Explain why 20 + (-12) + 12 is the same as 20 + 0??

Answer: Function g reflected function f across the x-axis.

For function g, as x approaches negative infinity, g(x) approaches negative infinity.

Function f is symmetrical about the point (4,6).

The correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.

Here given that the function g(x)= -(x-4)²+6

vertex of the graph of the function g is

dg/dx=0

⇒2(x-4)=0

⇒x-4=0

⇒x=4

putting x=4 in g(x) , g(4)= -(0-0)²+6=6

Hence the vertex of the graph of g is (4,6).

The parent function is f(x)= x²

here the vertex of the function is (0,0).

Option A: This option is true as the graph of function g is the inverse image of f. So,  Function g is reflected of function f across the x-axis.

Option B: This option is incorrect. as the vertex of the function f is transformed to (4,6) which is the vertex of g(x).

Option C:  This option is true because

 [tex]\lim_{x \to- \infty} g(x)[/tex]

= [tex]\lim_{x \to- \infty} -(x-4)^2+6\\[/tex]

= -(∞-4)²+6

=-∞²+6

=-∞

Hence as x approaches to the -∞, g approaches to the -∞

Option D. This option is incorrect because

if the function is always decreasing its derivative is negative for all x∈R

dg/dx<0

⇒2(x-4)<0

⇒x-4<0

⇒x<4

so the function is decreasing for x<4 not for all x.

Option E: This option is incorrect. because g is not always rather it is positive for 4-√6 < x < 4+√6

g(x)>0

⇒-(x-4)²+6 >0

⇒-(x-4)²>-6

⇒(x-4)²<6  

⇒|x-4|<√6

⇒4-√6<x<4+√6

so, g(x) is positive for 4-√6 < x < 4+√6

Option E:
This option is incorrect as g(x) is symmetrical about line x=4.

Therefore the correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.

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Answer:

(-1,-3)

Step-by-step explanation:

I hope this help

Answer:

900 miles

Step-by-step explanation:

well if you have 12.5 and you divide it by 2.5 you get 5. I do this because you need to find out how many time 2.5 goes into 12.5 so you can then multiply 180 by that number. 180*5=900

Greetings from Brasil...

→ Collinear points = points belonging to the same line

→ PQ is said to be equal to RS. Let’s call this distance X

→ let's call QR Y

With this information and the figure in the annex we can conclude that:

refer to attached

PQ = X

QR = Y

RS = PQ = X

then

PR = PQ + QR

16 = X + Y       i

PS = PR + RS

21 = 16 + X

X = 5       putting in i

16 = X + Y

16 = 5 + Y

Y = 11

So,

Collinear points are points on the same line.

The value of QR is 11

From the question, we have:'

This means that:

[tex]\mathbf{PR = PQ + QR}[/tex]

[tex]\mathbf{QS = QR + RS}[/tex]

[tex]\mathbf{PS = PR + RS}[/tex]

The given parameters are:

[tex]\mathbf{PS = 21}[/tex]

[tex]\mathbf{PR = 16}[/tex]

[tex]\mathbf{PQ = RS}[/tex]

Substitute the above values in [tex]\mathbf{PS = PR + RS}[/tex]

[tex]\mathbf{21= 16 + RS}[/tex]

Solve for RS

[tex]\mathbf{RS = 21- 16}[/tex]

[tex]\mathbf{RS = 5}[/tex]

This means that:

[tex]\mathbf{PQ = RS = 5}[/tex]

Substitute 5 for PQ in [tex]\mathbf{PR = PQ + QR}[/tex]

[tex]\mathbf{PR = 5+ QR}[/tex]

Substitute [tex]\mathbf{PR = 16}[/tex] in [tex]\mathbf{PR = 5+ QR}[/tex]

[tex]\mathbf{16 = 5+ QR}[/tex]

Solve for QR

[tex]\mathbf{QR = 16 - 5 }[/tex]

[tex]\mathbf{QR = 11}[/tex]

Hence, the value of QR is 11

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Answer:

Yes

Step-by-step explanation:

The constant is $1.75 each

Answer:

The mean is 41

Step-by-step explanation:

Here , we are interested in finding the mean.

Firstly, let the standard deviation be x and the mean be y.

We are told that 51 is 2 standard deviations above the mean. What this mean is that if we subtract 2 standard deviations from 51, we will arrive at the mean.

Mathematically;

51 - 2(x) = y

y + 2x = 51 •••••••••(i)

We are also told that 36 is one standard deviation below the mean. What this mean is that if we subtract one standard deviation from the mean, we will have 36

Mathematically, that would be;

y-36 = x •••••••(ii)

Substitute ii into i directly;

We have

y + 2(y-36) = 51

y + 2y -72 = 51

3y -72 = 51

3y = 51 + 72

3y = 123

y = 123/3

y = 41

Answer:

Step-by-step explanation:

-5 + 7p + 14 + 11p = 18p + 9

18p + 9 = 18p + 9

0 = 0

Pedro is correct

Answer:

5/7

Step-by-step explanation:

6/7-1/7=5/7

The answer is 6/7 - 1/7 = 5/7

Step by step explanation is in the image below. :)

Answer:

30,440 feet

Step-by-step explanation:

You simply just add 29,029 and 1411 because if you picture it on a number line, 29,029 would be to get to zero as well as 1411 going up in elevation.

Hey there! I'm happy to help!

Tom has 150 already saved and for every hour he works, he will gain an extra $25. After h hours, he will have $300,

So, we multiply 25 by n, because for every hour he will have 25 added to his total, and repeated addition is multiplication, so we multiply 25 by n.

We add 150 as that is what we already have saved.

Finally, we want this to equal 300.

So, here is our equation.

25n+150=300

Now we solve. We subtract 150 from both sides.

25n=150

We divide both sides by 25.

n=6

Tom will have to work six hours to buy the iPhone.

Have a wonderful day! :D

Answer:

25(6)+150=300

Step-by-step explanation:

25x+150=300

25x=300-150

25x/25=150/25

x=6

Answer:

-6430041/50000000000

Step-by-step explanation:

so -6 to the power of negative 5 is -0.00012860082 which as a fraction is -6430041/50000000000

Answer:

10

Step-by-step explanation:

if 4 cupcakes were 2/5 of what she started out with, i divided 4/2 and got 2 so 2 cupcakes per 1/5, 2*5=10 so 5/5 is the 10 cupcakes

Answer:

[tex]12x^{2} -5x -2[/tex]

Step-by-step explanation:

We multiply the first term 3x by 4x and then 3x multiplied by one. We proceed to multiply by -2 by 4x and multiplied by -2 +1. We finally add and get the result.

[tex]12x^{2} -5x -2[/tex]

Answer:

f(-2) = 21

Step-by-step explanation:

Step 1: Define

f(x) = 3x² - 4x + 1

f(-2) is x = -2

Step 2: Substitute and Evaluate

f(-2) = 3(-2)² - 4(-2) + 1

f(-2) = 3(4) + 8 + 1

f(-2) = 12 + 9

f(-2) = 21

the answer is it is function

Answer:

[tex]MP = (5,3)[/tex]

Step-by-step explanation:

[tex]MP= (\frac{x_1+x_2}{2}) (\frac{y_1+y_2}{2} )\\MP= (\frac{7+3}{2}) (\frac{11+-5}{2} )\\MP= (\frac{10}{2}) (\frac{6}{2} )\\MP= (5,3)[/tex]

Answer:

A

Step-by-step explanation:

2w means 2 pounds per week

you need less than or equal to because think about it like this

you want to be LESS THAN or EQUAL TO 190 pounds. on the right side is reality , what you really are. you need the right side to be LOWER or EQUAL to the left side!

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Solution :-

Following are the population of five major cities of India according to the Census of 2011.

1) Mumbai  

a) Indian System :

1,24,42,373 - One Crore Twenty Four Lakh Forty Two Thousand Three Hundred Seventy Three.

b) International system :

12,442,373 - Twelve Million Four Hundred Forty Two Thousand Three Hundred Seventy Three.

2) Delhi  

a) Indian System :  

1,10,34,555 - One Crore Ten Lakh Thirty Four Thousand Five Hundred Fifty Five.

b) International System :

11,034,555 - Eleven Million Thirty Four Thousand Five Hundred Fifty Five.

3) Bangalore  

a) Indian System :

84,43,675 - Eighty Four Lakh Forty Three Thousand Six Hundred Seventy Five.

b) International system :

8,443,675 - Eight Million Four Hundred Forty Three Thousand Six Hundred Seventy Five.

4) Hyderabad  

a) Indian System :

67,31,790 - Sixty Seven Lakh Thirty One Thousand Seven Hundred Ninety.

b) International System :

6,731,790 - Six Million Seven Hundred Thirty One Thousand Seven Hundred Ninety.

5) Ahmedabad  

a) Indian System :  

55,77,940 - Fifty Five Lakh Seventy Seven Thousand Nine Hundred Forty.

b) International System :

5,577,940 - Five Million Five Hundred Seventy Seven Thousand Nine Hundred Forty.

Answer:

Step-by-step explanation:

Comment me if you want to help me find my lost love

Since the measure of angle DOC = 44 degrees and it's the central angle of arc DC, the measure of arc DC = 44 degrees

A. Noncolinear

ABE although they are in the same side, but they don't lie on the same line.

so its a noncolinear.

Answer:

ABE although they are in the same side, but they don't lie on the same line.

so its a noncolinear.

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(f(x))

g(-x^2 - 1)

-x^2 + 0x + 4= -x^2 + 4

Answer:

m = [tex]\frac{k}{q^2}[/tex]

Step-by-step explanation:

Given m varies inversely as q² then the equation relating them is

m = [tex]\frac{k}{q^2}[/tex] ← k is the constant of variation

The cost of one pound beef is $3.2

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Cost 4.5 pound of beef = $14.40

So, the unit rate for beef

= 14.40 / 4.5

= $3.2

Hence, the cost of one pound beef is $3.2

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Answer: the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius

Step-by-step explanation:

Answer:Aka) A

Step-by-step explanation:

Answer:

Hope that will help you

Answer:

10y+16

Step-by-step explanation:

Distribute and combine like terms