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Harlamova29_29 [7]
3 years ago
9

Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x+2) ?

Mathematics
2 answers:
Ahat [919]3 years ago
7 0

Adding a value to the X value shifts the graph that many units to the left.

X+2 adds 2 to x, so the graph would shift 2 unites to the left.

The answer is:

The graph of g(x) is the graph of ​f(x)​ translated 2 units left.

klemol [59]3 years ago
5 0

Answer:

Option D.

Step-by-step explanation:

The transformation of a function is defined as

g(x)=kf(x+a)+b                .... (1)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The given relationship between two function is

g(x)=f(x+2)            .... (2)

On comparing (1) and (2) we get

h=2> 0, so the graph of g(x) is the graph of ​f(x)​ translated 2 units left.

Therefore, the correct option is D.

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Find a polynomial for the sum of the shaded<br> areas of the figure. A = 6, B = 4
soldi70 [24.7K]

Answer:

The polynomial for the sum of the shaded  \pi r² - 20 \pi

Step-by-step explanation:

Given as :

The figure is shown which is of concentric circle with radius B , A , r

The radius B = 4 unit

The radius A = 6 unit

Let The sum of shaded portion = x unit

Now, The circumference of circle = 2 \pi R , where R is the radius

So, for circle with radius B.

The circumference = 2 \pi R = 2 \pi B

Or, The circumference = 2 \pi × 4 = 8 \pi

<u>Similarly</u>

For circle with radius A.

The circumference = 2 \piR = 2 \pi A

Or, The circumference = 2 \pi × 6 = 12 \pi

Now, <u>The area of circle with radius r is</u>

Area = \pi ×radius × radius

Or, Area = \pi r²

Now,

The sum of shaded region area = The area of circle with radius r - ( The circumference with radius B + The circumference with radius A )

Or, The sum of shaded region area =  \pi r² - ( 8 \pi + 12 \pi )

Or,  The sum of shaded region area =  \pi r² - 20 \pi

Hence The polynomial for the sum of the shaded area is \pi r² - 20 \pi  Answer

5 0
3 years ago
The gas tank of a 2013 Honda Accord holds 17.2 gallons. How many pounds of carbon dioxide are produced by burning an entire tank
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3 years ago
MT&amp;A uses the function f(x)=475-15x-15x.to depreciate smart phones. where f represents the value of smart phone and x repres
Shalnov [3]

Answer:

Find the answers in the explanation

Step-by-step explanation:

The given function is

f(x)=475-15x

A.) To find f^-1 and explain what it represents in this situacions, let f(x) = y. That is,

Y = 475 - 15x

Interchange y and x and make y the subject of formula

X = 475 - 15y

-15y = x - 475

Y = 475/15 - x/15

Y = (475 - x) / 15

Therefore,

f^-1(x) = (475 - x) / 15

If the function depreciates the smartphone, then, the inverse function will appreciate it.

When will the deprecated value of smart phone be less than $100.00

Substitute 100 for f(x) and find x

100 = 475 - 15x

-15x = 100 - 475

-15x = - 375

X = 375/15

X = 25

Therefore, the deprecated value of smart phone be less than $100.00 in the next 26 months.

what does x represent in f^-1(x) =30?

X represent the number of months for the smartphone appreciations

What is the value of x?

Substitute the inverse function for 30 and make x the subject of formula in the equation

f^-1(x) = (475 - x) / 15

30 = (475 - x) / 15

Cross multiply

450 = 475 - x

X = 475 - 450

X = 25 months

Graph f(x) and f^-1 (x) on the same coordinate

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Mr. Epps buys 500 bags of balloons for the high school prom for $250 what is the cost per bag
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The answer would be 2

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