If g(x)=4x^(2)-16 were shifted 7 units to the right and 3 down, what would the new equation be?

If G(x)=4x^(2)-16 Were Shifted 7 Units To The Right And 3 Down, What Would The New Equation Be?

Answers

Answer 1

The equation of the transformed function is h(x) =  4(x - 7)² - 19 option (C) is correct.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

g(x) =  4x² - 16

The above function shifted 7 units to the right and 3 down.

Applying transformation:

x → (x - 7)

G(x) =  4(x - 7)² - 16

G(x) → G(x) - 3

h(x) =  4(x - 7)² - 16 - 3

h(x) =  4(x - 7)² - 19

Thus, the equation of the transformed function is h(x) =  4(x - 7)² - 19 option (C) is correct.

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Related Questions

Identify the method that will be used to solve for x for each equation.
4x = 20
x 119
5x + 6x = 22
5(x - 2) = 30

Answers

The solution of the equation 4x = 20, x – 11 = 9, 5x + 6x = 22, and 5(x – 2) = 30 will be 5, 20, 2, and 8.

What is the solution of the equation?

The solution of the equation means the value of the unknown or variable.

The equations are given below.

4x = 20

 x = 5

x – 11 = 9

      x = 20

5x + 6x = 22

       11x = 22

         x = 2

5(x – 2) = 30

   x – 2 = 6

         x = 8

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3.)3 * (2x - 6)
4.)2x * (5x + 11)

Answers

3) [tex]3(2x-6)=\boxed{6x-18}[/tex]

4) [tex]2x(5x+11)=10x^{2}+22x[/tex]


A sum of money is divided among three girls, Rheanna, Kerisha and Anne, in the ratio 2:3:7, respectively. If Anne gets $15
more than Kerisha, what is the value of the total sum that was shared?

Answers

Using proportions, it is found that the value of the total sum that was shared was of $45.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the rates, Anne's and Kerisha's proportions, out of the total value N, are given by:

[tex]A = \frac{7}{2 + 3 + 7}N = \frac{7N}{12}[/tex][tex]K = \frac{3}{2 + 3 + 7}N = \frac{3N}{12}[/tex]

The difference is of $15, hence:

[tex]A - K = 15[/tex]

[tex]\frac{7N}{12} - \frac{3N}{12} = 15[/tex]

[tex]\frac{4N}{12} = 15[/tex]

[tex]\frac{N}{3} = 15[/tex]

N = 15 x 3 = 45

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The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 240 bacteria, and the population after 9 hours is double the population after 1 hour. How many bacteria will there be after 4 hours? (Round your answer to the nearest whole number.)

Answers

Answer:

339

Step-by-step explanation:

Exponential Function

General form of an exponential function: [tex]y=ab^x[/tex]

where:

a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given information:

a = 240 (initial population of bacteria)x = time (in hours)y = population of bacteria

Therefore:  [tex]y=240b^x[/tex]

To find an expression for the population after 1 hour, substitute x = 1 into the found equation:

[tex]\implies y=240b^1[/tex]

[tex]\implies y=240b[/tex]

We are told that the population after 9 hours is double the population after 1 hour.  Therefore, make y equal to twice the found expression for the population after 1 hour, let x = 9, then solve for b:

[tex]\implies 2(240b)=240b^9[/tex]

[tex]\implies 480b=240b^9[/tex]

[tex]\implies 480=240b^8[/tex]

[tex]\implies 2=b^8[/tex]

[tex]\implies b=\sqrt[8]{2}[/tex]

[tex]\implies b=2^{\frac{1}{8}}[/tex]

Therefore, the final exponential equation modelling the given scenario is:

[tex]\implies y=240(2^{\frac{1}{8}})^x[/tex]

[tex]\implies y=240(2)^{\frac{1}{8}x}[/tex]

To find how many bacteria there will be after 4 hours, substitute x = 4 into the found equation:

[tex]\implies y=240(2)^{\frac{1}{8}(4)}[/tex]

[tex]\implies y=240(2)^{\frac{1}{2}}[/tex]

[tex]\implies y=339 \:\: \sf (nearest\:whole\:number)[/tex]

Therefore, there will be 339 bacteria (rounded to the nearest whole number) after 4 hours.

Which inequality represents all the solutions of
9(4x-8) < 4(6x + 9)?

Answers

Answer:

x < 9

Step-by-step explanation:

Our original inequality:

[tex]9(4x-8) < 4(6x+9)[/tex]

Firstly, let's expand the brackets on both sides:

[tex]36x - 72 < 24x + 36[/tex]

Now, we add the 72 over to isolate the [tex]x[/tex]:

[tex]36x < 24x + 108[/tex]

Next, we take away the [tex]24x[/tex] to isolate the [tex]x[/tex]:

[tex]12x < 108[/tex]

Finally, we divide both sides by 12 to convert the [tex]12x[/tex] to [tex]x[/tex]:

[tex]x < 9[/tex]

This means our final answer is [tex]x < 9[/tex].

La siguiente operación 147.3 = 441 es una:
División b- Sustracción c- Multiplicación
plis necesito la respuesta ahora dare estrellas lo juro

Answers

La operación que representa 147.3 = 441 es dada por una multiplicación, por eso opción c es correcta.

¿Qué operación está representada por 147 . 3 = 441?

El resultado del producto entre 147 y 3 es de 441, por lo que se hace una operación de multiplicación.

Así, hay que la opción c es correcta.

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Select the correct answer.
Gas station A has posted a chart that shows the price of gasoline in terms of the number of gallons.

Answers

The correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.

What is an expression?

Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.

Here we have two pieces of information

Gas station A:-

3 gallons for $9.15

1 gallons for  $9.15 / 3 = $ 3.05

Gas station B:-

P = 3.08g

It means that station B is selling the gasoline at a higher price.

Therefore the correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.

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Hey can I have help with this question. An explanation would be great as I find things difficult to understand :)

Answers

Answer:

[tex](0, -\frac{15}{2} )[/tex]

Step-by-step explanation:

When a straight line crosses the y-axis, the point that touches it is called the y-intercept. We can find the y-intercept by plugging in zero as the value for 'x', as any x value on the y-axis is zero. So plugging in x = 0 into the equation '3x - 2y = 15', we get -2y = 15, so y = -15/2. The point would be [tex](0, -\frac{15}{2} )[/tex], as x = 0 when y = -15/2.

N
O O
What is the slope of the line represented by the equation y = --- 5x?
0-5
4 ~/m ~/m
+
O 5
O

Answers

Yup that’s it ^jjjjjjjjjjkkkkkkk

2(2x – 1) + 7 < 13 or –2x + 5≤-10

Answers

Answer:

2, 7.5

Step-by-step explanation:

2(2x - 1) + 7 < 13

4x - 2 + 7 < 1

4x + 5 < 13

4x < 8

x < 2

-2x + 5 ≤ -10

-2x ≤ -10 - 5

-2x ≤ -15

x ≤ -15 / -2

x ≤ 7.5

Change the decimal to a fraction. (Use the “/“ in your fraction.) 0.45454545….

Answers

The decimal: 0.4545...

Can be written in fraction form as 45/99.

How to write the number as a fraction?

Here we have the number:

N = 0.4545...

Notice that the repeating digits are two, 4 and 5.

Then we can multiply our number by 100 (same number of zeros as repeating digits) so we get:

100*0.4545... = 45.4545...

Now if we subtract the original number, we get:

45.4545... - 0.4545... = 45

This means that:

(100 - 1)*0.4545... = 99*0.4545... = 45

Then we can multiply and divide our number by 99, so we get:

[tex]0.4545... = 0.4545...\frac{99}{99} = \frac{45}{99}[/tex]

So the fraction is 45/99

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Find the vertex and focus of the
parabola:
x² + 14x-8y + 65 = 0

I can’t figure this out!!!

Answers

Answer:

[tex]\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}[/tex]

Step-by-step explanation:

Completing the square :

x² + 14x - 8y + 65 = 0

x² + 14x + 49 - 49 - 8y + 65 = 0

(x + 7)² - 8y + 16

(x + 7)² = 8y - 16

⇒ x = -7, y = 2 (Vertex)

Finding a :

⇒ x² = 4ay

⇒ (-7)² = 4(2)a

⇒ a = 49/8

Finding the focus :

⇒ (0, a)

⇒ (0, 49/8) (Focus)

For an each situation, it begin with the square field, measuring X centimetres by X centimetres. The dimensions of this square are to be changed. How do you write an expression for the area of the new square field, and then expand, and simplify? :/

A). The length of a side is being increased by 8 cm.
B). The length is being increased by 12 cm and the width is being decreased by 7 cm.

Answers

#A

New side

X+8

Area

(x+8)²x²+16x+64 cm²

#2

Now it has turned rectangle

Sides

x+12 and x-7

Area

(x+12)(x-7)

Answer:

A)  (x + 8)² cm² = (x² + 16x + 64)  cm²

B)  (x + 12)(x + 7) cm² = (x² + 19x + 84) cm²

Step-by-step explanation:

Formula

Area of a square = s²  (where s is the side length)

Given side length of square field:

x cm

⇒ Area of field = x² cm²

Part A

If the side length of the square field is increased by 8 cm then:

⇒ new side length = (x + 8) cm

Substitute the new side length into the formula for the area of a square:

Area of field = (x + 8)² cm²

Expand and simplify:

Area = (x + 8)²

Area = (x + 8)(x + 8)

Area = x(x + 8) + 8(x + 8)

Area = x² + 8x + 8x + 64

Area = (x² + 16x + 64)  cm²

Part B

If the side length of the square field is increased by 12 cm and the width is decreased by 7 cm then:

⇒ new side length a = (x + 12) cm

⇒ new side length b = (x - 7) cm

Substitute the side lengths into the formula for area of a square:

⇒ Area of a square = s × s

⇒ Area of a square = a × b

Area of the field = (x + 12)(x + 7) cm²

Expand and simplify:

⇒ Area = (x + 12)(x + 7)

⇒ Area = x(x + 7) + 12(x + 7)

⇒ Area = x² + 7x + 12x + 84

Area = (x² + 19x + 84) cm²

Given parallelogram ABCD and AB || CD, if mAB = -5 then mCD must be:
A)-5
B)
- 1
——
5

C) 5

D) 1

5

Answers

The slope of CD, which is parallel to AB must be: A. -5.

What is the Slope of Parallel Segments?

If two line segments are parallel to each other, their slope value (m) would be equal to each other.

Side AB and CD in the parallelogram are parallel segments, therefore, their slope (m) would be the same.

Slope (m) of AB = -5, therefore, the slope of CD must be: A. -5.

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find sizes of unknown angles​

Answers

Answer:

a=75

b=70

c=110

d=105

e=110

f=105

Step-by-step explanation:

John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.

Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?

w(w – 2) = 48
w(w + 2) = 48
2w(w – 2) = 48
2w(w + 2) = 48

Answers

The equation that could John solve to find w, the greatest width in centimeters he can use for the mosaic is option B: w(w + 2) = 48.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The mosaic to be formed is rectangular in shape.

Area of a rectangle = length x width

The length is longer than the width by 2,

So, length = w+2

Area of a rectangle = (w+2) x w

The correct equation is B: w(w + 2) = 48

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Answer: B

Step-by-step explanation:

cotpheta•sin2pheta=

1+cos2pheta
1+cospheta
1+sin2pheta ​

Answers

Answer:

Step-by-step explanation:

Did you mean.

[tex] = \cot( \theta) . \sin(2 \theta) [/tex]

[tex] = \frac{ \cos( \theta) }{ \sin( \theta) } .(2 \sin( \theta) \cos( \theta) )[/tex]

[tex] = \frac{2 \sin( \theta) \cos {}^{2} ( \theta) }{ \sin( \theta) } [/tex]

[tex] = 2 \cos {}^{2} ( \theta) [/tex]

[tex] = 2.(1 - \sin {}^{2} ( \theta) )[/tex]

[tex] = 2 - 2 \sin {}^{2} ( \theta) [/tex]

No option Solution.

5(b)
Joe has a bucket containing 1370cm³ of water measured to the nearest 10 cm³.
Joe Says
"If I tip my bucket of water in the cuboid container, it will never overflow"
Is Joe correct?
You must explain your answer

Answers

If the side length is greater than 11.11 cm then it will not overflow.

Otherwise, it will overflow.

If Joe tips the bucket of water in a cuboid container and the water is not overflowing then the cuboid container must be of volume greater than 1370 cm³.

We find the cube root of 1370 cm³.

[tex]\sqrt[3]{1370} \approx11.11[/tex]

Then the cuboid container should have a side of length greater than 11.11 cm.

Here the statement  "If I tip my bucket of water in the cuboid container, it will never overflow" is correct or wrong based on the information that the container has a side length lesser or greater than 11.11 cm.

If the side length is greater than 11.11 cm then it will not overflow.

Otherwise, it will overflow.

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Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given that the point-slope form is y+1=3/3(x-8)

Answers

The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

The given coordinate are (8, -1) and (2, -5).

What is the slope of an equation?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

The slope of the equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].

The standard form of an equation is Ax + By = C.

The given the point-slope form is [tex]y+1=\frac{2}{3} (x-8)[/tex].

Multiply each term by 3 of the equation.

[tex](y+1) \times3=\frac{2}{3} (x-8) \times3[/tex]

⇒3y + 3 = 2x - 16

Subtract 2x from both sides of a equation.

That is, -2x + 3y + 3 = - 16

Subtract 3 from both sides of a equation.

That is, -2x + 3y = - 19

Multiply each term by - 1 from both sides of an equation.

That is, 2x - 3y = 19

Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

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Mike has 21 pounds of tomatoes and 9 pounds of mixed peppers from his garden that he will use to make salsa and tomato sauce. The graph represents the system of equations shown.

A system of equations. x plus 5 y equals 21. x plus y equals 9.

The variable x represents the number of batches of salsa that can be made and y represents the number of batches of tomato sauce that can be made.

Answers

Answer:

x= 6 , y = 3

Step-by-step explanation:

x + 5y = 21

i am using trail and error method and i got the answer easily

the logic behind this is simple

the first equation is x + 5y = 21 so we can say that y  will be 5 x 1 , 5 x 2 , 5 x  3 , 5 x 4

first i did 5 x 4 = 20

x + 5 x 4 = 21

x= 1 but the equation x + y = 1 + 4 = 5  which is not equal to 9

second i tried with 5 x 3 =15

and the equation will be

x + 5 x 3 = 21

6 + 15 = 21

this time the second equation became true

x + y = 9

6 + 3 = 9

the no of pounds of salsa = 6

no of pounds of tomato = 3

Zippy company manufactured 10,000 units in december with a total product cost of $22,900 they had zero finished goods inventory at the start of december. in december zippy sold 7,796 units at a unit price of $5.54. period expenses were $4,723. what is the amount of zippy's gross profit (otherwise know as gross margin).? round any intermediate calculations to four decimal places

Answers

The amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.

Gross profit

Sales revenue $43,189.84

(7,796 units × $5.54)

Less Cost of goods sold $17,852.84

[($22,900/10,000)×7,796]

Gross profit $25,337

( $43,189.84-$17,852.84)

Therefore the amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.

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(This is an Edge question)

Question:
Which expression is equivalent to negative 3 minus 3 times a number minus 1 plus a number.
[tex] - 3 - 3x - 1 + x[/tex]


Answer Choices:
A.
[tex]2x - 4[/tex]

B.
[tex] - 2x + 4[/tex]

C.
[tex] - 2x - 4[/tex]

D.
[tex]4 - 2x[/tex]


I will verify the answer and give Brainlyest for fastest and most accurate answer and 15 pts.

Answers

Answer:

The answer is C. -2x -4

Step-by-step explanation:

Your given information.

-3 - 3x - 1 + x

Combine and simplify common numbers/variables.

(-3x + x) + (-3 - 1)

-2x - 4

3.5 decimals to mixed numbers

Answers

1 2/3
It’s one and two thirds written out

suppose your household income increased to $2,000.00 and your energy bill came from $180.00 how many percent of your household income is being spent on electricity​?​

Answers

hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა

⊱┈────────────────────────┈⊰

[tex]\large \bold {ANSWER}[/tex]

[tex]\implies \boxed{\underline{\huge{\tt{\orange{\: \: 9\% \: \: }}}}}[/tex]

9% of the family income is being spent to pay the energy bill.

[tex]\large \bold {SOLUTION}[/tex]

HOW TO FIND OUT THE PERCENTAGE?

If your income is now $2,000.00 and you have withdrawn $180.00 from the value, then we say that the $2,000.00 is equivalent to 100% of the value, that is, the total amount. And the amount that was withdrawn will be X because we still don't know how much percent is equivalent to $ 180.00 of this value.

To solve, we will use the simple rule of three like this:

[tex]\frac{2000}{180} = \frac{100}{x}[/tex]

With this we will multiply the denominator of one with the numerator of the other, being:

2000 * X and 180 * 100Where: 2000 * x is equal to 2000xAnd 180 * 100 is equal to 18,000

Knowing this, we will solve it this way:

2000x = 18,000

To start we will isolate the unknown(x) from the values taking the 2000 to the other side of the equality turning it into the denominator of 18,000.

[tex]x = \frac{18000}{2000}[/tex]

And to finish, we cut the 3 zeros of the numerator with the d 3 zeros of the denominator getting 18 / 2. Now it's just dividing.

[tex]\begin{gathered}x = \frac{18}{2} \\ \\ x = 9\end{gathered}[/tex]

We can conclude that the amount spent to pay the energy bill is equivalent to 9% of the family income.

PLEASE HELP!!! I will give brainliest pleasee help. each question has to be solved, there are no options for answers.

Answers

The intersecting secant theorem states the relationship between the two intersecting secants of the same circle. The given problems can be solved using the intersecting secant theorem.

What is Intersecting Secant Theorem?

When two line secants of a circle intersect each other outside the circle, the circle divides the secants into two segments such that the product of the outside segment and the length of the secant are equal to the product of the outside segment other secant and its length.

a(a+b)=c(c+d)

1.)

6(x+6) = 5(5+x+3)

6x + 36 = 25 + 5x + 15

x = 4

2.)

4(2x+4)=5(5+x)

8x + 16 = 25 + 5x

3x = 9

x = 3

3.)

8x(6x+8x) = 7(9+7)

8x(14x) = 112

112x² = 112

x = 1

4.)

(x+3)² = 16(x-3)

x² + 9 + 6x = 16x - 48

x² - 10x - 57 = 0

x = 14.0554

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For any positive numbers a, b, and d, with b 1,


A.
logb a logb d

B.
logb a + logb d

C.
d logb a
done

D.
logb a - logb d

Answers

Answer:

D

Step-by-step explanation:

using the rule of logarithms

log x - log y ⇔ log ( [tex]\frac{x}{y}[/tex] )

then

[tex]log_{b}[/tex] ( [tex]\frac{a}{d}[/tex] ) = [tex]log_{b}[/tex] a - [tex]log_{b}[/tex] d

Please help!!!!
A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 135 feet. The smallest path bordering the patch of grass measures 60 feet. The smallest angle formed by the paths measures 26°. What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest degree. Show all your work.

Answers

The measure of the largest angle of the triangular patch of grass is 81 degrees

Application of sine rule

In order to determine the measure of the largest angle, we will use the expression below;

[tex]\frac{60}{sin26^0} =\frac{135}{sinx^0}[/tex]

Cross multiply

135sin26 = 60sinx

sinx = 135sin26/60

sinx = 59.18/60
sinx = 0.986

x = 80.5 degrees

Hence the measure of the largest angle of the triangular patch of grass is 81 degrees

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red was rotated to form blue
describe the rotation

Answers

Red was rotated to form blue as the figure was turned in different directions.

What is rotation?

A rotation simply means a transformation that turns a figure about a fixed point called the center of rotation.

An object and its rotation are simply the same shape and size, but the figures may be turned in different directions. In this case, red was rotated to form blue.

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I need help please :3

Answers

Answer:

32ounces

Step-by-step explanation:

24/3=8pounds

8pounds=8x16=128ounces

but each 8 pounds is split into quarters so

8/4=2pounds=32ounces

32 ounces

24 divided by 3 is 8,
8 divided by 4 is 2,
So 2 times 16 is 32 ounces

what is the answr to -5(b + 1) = 8

Answers

[tex] - 5(b + 1) = 8 \\ - 5b - 5 = 8 \\ - 5b = 8 + 5 \\ - 5b = 13 \\ b = \frac{ - 13}{5} [/tex]

PLEASE GIVE BRAINLIEST

\\\///\\\///\\\///\\\///\\\///\\\///\\///\\\///\\\///\\\///\\\///\\\//\\//\\//\\//\\\///\\//\\\///\\\///\\\///\

                                      [tex]\Rsh[/tex] Hey! [tex]\Lsh[/tex]

[tex]\Rsh[/tex]Let's solve this! We can do this! [tex]\Lsh[/tex]

>>> First, let's multiply -5 by b and 1. Then we obtain

[tex]\pmb{-5b-5=8}[/tex].

>>> Now we add 5 to both sides.

[tex]\pmb{-5b=13}[/tex]

>>> And then, divide both sides by -5.

[tex]\pmb{b=-\dfrac{13}{5}}[/tex]

>>> That is the value of b.

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Hope the answer - and explanation - assisted you!

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Development refers to the pattern of continuity and change in human capabilities that occurs _____. Hi. how can i Find the *number* of terms of a finite geometric sequence?r= .75a= 40sum= 280 non homogeneous recurrence relation2fn - 6fn-1 = (n+1)(3^n) Solve for x......[tex]4x + 10 = 2x + 26[/tex] Woodrow Wilsons progressive platform was known as the Help me please!! Is for my finals!! ) Which of the following spices tastes hot? A. Coriander B. Black Pepper C. Turmeric D. Coriander-cumin Estimate the gravitational force of attraction between two people sitting side by side on a park bench. How does this force compare with the gravitational force exerted on each of them by the Earth when two cars arive at a four way stop which car must yield the right of way IMMIGRATIONHow did the United States respond politically and socially to the wave of immigration in the late 1800s?Use evidence from the cartoon and facts from the unit of study to support your answer. Respond in a CLEAR paragraph. A help desk can answer 120 calls per hour. The demand rate is 150 calls per hour. What are the cycle time (in minutes per call) and utilization of the call center? In 2005, an area vocational school had an enrollment of 325 men and 123 women. In 2006, there were 149 women. What was the percent increase of women students? Your final answer should be rounded to the nearest whole percent. Discuss how the research in this article shows how new technology and experimental methods can lead to changes in theories. A healthy husband and wife, ages 45 and 40 respectively, wish to start funding for retirement at age 65. What is the most appropriate time horizon for the portfolio can someone please help mee True OR False ------------------------x - 62 = 44, x = 106 How to graph -x^2-2x+6 What are the three computer components that hold a dangerous amounts of electricity? Even when its unplugged. What do you call the amount of three-dimensional space a form occupies? Which statement best explains how the symbol of the desert develops meaning in The Alchemist?It expresses the boy's fear that he has made a mistake.It inspires the boy to keep pushing forward.It reveals the boy's hopes and ambitions.It represents the struggles the boy will face.