Describe how the graph of y = x^3 can be transformed to the graph of the equation.

13.) y=2x^3.


14.) y=(2x)^3.


15.) y=(0.2x)^3

Answers

Answer 1
13. Vertical stretch by 2
14. A horizontal compression by 1/2
15. A horizontal stretch by 5
Answer 2
Final answer:

Transformations of the graph y = x^3 to y=2x^3, y=(2x)^3, and y=(0.2x)^3 include a vertical stretch by a factor of 2, a horizontal compression by a factor of 2, and a horizontal stretch by a factor of 5 respectively.

Explanation:

The transformation of the graph of y = x^3 to the graphs of the equations: 1) y=2x^3, 2) y=(2x)^3, and 3) y=(0.2x)^3, is based on changes in scaling and stretching.

For the equation y=2x^3, the graph of y = x^3 is vertically stretched by a factor of 2. This means that the value of y is doubled for each corresponding x value in the original graph. For the equation y=(2x)^3, the graph of y = x^3 is horizontally compressed by a factor of 2. This means that 'x' values in the original function are halved to obtain the corresponding 'x' values in the new function. The shape remains unchanged, but the graph is ‘narrower’ along the x-axis. For the equation y=(0.2x)^3, the graph of y = x^3 is horizontally stretched by a factor of 5 (1/0.2). This means that 'x' values in the original function are multiplied by 5 to obtain the corresponding 'x' values in the new function. The shape remains unchanged, but the graph is ‘wider’ along the x-axis.

These transformations are characterized as vertically stretched, horizontally compressed, and horizontally stretched respectively.

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Related Questions

Evaluate 6 • 3 ÷ start root 9 end root – 1.
A. 2
B. 3
C. 5
D. 6

Answers

6 * 3 / sqrt9

Using PEMDAS, solve SQRT first.

6 * 3 / 3

Using PEMDAS, solve 6 * 3.

18 / 3

Solve.

6.

Your answer is 6.

Answer:

It's 5 for connexus students, I did it already.

Step-by-step explanation:


What is the equation of the graphed line written in standard form?

A. –3x + y = –4
B. y = 3x – 4
C. y + 3x = 4
D. 3x – y = 4

Answers

Answer: D. 3x – y = 4


Step-by-step explanation: Standard form of a linear equation is of the form

ax+by =c.

We are given two points on the graph (2,2) and (0,-4).

Slope of the line: m =[tex]\frac{y_2-y_1}{x_2-x_1} =\frac{-4-2}{0-2} = \frac{-6}{-2} =3[/tex].

Applying point-slope form

y-y1 = m(x-x1)

y-2 = 3(x-2)

y-2 = 3x -6

Adding 2 on both sides, we get

y-2+2 = 3x -6+2

y = 3x - 4

Subtracting 3x from both sides, we get

y -3x = 3x-3x - 4

-3x + y= -4.

Multiplying whole equation by -1, we get

3x -y =4.Therefore, correct option is D option.

Answer:

Step-by-step explanation:

Sal washed 5 cars in 50 minutes unit rate

Answers

50 x 5 and you get ur answer

it took him 10 minutes to wash each car

which is the graph of linear inequality 2y>X-2

Answers

[tex]2y > x-2\qquad|:2\\\\y > \dfrac{1}{2}x-1[/tex]

for < or > line is - - - - - - - -

for ≤ or ≥ line is _________

for < or ≤ shaded below the line

for > or ≥ shaded above the line

Therefore your answer is the third graph.

Answer:

Option C. is the correct option.

Step-by-step explanation:

The given inequality is 2y > x - 2

1). As we know on a graph > (greater than) sign reflects the shaded part above the line

and < (less than) tells about the shaded region below the line.

2). If there is a sign of equality ≥ or ≤ then the line is denoted by a solid line in the graph.

When signs are in the form of > or < only then line will be in the dotted form.

By these rules we can easily say shaded area above the dotted line represents the solution area of the inequality 2y > x - 2.

Therefore, option C is the answer.

If 80 is decreased by 30%, what is the new amount?

Answers

The new amount to this equation is 56 how this helped

Answer:

The answer is 56.. hope I helped thanks and bye.

Write in algebraic expression ( 12 less than the amount y divided by 2)

Answers

y-12÷2

because it says 12 less than y we subtract y-12 but then it says divided by 2 so then it is reasonable to say y-12÷2

Write (2x + 1)(3x - 8) in expanded form

Answers

The answer is: 6x^2-13x-8

Final answer:

The expanded form of the algebraic expression (2x + 1)(3x - 8) is 6x² - 13x - 8.

Explanation:

To expand the algebraic expression (2x + 1)(3x - 8), we'll use the distributive property, which states that a(b + c) = ab + ac. First, we multiply 2x by each term in the second parentheses (3x and -8), and then we multiply 1 by each term in the second parentheses. Let's do this step by step:

Multiply 2x by 3x to get 6x².Multiply 2x by -8 to get -16x.Multiply 1 by 3x to get 3x.Multiply 1 by -8 to get -8.

Now, we combine these terms:

6x² - 16x + 3x - 8

Simplify by combining like terms:

6x² - 13x - 8

Therefore, the expanded form of (2x + 1)(3x - 8) is 6x² - 13x - 8.

Find the coordinates of the midpoint of the segment with the given endpoints A(1,2) and B(3,6).

Answers

midpoint = (2, 4 )

using the midpoint formula

midpoint = [ [tex]\frac{1}{2}[/tex] (1 + 3 ), [tex]\frac{1}{2}[/tex] (2 + 6 )] = (2, 4)


Final answer:

The midpoint of the line segment with given endpoints A(1,2) and B(3,6) can be found using the formula for a midpoint, which is ((x1+x2)/2, (y1+y2)/2). Substituting the coordinates of points A and B into this formula gives us the midpoint coordinates as (2,4). So the midpoint is (2,4).

Explanation:

The question is asking for the midpoint of the line segment with given endpoints A(1,2) and B(3,6). We can calculate this using the formula for the midpoint of a segment, which is ((x1+x2)/2, (y1+y2)/2). In this case:

x1 = 1 (the x-coordinate of point A) y1 = 2 (the y-coordinate of point A) x2 = 3 (the x-coordinate of point B) y2 = 6 (the y-coordinate of point B)

Substituting these values into the formula gives us the midpoint = ((1+3)/2, (2+6)/2) = (2,4). Therefore, the coordinates of the midpoint of the segment with the given endpoints A(1,2) and B(3,6) are (2, 4).

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How will the federal tax affect a gross bi weekly pay of $740 for a single person claiming 1 exemption? a. It increases gross pay by $62. b. It decreases gross pay by $62. c. It increases gross pay by $65. d. It decreases gross pay by $65.

Answers

How will the federal tax affect a gross biweekly pay of $740 for a single person claiming 1 exemption?

a.

It increases gross pay by $62.

b.

It decreases gross pay by $62.

c.

It increases gross pay by $65.

d.

It decreases gross pay by $65.

its d

Answer:

d

Step-by-step explanation:

Round 146.56 to the nearest tenth.

Answers

Because the 6 in the hundredths place is bigger than 5( the maximum) the tenths place will automatically round up to the next following number. The answer will be 146.6

The answer will be 146.6

Please Help <3 Please Help <3

Answers

Hey, there! For this question, we can just start by plugging in the known values. [tex](f + g)(x)[/tex] can be rewritten as [tex](\frac{x}{2} - 3 + 3x^2 + x - 6)(x)[/tex].

Combine like terms: [tex](\frac{x}{2} + x - 3 - 6 + 3x^2)(x)[/tex]

If you add x to [tex]\frac{x}{2}[/tex], x will become [tex]\frac{2x}{2}[/tex], which means that x/2 + x = 3/2x.

--> [tex](\frac{3}{2}x - 9 + 3x^2)(x)[/tex]

If you rearrange this, then your answer will be option b. Hope this helps.

       f(x) = [tex]\frac{x}{2}[/tex] - 3

    + g(x) = 3x² + x - 6

f(x) + g(x) = 3x² + [tex]\frac{x}{2}[/tex] + x  -3 - 6

              = 3x² + [tex]\frac{3}{2}x[/tex] - 9

Answer: B

Twice a number decreased by 8 is 2 less than half the number. What is the number?

Answers

Answer:

4

Step-by-step explanation:

with th information given we can express the equation:

[tex]2x-8=\frac{x}{2} -2[/tex]

where [tex]x[/tex] is the unknown number.

to clear for [tex]x[/tex] first we multiply the equation by 2, to eliminate the fraction:

[tex]2(2x-8=\frac{x}{2}-2 )\\4x-16=x-4[/tex]

moving all terms with [tex]x[/tex] to the left:

[tex]4x-x-16=-4\\3x-16=-4[/tex]

and adding +16 to each side:

[tex]3x-16+16=-4+16\\3x=12[/tex]

and finally, dividing by 3

[tex]x=\frac{12}{4} =4[/tex]

the number is 4.

Just the two circled ones please- unit rates. Also can someone explain how they got the answer? I am having trouble with these two

Answers

4.

In both cases divide the number of laps by the number of minutes to find the unit rate in laps per minute.

30 laps in 12 minutes: (30 laps)/(12 minutes) = 2.5 laps/minute

120 laps in 48 minutes: (120 laps)/(48 minutes) = 2.5 laps per minute

The rates are equivalent.

6.

I can't see the dimensions of the picture.

Do this:

Do these two divisions.

Divide the width by the length of the poster and of the picture.

Poster: (60 inches)/(100 inches) = 0.6

Picture: (width of picture)/(length of picture) = ?

If the second division also equals 0.6, then the ratios are equivalent.



Solve the following equation then place the correct number in the box provided 3(2x+5)> 2(x+6)

Answers

6x+15>2x+12. 4x>-3. x>-3/4

The answer is actually x ≥ -3/4

y=5 horizontal or vertical? x=3 horizontal or vertical?

Answers

Y= vertical & x= horizontal

y=vertical and x=horizontal

Hope this helps ^_^

you have 2/4 of a pizza and you want to share it equally between 2 people. How much of the pizza does each person get?

Answers

Hi CaCahead23,

Question:

You have 2/4 of a pizza and you want to share it equally between 2 people. How much of the pizza does each person get?

Solution:

2/4 / 2 = 1/4

Answer:

Each person gets 1/4 of a pizza.

each person gets 1 pizza

e graph shows the altitude of a helicopter over time.

A graph measuring altitude and time. A line runs through coordinates (0, 10,000) and (15, 4000) and shows a decrease in altitude as time increases

What is the slope of the line and what does it mean in this situation?


The slope is –2000 . This means that the helicopter descends 2000 ft each minute.

The slope is –400 . This means that the helicopter descends 400 ft each minute.

The slope is 400. This means that the helicopter ascends 400 ft each minute.

The slope is 2000. This means that the helicopter ascends 2000 ft each minute.

Answers

Let

x-------> the time

y-------> the altitude of a helicopter

Step 1

Find the slope of the line

we know that

the slope m of the line between two points is equal to

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

we have

[tex](x1,y1)=(0,10,000)\\(x2,y2)=(15,4,000)[/tex]

substitute in the formula

[tex]m=\frac{(4,000-10,000)}{(15-0)}[/tex]

[tex]m=\frac{(-6,000)}{(15)}[/tex]

[tex]m=-400\frac{feet}{minute}[/tex]

therefore

the answer is the option

The slope is [tex]-400[/tex] . This means that the helicopter descends [tex]400[/tex] ft each minute.


Answer:

-400

Step-by-step explanation:

what's 5÷251? could someone help me?

Answers

50.2
[tex]251 \div 5 = 50.2[/tex]


well 251 cannot go into 5 as a whole number because its way bigger than 5 so, it will be a decimal.


Your answer is

5/251 = 0.01992031872


Identify the slope of the line shown in the graph below

a
slope = 5

b
slope = undefined

c
slope = 0

d
slope = 1


Answers

B. Slope = undefined

What’s the place value of 3 in 167.43

Answers

Note the place values:

1 : hundred

6 : tens

7 : ones

.

4 : tenths

3 : hundredths

Look at the place value for 3. It is in the hundredths value, therefore, Hundredths is your answer

~Rise Above the Ordinary

The place value of 3 in 167.43 is 78.60

Jackie had $135 to spent at the mall she spent 29% of the money on a dress. Jackie spent $_ on the dress ?

Answers

Jackie spent $39.15 on the dress.


How do I write a fraction in the simplest form

Answers

Ask if the numerator and denominator can be divided by the same number, which is called a common factor.

See if at least one number in the fraction is a prime number.

Simply just find the least common factor between the numerator and the denominator of the fraction, For example, 2/4, you know that between the two numbers, they both share the same common factor,  2, so divide 2 on the top and the bottom, and then your final  answer would be 1/2. However, if there seems to be no common factor between the numerator and the denominator for a fraction, do not simplify it any more. You cannot have a decimal as a numerator or a denominator. For example,  3/5 has no common factor so you do not have to simplify it as it is already at its most simplest form.

Hope you found this helpful:)


A washer and a dryer cost 634 dollars combined. The washer cost 66 dollars less than the dryer. What is the cost of the dryer?

Answers

Steps to Solve:

1.  634 / 2 = 317

2. 317 + 66 = 383

Answer:

A = $383

Notes:

Read the question, this problem is not that hard to solve!

U have to do 634 divided by 66 so that would be 9.60606

Are 5/6 and -4.713 on the same side or the opposite side of zero ?

Answers

they are on opposite sides of zero because one number is negative and one is positive

Please help me and let me know if number a is wrong or not

Answers

its kinda upside down


it’s wrong. it would be 2A/b

Tell whether the two quantities vary directly. Explain your reasoning. The cafeteria provides three meals per day.

Answers

Answer:

The cafeteria provides three meals per day.

Reason 1

Yes, they vary directly  

As number of days increases ,Total number of meals i.e

1st day ⇒ 3

2nd day⇒6

3 rd day⇒9

4th day⇒12

......................

.........................

increases.

Total number of Meals = k×Number of days

But there is another possibility also

Reason 2

1 st day ⇒ 3

2nd day ⇒3

3rd day⇒ 3

.....................

.....................

As you can see from the above expression On each day number of meals is  

constant.

So we can say that ,

On each Day=Constant amount of meal=3

So, there is no Proportionality between Days and Meal.




A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 cm. A pyramid with the same base and half the height of the prism is placed inside the prism as shown in the figure. the volume of the space outside pyramid but inside the prism is blank cubic centimeters

Answers

the volume of the prism w/o pyrqmid volume is 200cm^3

pyramid volume is v=(1/3)bh
b=base
h=height

prism volume 5×5×25=300 cm^3

pyramid volune
(1/3)×(5×5)×12=100 cm^3

300-100=200 cm^3

Answer:

Volume of the empty space (outside pyramid) is 225 cm².

Step-by-step explanation:

Dimensions of the rectangular prism = 5cm × 5cm × 12cm

Volume of a triangle is represented by the expression,

[tex]V_{1}[/tex] = Length × Width × Height

   = 5×5×12

   = 300 cm²

A rectangular pyramid with half the height and same base of the prism, has been inserted inside the rectangular prism then,

Volume of pyramid is represented by the expression,

[tex]V_{2}=\frac{1}{3}(\text{Area of the base})\times (\text{Height})[/tex]

    = [tex]\frac{1}{3}(5\times 5)\times (6)[/tex]

    = 75 cm²

Therefor, volume of the space left in the blank prism

[tex]V_{1}-V_{2}=300-75[/tex]

            = 225 cm²

What percent of her overall bill did Bella save?
Original price: $225
Price after discounts: $180

Answers

Answer:

you still need the answer after all these years??? XD

Step-by-step explanation:

How can you use a number line to compare any two numbers

Answers

no. you many not       .....

You can use a number to compare two numbers by figuring out which one is least and which one is greater or if something is positive or negative.

name 5 consecutive integers where the middle one is 0

Answers

-52, -37, 0, 23, 67

Any numbers would work as long as their in correct order, and 0 is the middle number. Remeber that with negatives, ordering is different!

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