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2 years ago

if the graph of f(x)=x^2 is shifted 4 units to the left, then what would be the equation of the new graph?

Mathematics

1 answer:

Alecsey [184]2 years ago

3 0

Answer:

Step-by-step explanation:

Be careful. You can be confused by shifting left or right because the result is the opposite of what you might think.

f(x) = x^2

f(x + 4) = (x + 4)^2

To show you this in graphical form, see below.

Red: f(x) = x^2

Blue: f(x) = (x+4)^2 Notice that the blue graph is the the LEFT of the red graph

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A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below.

Annette [7]

The most appropriate choice for maxima and minima of a function will be given by

Rectangle of length 72 feet and breadth 36 feet has largest area

What is maxima and minima?

Maxima of function f(x) is the maximum value of the function and minima of function f(x) is the minimum value of the function.

Here,

Let the length be x feet and breadth be y feet

The farmer has 144 feet of fencing

Three of the sides will require fencing and the fourth wall already exists.

So,

x + y + y =1 44

x + 2y = 144

Area of rectangle(A) = xy $ft^2$

= (144 - 2y)y

= $144y - 2y^2$

$\frac{dA}{dy} = \frac{d}{dy}(144y - 2y^2)$

= $144 - 2\times 2y^{2-1}\\144 - 4y$

For largest area,

$\frac{dA}{dy} = 0$

$144 - 4y = 0 \\4y = 144\\y = \frac{144}{4}\\y = 36$

$\frac{d^2A}{dy^2} = \frac{d}{dy}(144 - 4y)\\=0-4\\=-4 < 0$

Hence area is maximum

For largest area, y = 36 feet

$x = 144 - 2\times 36\\x = 144-72\\$

$x = 72$ feet

So length of rectangle is 72 feet, breadth of rectangle is 36 feet

To learn more about maxima and minima of a function, refer to the link:

brainly.com/question/14378712

#SPJ9

3 0

1 year ago

Select the expression equivalent to (4x + 3) + (-2x +4).

olga nikolaevna [1]

Answer:

Step-by-step explanation

4 0

3 years ago

Read 2 more answers

I need someone to Solve this equation with a substitution method only

nikklg [1K]

Answer:

X=1

Step-by-step explanation:

1. Since y equals both 2x+5 and 4x+5, you can substitute 2x+5 for y into the first equation.

2. You then have 2x+5=4x+3

3. Then, solve the equation

4. 5=2x+3 (Subtract 2x from both sides)

5. 2=2x (Subtract 3 from both sides)

6. x=1 (Divide both sides by 2)

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3 years ago

Customers per day: 98, 87, 93, 82, 101, 99, 97, 97, 91<br> Find the mean to the nearest tenth:

notsponge [240]

<h2>Mean = 93.3 (to nearest tenth).</h2><h2 /><h2>Mean = 93.3 (to nearest tenth).Median = 97.</h2><h2 /><h2>Mean = 93.3 (to nearest tenth).Median = 97.Mode = 97.</h2><h2 /><h2>Mean = 93.3 (to nearest tenth).Median = 97.Mode = 97.Step-by-step explanation:</h2><h2 /><h2>Mean = 93.3 (to nearest tenth).Median = 97.Mode = 97.Step-by-step explanation:Arrange the data in ascending order:</h2><h2 /><h2>Mean = 93.3 (to nearest tenth).Median = 97.Mode = 97.Step-by-step explanation:Arrange the data in ascending order:79 82 87 91 93 97 97 98 99 101 102</h2><h2 /><h2>Mean = 93.3 (to nearest tenth).Median = 97.Mode = 97.Step-by-step explanation:Arrange the data in ascending order:79 82 87 91 93 97 97 98 99 101 102There are 11 numbers.</h2><h2 /><h2>Mean = 93.3 (to nearest tenth).Median = 97.Mode = 97.Step-by-step explanation:Arrange the data in ascending order:79 82 87 91 93 97 97 98 99 101 102There are 11 numbers.The Median is the center value (= the 6th</h2><h2>Mean = 93.3 (to nearest tenth).Median = 97.Mode = 97.Step-by-step explanation:Arrange the data in ascending order:79 82 87 91 93 97 97 98 99 101 102There are 11 numbers.The Median is the center value (= the 6thnumber) = 97.</h2><h2 /><h2>Mean = 93.3 (to nearest tenth).Median = 97.Mode = 97.Step-by-step explanation:Arrange the data in ascending order:79 82 87 91 93 97 97 98 99 101 102There are 11 numbers.The Median is the center value (= the 6thnumber) = 97.The mode = highest occurring value = 97.</h2><h2 /><h2>Mean = 93.3 (to nearest tenth).Median = 97.Mode = 97.Step-by-step explanation:Arrange the data in ascending order:79 82 87 91 93 97 97 98 99 101 102There are 11 numbers.The Median is the center value (= the 6thnumber) = 97.The mode = highest occurring value = 97.The mean = sum / 11 = 93.3.</h2>

7 0

2 years ago

Read 2 more answers

Solve for x? and the lengths missing side

Yuliya22 [10]

Answer:

X = 15, the missing length (c) is 10

Step-by-step explanation:

Using Pythagorean’s Theorem we know that a^2 + b^2 = c^2

We have side a and b, represent a as 6 and b as 8.

We have 6^2 + 8^2 = c^2

Which equals 100 = c^2

10 = c

Side C is 10, and (x - 5) = 10

X = 15

Please mark BRAINLIEST!

8 0

3 years ago

Read 2 more answers

if the graph of f(x)=x^2 is shifted 4 units to the left, then what would be the equation of the new graph?​

if the graph of f(x)=x^2 is shifted 4 units to the left, then what would be the equation of the new graph?