The graph of a function is a transformation of the graph of its parent function in which the graph is
vertically stretched by a factor of 2;
• shifted left 3 units; and
• shifted up 2 units.

The Graph Of A Function Is A Transformation Of The Graph Of Its Parent Function In Which The Graph Isvertically

Answers

Answer 1

The equation for the function after the transformations is given as follows:

[tex]y = 2\sqrt{x + 3} + 2[/tex]

What is a translation?

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.

For a vertical stretch by a factor of a, the function is multiplied by a.

The parent function for this problem is given as follows:

[tex]y = \sqrt{x}[/tex]

Hence the function after each transformation is defined as follows:

Vertical stretch by a factor of 2: [tex]y = 2\sqrt{x}[/tex]Shift left 3 units: [tex]y = 2\sqrt{x+3}[/tex]Shift up 2 units: [tex]y = 2\sqrt{x+3} + 2[/tex]

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Related Questions

How many feet apart is 535 and -8

Answers

Answer:

543 fee

Step-by-step explanation:

The difference between 535 and -8 is the distance between them, but it is not specified in what unit this distance should be measured. If you meant to find the difference in feet, then:

535 - (-8) = 535 + 8 = 543

So the distance between 535 and -8 in feet is 543 feet.

Lin rolls a six-sided number cube then chooses one card from a deck of three cards numbered 1 through 3. What is the probability that the number cube and the card have the same number?

Answers

The probability that the number cube and the card have the same number is 2/39.

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Outcomes of cube = { 1, 2, 3, 4, 5, 6}

Outcome of Card = {1, 2, 3} from each group.

So, we have three number both in common as {1, 2, 3}

So, the probability that the number cube and the card have the same number is

= 1/6 x 16/52

= 8/156

= 2/39

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How to create the great paper outline templete?

Answers

First we need to select the subject to create the great paper outline template. Then follow the steps to create a paper.

Step 1: Choose the topic for the paper.

Step 2: Make a list of all the concepts you wish to discuss or incorporate.

Step 3: Separate similar concepts into smaller groupings.

Step 4: Put your concepts in order of importance: What ought the reader to discover first? What matters the most? Which conclusion will best suit your paper?

Step 5: Make good headers and subheadings for your documents.

Step 6: Format the outline in decimal, full-sentence, or alphanumeric form.

Step 7: State and review the paper by oneself first.

Follow all the steps to create the great paper outline template.

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the line pot shows the weight of 10 eggs laid by one head what is the total weight and an ounces of the four heaviest eggs ​

Answers

The total weight of the four heaviest eggs, in ounces, is 8 ³ / ₄ ounces .

How to find the total weight ?

Given the line plot, the weights of the heaviest eggs are :
2 ¹ / ₂ , 2 ¹ / ₄ , 2, 2

This is because these are the highest numbers on the line plot.

The total weight of these four heaviest eggs is :

= 2 ¹ / ₂ +  2 ¹ / ₄ +  2 + 2

= 4 ³ / ₄ + 4

= 8 ³ / ₄ ounces

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2.5b +5r = 80
The given equation describes the relationship
between the number of birds, b, and the number of
reptiles, r, that can be cared for at a pet care business
on a given day. If the business cares for 16 reptiles on
a given day, how many birds can it care for on this
day?

Answers

The number of birds they can take care on that day is zero.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 2.5b + 5r = 80.

Where, b represents the number of birds and r represents the number of reptiles.

On a given day. If the business cares for 16 reptiles, Therefore,

2.5b + 5(16) = 80.

2.5b + 80 = 80.

2.5b = 0.

So, They can not take care of any birds during the day.

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find the angle of a sector if the radius is 14cm and area of the circle is 462cm^2​

Answers

Answer: its 270.1087 degrees

Step-by-step explanation:

What is 7 Roman numbers?

Answers

Answer:

VII

Step-by-step explanation:

HELP DUE TONIGHT!
Find the volume of a cone with a base diameter of 6 in and a height of 6 in. Write the exact volume in terms of , and be sure to include the correct unit in your answer.​

Answers

The volume of the cone with a base diameter of 6in and height of 6in is 6π in³.

What is the volume of the cone?

The volume of a cone is expressed as;

V = (1/3)πr²h

Where r is radius of the base, h is the height of the cone and π is constant pi.

Given the data in the diagram;

Diameter d = 6inRadius r = diameter/2 = d/2 = 6in/2 = 3inHeight h = 6Volume V = ?

Plug the given values into the above formula and solve for the volume of the cone.

V = (1/3) × π × r² × h

V = (1/3) × π × ( 3in )² × 6in

V = 18π/3 in³

V = 6π in³

Therefore, the volume of the cone is 6π cubic inches.

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Michelle sells ice cream bars at the beach. In addition to a fixed salary, she earns a commission for each ice cream bar she sells. The table shows Michelle's total earnings, y, from selling x bars of ice cream:

Ice Cream Sales and Earnings
Number of Bars Sold (x) Total Earnings (dollars) (y)
0
50
1
56
2
62
3
68
Which equation best shows the relationship between x and y? (1 point)

y = x + 50
y = 6x + 50
y = 6x + 56
y = x + 56

Answers

Answer:

y= 6x+50

Step-by-step explanation:

y= 6x+50

if the number of bacteria in a colony doubles every 384 hours and there is currently a population of 2,150 bacteria, what will the population be 1,152 hours from now?

Answers

The population be 1,152 hours from now will be 17200

What is exponential growth?

Exponential growth is a process of increasing a quantity over time. It occurs when the rate of change of a quantity with respect to time is proportional to the itself.

Given that, the number of bacteria in a colony doubles every 384 hours and there is currently a population of 2,150 bacteria,

The exponential growth law for this problem is :-

p(t) = 2150(2)ⁿ/₃₈₄

where t is in hours. Plug t = 1152 into the equation and evaluate.

p(1152) = 2150(2)¹¹⁵²/₃₈₄

= 2150(2)³

= 17200

Hence, the population be 1,152 hours from now will be 17200

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what is 1.18x4?
PLEASE I NEED HELP

Answers

Answer:

4.72

Step-by-step explanation:

for essy calculation remove the decimal point

[tex] \frac{0.18}{100} [/tex]

=

[tex] \frac{18}{100} [/tex]

then multiply by 4

you will get

[tex] \frac{18 }{25} [/tex]

= 4.72


Hitler traveled 75 kilometers in 90 minutes. If he travels at the same speed, how
many kilometers would Hitler cover in 30 minutes?


A.20
B.24
C.25
D.30

Answers

Step-by-step explanation:

You can make a ratio. Put the first part of the question together and put the second part together.

[tex] \frac{75}{90} = \frac{x}{30} [/tex]

Next we cross multiply

[tex](75)(30) = 90x[/tex]

[tex]2250 = 90x[/tex]

Lastly we divide by 90

[tex]x = 25[/tex]

C bcs 90 divided by 3 is 30 and then 75 divided by 3 is 25 so every 30 minutes he travels 25 kilometers

The Beach Shack rents boats for $60 the first hour and $30 each hour after that. The Surf
Shop rents boats for $40 an hour. At what number of hours are the rental fees for a boat
from each shop equal?

Answers

Answer:

After 3 hours.

Step-by-step explanation:

60 + 30x = y

40x = y

Beach Shack:

60, 90, 120, 150, 180, 210

Surf Shop:

40, 80, 120, 160, 200

The graph shows a scuba diver's ascent over time. Use the graph to write an equation in slope-intercept
form that represents the diver's depth over time.
The equation that represents this situation is

Answers

The equation that represents the situation is m= 1/8s-10

What is a Graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

When

s= 0, m= -10

When

s= 80, m= 0

[tex]\frac{0-(0-10)}{80-0} = \frac{10}{80} = \frac{1}{8}[/tex]

m-0 = 1/8(s-80)

m= 1/8s-10. The equation

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Help m please,,,,,,,,,,,,

Answers

Answer:

-2

Step-by-step explanation:

?

Change each algebraic fraction into an equivalent fraction with the denominator of 24a^3b^2.

Answers

The algebraic fraction which is an equivalent fraction with the denominator 24a^3b^2 is 15b/24a^3.

To find an equivalent fraction with the denominator 24a^3b^2, we need to find a common denominator for the two fractions 5b and 8a^3. This common denominator is 24a^3b^2.

To find an equivalent fraction for 5b, we can multiply both the numerator and denominator by the same factor to obtain the desired denominator. To do this, we need to find a factor that would give us a denominator of 24a^3b^2 when multiplied with 8a^3.

The factor that would give us a denominator of 24a^3b^2 is 3.

So, the equivalent fraction for 5b with the denominator 24a^3b^2 is (5b * 3)/(8a^3 * 3) = 15b/24a^3.

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tell me the answer please how many students are vegetarian

Answers

Answer:

2 boys must be vegetarian.

If all 34 girls were vegetarian, there would have to be 2 boys to add up to 36.

Camilla took a $23,500 secured auto loan that
allows her to make no payments for 18
months. If interest is still compounded
monthly at a rate of 6.3%, what will her
balance be in 18 months when she starts
making payments?

Answers

7.3% and 73.6 and 937.666 8376.77

HELP PLEASE i need the answer for as may as possible o have done the first two!!( A1 and A2) WITH AN EXPLANATION PLEASE IM SO CONFUSED

Answers

1. The values of x in the equation are 1 and 10.

2. The values of x are 1 and -4.

How to calculate the values

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

1. y = x²

y = 11x - 10

Combine both variables

x² - 11x + 10

x² - x - 10x + 10

x(x - 1) - 10(x - 1)

x - 10 and x - 1 = 0

x = 10 and 1

2. y = x².

y + 3x = 4

x² + 3x - 4

x² +4x - x - 4

x(x + 4) - 1(x + 4)

(x - 1)(x + 4)

x = 1 and -4

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HELP ! A phone company offers two monthly plans. Plan A costs $30 plus an additional $0.03 for each minute of calls. Plan B has no initial fee but costs $0.18 for each minute of calls. What is the cost when the two plans cost the same for a set number of minutes?
Group of answer choices

$100

$200

$36

$30

Answers

The cost when the two plans cost the same for a set number of minutes is $36. Option C is correct.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Plan A costs $30 plus an additional $0.03 for each minute of calls.

This can be expressed in equation as

y=30+0.03x

Plan B has no initial fee but costs $0.18 for each minute of calls.

y=0.17x

Now we have to find the cost when the two plans cost the same for a set number of minutes

30+0.03x=0.18x

30=0.18x-0.03x

30=0.15x

Divide both sides by 0.15

x=200

when the number of minutes of calls is 200, the two plans cost the same.

To find the cost when the two plans cost the same,

we can substitute x = 200 into either expression for Cost_A or Cost_B:

Cost_A = 30 + 0.03(200) = $36

Cost_B = 0.18(200) = $36

Therefore, the cost when the two plans cost the same for a set number of minutes is $36. Option C is correct.

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HELP DUE TONIGHT!
Find the volume of a cone with a base radius of 4 m and a height of 12 m. Write the exact volume in terms of , and be sure to include the correct unit in your answer.​

Answers

The volume of the cone is 64π

How to determine the volume of teh cone

From the question, we have the following parameters that can be used in our computation:

Height, h = 12 m

Radius, r = 4 m

The volume is calculated s

V = 1/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 1/3π * 4² * 12

Evaluate

V = 64π

Hence, the volume is 64π

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Reese wants the find the equation of the line that passes through the point (-4, 8) and has a slope of 3. Help her complete the work below.

Reese will first need to use _______ Formula to plug in ________ for x1

, ________ for y1, and ________ for the m

. Reese's final answer will be _________, which is written in _________ Form.


Answers:

A. Slope

B. 3

C. y=3x+20

D. Standard

E. -4

F. y=3x+12

G. Slope Intercept

H. Point Slope

I. 8

J. y=3x+4

Answers

Answer:

Reese will first need to use point slope Formula to plug in- 4   for x1,  8 for y1, and 3 for the m

Reese's final answer will be y = 3x + 20, which is written in slope intercept Form.

Step-by-step explanation:

The answers in terms of the choices and order in which the blanks appear are

H. Point Slope

E. -4

I. 8

B. 3

C. y=3x+20

G. Slope Intercept

The point slope form for a line
y - y1 = m(x - x1)

Pugging in x1 = -4, y1= 8 and m = 3 gives
y -8 = 3(x - (-4))

y - 8 = 3x + 12  Move -8 to right side
y = 3x +12 + 8
y = 3x + 20

substitution y=2y-2 and y=2x-5y=1

Answers

Answer:

We can solve for y in the equation y = 2y - 2 by substituting y = 2x - 5.

Starting with y = 2y - 2, we substitute y = 2x - 5:

2x - 5 = 2(2x - 5) - 2

Expanding the right side:

2x - 5 = 4x - 12

Next, we isolate y by subtracting 2x from both sides:

-2x - 5 = 4x - 12

Adding 2x to both sides:

-5 = 6x - 12

Adding 12 to both sides:

7 = 6x

Finally, we divide both sides by 6 to solve for x:

x = 7/6

So, y = 2x - 5 = 2(7/6) - 5 = 7/3 - 5 = -14/3.

Therefore, y = -14/3 is the solution to the system of equations y = 2y - 2 and y = 2x - 5.

Step-by-step explanation:

please help! it’s pretty easy I just am confused!

Answers

Answer:

since p is irrational it is not expressible as a ratio of two integers and has an infinite and nonrecurring expansion when expressed as a decimal

Step-by-step explanation:

so a

1/4 x = 3/2
FIND
X
PLEASE

Answers

The answer to your question is X=6

The Community Swimming Pool charges a flat rate of $50 for a birthday party plus $2.50 for each person. Deborah can’t spend more than $100. How many friends can she invite?

Answers

Answer:

she can only invite 20 people max

Step-by-step explanation:

2.50x20= 50 + fee =100


Find the side length of a square with diagonals 18 cm long.

Answers

Answer:

162cm²

Step-by-step explanation:

Formula of square with diagonals=1/2*d²

=1/2*(18)²

=1/2*324cm²

we get,

=162cm²

Which choice is equivalent to the expression below?
√50 -√2

Answers

The simplified form of the expression √50 - √2 is 4√2.

What is the simplified form of the expression?

Given the expression in the question;

√50 - √2

To evaluate, first we simplify each term

√50 - √2

Factor out 25 from 50

√( 25(2) ) - √2

Now, rewrite 25 as 5²

√( 5²(2) ) - √2

Take the square root of 5² to pull it out of the radical

5√2 - √2

Now, subtract √2 from 5√2

4√2

Therefore, the simplified form is 4√2.

Option C) 4√2 is the correct answer.

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Find the measure of

Answers

A. 63

The angle shown is 90 degrees, if you take 90 and subtract 27 you get 63.

Please answer with the work shown

Answers

The area and the perimeter of the various given figures above are listed below:

1.) area=70 cm²

perimeter = 29cm

2. area= 80mm²

perimeter = 36mm

3.) area=108m²

perimeter = 42m

4.) area=72cm²

perimeter = 34cm

How to calculate the area and perimeter of the given figures above?

For figure 1;

The area of the given figure = length×width.

Where;

Length = 7cm, width = 10

area = 7×10 = 70 cm²

The perimeter = summation of the whole sides.

= 10+7+5+4+3

= 29cm

For figure 2;

The area of the given figure = length×width.

Where;

Length = 8 mm; width = 10mm

area = 8×10 = 80mm²

The perimeter = 6+8+6+10+(8-6)+(10-6)

= 6+8+6+10+2+4

= 36mm

For figure 3;

The area of the given figure = length×width.

Where;

Length= 6+3 = 9m

width ,= 8+5 = 12m

area = 9×12 = 108m²

The perimeter: 2( 9+12) = 42m

For figure 4;

The area of the given figure = length×width.

Where;

Length= 8cm

width = 4+5 = 9cm

area = 8×9 = 72cm²

The perimeter = 6+4+5+8+(5+4)+(8-6)

= 6+4+5+8+9+2

= 34cm.

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