - 30614)^2 = 12439729 (20966 - 30614)^2 = 93083904 (37741 - 30614)^2 = 50794129 And now the average of the squares (2621161 + 47886400 + 558009 + 12439729 + 93083904 +50794129) / 6 = 34563888.67 And finally, take the square root to get the standard deviation. sqrt(34563888.67) = 5879.1 Now for the second data set of western states. First, the mean (72964 + 70763 + 101510 + 62161 + 66625 + 54339) / 6 = 71393.67 Now the squares of the differences (72964 - 71393.67)^2 = 2465946.778 (70763 - 71393.67)^2 = 397740.4444 (101510 - 71393.67)^2 = 906993533.4 (62161 - 71393.67)^2 = 85242133.78 (66625 - 71393.67)^2 = 22740181.78 (54339 - 71393.67)^2 = 290861655.1 And the average of the squares is 218116865.2 Finally, the square root of the average is 14768.78 So the standard deviation of the 2nd data set is 14768.78 And since the standard deviation of the 2nd data set is larger than the standard deviation of the 1st data set, that means that the 2nd data set is more variable.

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3 years ago

What is the sum of the first 51 consecutive odd positive integers?

Angelina_Jolie [31]

We call:

$a_{n}$ as the set of the first 51 consecutive odd positive integers, so:

 $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

 $a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}$

Then:

 $a_{n} = a_{1} + (n-1)d$

So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

 $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$

Therefore, we need to find:
 $a_{k} = a_{51}$

Given that $a_{1} = 1$ , then:

$a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1$

Thus:
$a_{k} = a_{51} = 2(51)-1 = 101$

Lastly:

$S_{51} = ( \frac{1 + 101}{2} ).51 = 2601$

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3 years ago

What is the range of the function y=3^x x>0 R y<0 y>0

Dima020 [189]

Answer:

The range is y > 0

Step-by-step explanation:

3^x is always greater than 0 and cannot be negative unless x is not real

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3 years ago