Can you help me find x?

The parabola's conventional form is y^2=4ax, which results in a parabola with an axis parallel to the x-axis, a vertex at the origin, a focus at (a,0), and a directrix at (x=a).

Since a=2 in your example, y^2=4ax is the result. The y-axis serves as the parabola's axis. The directrix equation is y = -a, which is equivalent to y = -12. There is a parabola's vertex at (0,0).

You must be aware that a parabola's equation in a vertex form is y=a(xh)^2+k, where a stands for the equation's slope, in order to determine the focus of a parabola. We can deduce from the formula that the parabola's focus lies at (h, k+1/4a).

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Answer:

option 3 = 20w^5

Step-by-step explanation:

attached the solution, hope that helps ....

Answer:

max : 2, min : -2

Step-by-step explanation:

this question is kinda hard and brain-intensive but i think i am right

Answer:

max : 2, min : -2

Step-by-step explanation:

max : 2, min : -2

The expression 1.3H represents the relationship between the number of health points restored by Eiko's healing spell with and without the magic ring.

H represents the number of health points restored by the spell without the ring. The expression 0.3H represents the additional 30% increase in the power of the spell due to the magic ring, as the ring increases the spell's power by 30%.

Adding the two, H + 0.3H, gives us the total number of health points restored by the spell with the magic ring, which is equal to 1.3 times the number of health points restored by the spell without the ring.

So, when Eiko is wearing the magic ring, her healing spell restores 1.3 times as many health points as without the ring, represented by the expression 1.3H.

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The area of the composite figure is 124 square miles.

Composite figures are the result of uniting two or more geometric figures, in this case, we need to determine the area of a composite figure that results from the union of two right triangles and two rectangles, whose area formulas are described below:

Rectangle

A = w · l

Right triangle

A = 0.5 · w · l

Where:

Now we proceed to calculate the area of the composite figure:

A = 0.5 · (6 mi) · (18 mi) + 0.5 · (8 mi) · (3 mi) + (6 mi) · (5 mi) + (4 mi) · (7 mi)

A = 124 mi²

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The length of the longer base of the trapezoid is TP = 13 units

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the trapezoid be A = 100 units²

Now , the length of the longer base b = 32 units

The length of the shorter base a = 8 units

Let the height of the trapezium be = h

Area of Trapezoid = ( ( a + b ) h ) / 2

Substituting the values in the equation , we get

100 = ( 32 + 8 ) x h / 2

200 = 40h

Divide by 40 on both sides of the equation , we get

h = 5 units

Now , the height be PE , where E lies 12 units from T

Now , from the Pythagoras equation , we get

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

TP² = PE² + TE² , where PE is the height of the triangle

TP² = 5² + 12²

TP² = 169

Taking square roots on both sides of the equation , we get

TP = 13 units

Hence , the length of the trapezium is 13 units

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The angle between lines 2x 3y =- Z is 90°

We will simplify the given equation of lines in the standard form of x/a=y/b=z/c

where a, b and c are the direction ratios of the line.

We will calculate the angle between these lines using the formula:

[tex]cos\alpha =\frac{a_{1}a_2 +b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2} }[/tex]

we are given two lines as 2x = 3y = – z and 6x = -y = -4z

We can write them in standard form xa=yb=zc

as:

For 2x = 3y = – z ⇒x/1/2=y/1/3=z/−1/4

Comparing this equation with the standard equation, we get the direction ratios of this line:

a₁= 1/2

b₁=1/3

c₁ = -1

For 6x = -y = -4z ⇒x/1/6=y−1=z/−1/4

Comparing this equation with the standard equation, we get the direction ratios of this line:

a₂= 1/6, b₂= -1, c₂= −1/4

Now, putting these values of a₁, a₂, b₁, b₂, c₁, and c₂

in the equation of cosα, we get

[tex]cos\alpha =\frac{a_{1}a_2 +b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2} }[/tex]

[tex]cos\alpha =\frac{\frac{1}{2} *\frac{1}{6} +\frac{1}{3} *(-1)+(-1)\frac{(-1)}{4} }{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } }[/tex]

[tex]cos\alpha =\frac{\frac{1}{12} -\frac{1}{3} +\frac{1}{4} }{{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } } }[/tex]

[tex]cos\alpha =\frac{\frac{1}{12} -\frac{1}{12} }{{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } } }[/tex]

cosα=0°

cos⁻¹(cosα)=cos⁻¹(0)

α=90°

Therefore, the angle between the lines 2x = 3y = – z and 6x = -y = -4z is 90°

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Yes, the given set  A={x:x²=4 and 3x=9(0)}  is an empty set.

Given the set:

A={x:x²=4 and 3x=9(0)}

Consider the equation:

x²=4

Solve for x:

x²=4⇒x=±2

Consider the other equation:

3x = 9

Solve for x:

3x = 9⇒x = 3

Because the square of the set element should be 4, the element should be 2 or -2, but 2 or -2 multiplied by 3 gets 6 or -6, which is not equal to 9. As a result, no element exists that can meet both conditions.

The value of ‘x’ is not same in both cases, so this is a null set.

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The cost of lower and upper level seats are $28 and $18 each, respectively.

Let x be the cost of the lower level seats

We know that the upper level seats are $10 cheaper, so their cost can be expressed as the algebraic expression x - 10.

We also know that the total number of seats is 8000, and 3000 of them are upper level seats, and a sellout has a total revenue of $194 000.

So we can set up the following algebraic equation:

(8000 - 3000)x + 3000(x - 10) = 194 000

Simplify the equation and solve for the value of x.

5000x + 3000x - 30 000 = 194 000

8000x = 224 000

x = 28

So, the cost of the lower section seats is $28 and the cost of the upper level seats is $18.

The problem seems incomplete, it must have been

"In a small hockey arena with 8000 seats there are 3000 upper level seats which are $10 cheaper than the remaining lower section seats. For a sellout to a Memorial Cup game the total revenue was $194 000. Find the cost of each type of ticket."

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For seven hours of landscaping, Company B would be less expensive than Company A.

An equation is defined as any pair of expressions that both contain the equal sign.

Because of this, Company charges $35 per hour and a $250 equipment fee, compared to Company B's $25 per hour and $300 equipment fee.

For t hours of landscaping, Company A will bill the following:

A = 35t + 250 (1) (1)

In a similar vein, Company B bills the following sum for t hours of landscaping:

B = 25t + 300 (2) (2)

Solve equation (1) now with t = 7:

A = 35 (7) + 250

A = 245 + 250

A = 495

So, for 7 hours of landscaping, business A would bill $495.

Similarly, when equation (2) is resolved for t = 7,

B = 25(7) + 300

B = 175 + 30

B = 475

So, for 7 hours of gardening, business B would bill $475.

Therefore, for seven hours of landscaping, Company B would be less expensive than Company A.

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Step-by-step explanation:

domain : the interval or set of all valid x-values.

range : the interval or set of all valid y-values (function result values).

A is correct

theoretically all real numbers are valid as x. but for this application of the function only non-negative integer values make sense (e.g. half a cycle does not make any sense).

C is correct

via A we are allowing all real numbers to be valid input values, so, we have to allow also all real numbers to be valid output (function result) values.

D is correct

the y-intercept means the y-value, when the function curve intersects the y-axis.

this is only possible, when x = 0.

5⁰ = 1

as any x⁰ = 1

F is correct

the bigger x, the bigger 5^x.

and the smaller x, the closer y, the function result, gets to 0. particularly, when we allow negative input values (as we said in A).

The rise and run of the line may be determined using two of its points, and the slope can be calculated.

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The correct matches are: A. Slope = 1.56, B. Slope = 0.86, C. Slope = 3

D. Slope = -5.61, E. Slope = -0.44  

Given two line-side coordinates, use the slope formula to determine the slope of the line. Slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations.

Here are the correct matches of each pair of points to the slope of the line that joins them:

A. (9, 10) and (7.2) - Slope = (10 - 7.2)/(9 - 7.2) = 2.8/1.8 = 1.56

B. (-8,-11) and (-1,-5) - Slope = (-5 - (-11))/(-1 - (-8)) = 6/7 = 0.86

C. (5,-6) and (2,3) - Slope = (3 - (-6))/(2 - 5) = 9/3 = 3

D. (6.3) and (5,-1) - Slope = (-1 - 6.3)/(5 - 6.3) = -7.3/1.3 = -5.61

E. (4,7) and (6.2) - Slope = (6.2 - 7)/(4 - 6.2) = -0.8/1.8 = -0.44

So, the correct matches are:

A. Slope = 1.56

B. Slope = 0.86

C. Slope = 3

D. Slope = -5.61

E. Slope = -0.44      

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The number of laps that Noriko needs to run is given as follows:

6 laps.

The number of laps that Noriko needs to run is obtained applying the proportions in the context of this problem.

The length of one lap is given as follows:

1/6 miles.

Hence the number of laps that Noriko needs to run for a total of one mile is obtained dividing one mile by the length of a single lap, as follows:

1/(1/6) = 6 x 1 = 6 laps.

Each lap around the school's track is of 1/6 mi.

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First and fourth options are in dilation  that is an enlargement  as k>1 for enlargement in the expression  (kx, ky).

Dilation is the enlarging or shrinking of a fine element( a point on a match grid, polygon, line member) using a specific scale factor. Dilation is one of the five major metamorphoses ingeometry.When a dilation in the match aeroplane has the origin as the center of dilation, you can find points on the dilated image by multiplying the x- and y- equals of the original figure by the scale factor. For scale factor k, the algebraic representation of the dilation is( x, y) →( kx, ky)

The introductory formula to find the scale factor of a ballooned figure is Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

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The complete question is :

Which of the following algebraic rules that represent a dilation that is an enlargement?

1  (1 1/3 x, 1 1/3y)

2 - (1/2 x, 1/2y)

3 - ( 0.1 x, 0.1 y)

4  (3 1/10 x, 3 1/10y)

Answer:

Step-by-step explanation:

the degree of a polynomial is determined by the biggest exponent. For example, in this equation: 6x^4+3x^3+3x^2+2x+1, you can see that the biggest exponent is the 4, so it would be a polynomial of the 4th degree.

The number is one more than 39 is 40

Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number.

It is a mathematical term used to compare two quantities and to establish a relationship between two quantities in which one term is greater than the other. The terms greater than, less than, and equal are used to compare two numbers, amounts, or amounts. Each term has a separate letter. B. "greater than" is represented by ">".

According to the Question:

To better understand this question,

It can be expressed as 1 more than 39, 1 more than 39, 39 plus 1.

Thus,

1 more than 39 is the same as 39 plus 1. So the answer for 1 greater than 39 is calculated as:

Therefore,

1 + 39 = 40.

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The water level will increase by 0.00167 inches, so the correct option is A.

We know that Lisa spilled a volume of 1 quart of water on its pool, and the dimensions of the pool are:

12ft = 12*(12 inches) = 144 inches

20ft = 20*(12 inches) = 240 inches.

And we know that:

1 quart = 57.75 in³

Then if the level change is H, then then we can write the equation for the volumes:

1 quart = volume of increase in the pool

1 quart = (144 in)*(240 in)*H

57.75 in³ =  (144 in)*(240 in)*H

H = (57.75 in³)/( (144 in)*(240 in))

H = 0.00167 in

So the correct option is A.

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They spend $52 in total for the movie ticket and popcorn.

The substitution method is a simple way to solve a system of linear equations algebraically and find the solutions of the variables.

Given that,

Tickets (t) = $8

Popcorn & Soda (s)= $5

Friends = 4

Since all friends bought the same thing the equation will be set as

4(t +s) = m OR 4t +4s = m

Using substitution, you plug each variable

t = 8 and s = 5

4((8) + (5)) = m

4(8+5) = m => 4(13) =m => 52=m

OR

4(8) + 4(5) = m => 32 + 20 = m =>

52 =m

Thus, They spend $52 in total for the movie ticket and popcorn.

Complete question: Four friends went to the movies each ticket cost $8 and each person bought popcorn and a soda for $5 how much did they spend in all? let m stand for the amount of money spent

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The segment addition postulate holds true in this example.

The segment addition postulate states that if two line segments have the same end points, then the two segments are congruent. This postulate can be expressed using the following formula: AB + BC = AC. This formula states that the sum of the lengths of two segments with the same endpoints (AB and BC) is equal to the length of the third segment (AC). To illustrate this rule, imagine a line segment AB with a length of 5 units. If we add another line segment BC to the same line segment, with a length of 3 units, then the combined length of the two segments (AB + BC) would be 8 units, which is also the length of the third segment (AC). Therefore, the segment addition postulate holds true in this example.

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Complete question:

Is the Segment Addition Postulate true?

The lateral surface area of a cylinder is 1110.8 cm².

Consider a very thin cross section of a cylinder whose thickness is [dh] {differential or very small value}. The volume of this cross section would be -

dV = πr² dh

For complete cylinder -

∫dV = πr² ∫dh

[V - 0] =  πr² [h - 0]

V =  πr²h

Given are the dimensions of a cylinder are shown in the diagram.

We can write the lateral surface area as -

LSA = 2πrh

LSA = 2 x 3.14 x 8.8 x 20.1

LSA = 1110.8  square centimeters.

Therefore, the lateral surface area of a cylinder is 1110.8 cm².

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Answer:

[tex]\textsf{1)} \quad 4.1875[/tex]

[tex]\textsf{2)} \quad \dfrac{1}{2}x^{4}-x^{3}+x^{2}-3x+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration:

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

The area between a curve and the x-axis can be found using definite integration.  The definite integral of f(x) with respect to x between the limits x = a and x = b:

[tex]\displaystyle \int^b_a \text{f}(x)\; \text{d}x=\left[\text{g}(x)\right]^b_a=\text{g}(b)-\text{g}(a)[/tex]

where a is the lower limit and b is the upper limit.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}\left(+\text{C}\right)$\end{minipage}}[/tex]

Given function:

[tex]\text{f}(x)=\dfrac{1}{4}x^3+\dfrac{1}{6}x+1[/tex]

From inspection of the given graph:

Therefore:

[tex]\begin{aligned}\displaystyle\int^2_{-1}\left(\dfrac{1}{4}x^3+\dfrac{1}{6}x+1\right)\;\text{d}x&=\left[\dfrac{1}{4\cdot4}x^{3+1}+\dfrac{1}{6\cdot 2}x^{1+1}+x\right]^2_{-1}\\\\&=\left[\dfrac{1}{16}x^4+\dfrac{1}{12}x^2+x\right]^2_{-1}\\\\&=\left(\dfrac{1}{16}(2)^{4}+\dfrac{1}{12}(2)^2+(2) \right)-\left(\dfrac{1}{16}(-1)^4+\dfrac{1}{12}(-1)^2+(-1)\right)\\\\&=\left(1+\dfrac{1}{3}+2\right)-\left(\dfrac{1}{16}+\dfrac{1}{12}-1\right)\\\\&=\dfrac{10}{3}+\dfrac{41}{48}\\\\&=\dfrac{67}{16}\\\\&=4.1875\end{aligned}[/tex]

[tex]\begin{aligned}\displaystyle \displaystyle \int (x^2+1)(2x-3)\; \text{d}x&=\displaystyle \int \left(2x^3-3x^2+2x-3\right)\; \text{d}x\\\\&=\dfrac{2}{4}x^{3+1}-\dfrac{3}{3}x^{2+1}+\dfrac{2}{2}x^{1+1}-3x+\text{C}\\\\&=\dfrac{1}{2}x^{4}-x^{3}+x^{2}-3x+\text{C}\end{aligned}[/tex]

The total length of the two boards is 9 inches.

An inch can be defined as a unit of length in the customary system of measurement. Length in inches is either represented by in or ''. For instance, 5 inches can be written as 16 in or 16''. of a foot.

as given, a carpenter has a board that is three and one fourth inches long

i.e. the carpenter has a board that is 3.25 inches long.

and a second board to the end that is five and three fourth inches long

i.e. another board that is 5.75 inches long.

When joined together, the total length of the two boards is 3.25 inches + 5.75 inches = 9 inches.

Therefore, the total length of the two boards is 9 inches.

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A function's range is the set of values which that function can take. This represents the collection of values that the function returns after we enter an x value.

The domain of a procedure is the set of values that can be plugged into it. This set contains the x values in a function like f. (x).

A function's range is indeed a set of integers that it can generate.

In certain terms, this is the set of y-values obtained by plugging all possible x-values into the function. The domain is the set of all potential x-values.

A function in mathematics is a defined interaction between this and an autonomous variable (x) and a completely reliant variable (y).

A function's range refers to all of the potential values for y. The method used to calculate a function's range is y = f. (x).

The distinction between the lowest and highest numbers is called the range. When there are extraordinarily high or low values, the range can be deceiving.

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According to the solving the probability  of the spinner and the dice

A.  = 1 / 2.

B.  = 1/6.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures as well as the risk of health impacts are related.

for the spinner

total number of division = 4

the pink colored  sections = 2

Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.

Probability = 2 / 4.

Probability = 1 / 2.

for the Dice

total number of division = 6

the pink colored  sections = 1

Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.

Probability = 1/6.

Probability = 1/6.

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The exponential equation that describes the monster's growth, in meters, is given as follows:

y = 0.02(5)^x.

The height of the monster after 3.7 days is given as follows:

19.3 meters.

An exponential function is defined as follows:

y = ab^x.

For which the parameters are given as follows:

Considering the initial height of the monster and the fact that the height is multiplied by five each day, the function is given as follows:

y = 0.02(5)^x.

Hence the height after 3.7 days is given as follows:

y = 0.05(5)^3.7

y = 19.3 meters.

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The percent salinity of the resulting mixture is given as follows:

2.63%.

The percent salinity of the resulting mixture is obtained applying the proportions in the context of the problem.

The proportions are obtained applying the weighed mean, as follows:

0 x 1000 + 0.035 x 3000 = 105 gallons of salt.

Considering that the total mixture is of 1000 + 3000 = 4000 gallons, the percentage of salt in the resulting mixture is given as follows:

105/4000 x 100% = 2.63%.

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A solution set in of a linear equation system mathematics  to the set of values correctly solve such system which inputted into a system of equations correctly .

The main steps to follow  calculating solution sets for a  linear equations of system

first step is to Convert the  system into a matrix equation

secondly Rewrite  matrix equation into  an augmented matrix

next step is Computing the reduced echelon form of the augmented matrix by use of Gaussian elimination processes

after that The reduced echelon form of the matrix will provide the values for the unknown variables,

using these solutions to writing down the parametric vector equation form that contain the complete set of solutions for the system.

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The product of 4 and 0 is zero.

We know that a product is an operation where two or more numbers are multiplied together to get a single result.

In case of small numbers a multiplication is considered repeated addition, and we can solve simple multiplication problems by adding repeatedly.

Generally, the types of multiplication method : addition method, long multiplication, grid method, drawing lines and by splitting two digit numbers into Tens and Ones

We know that if we multiply any non-zero real number by zero then the result / product is always 0.

This property of multiplication is called as the Zero property of multiplication.

So, the product of 4 and 0 is always zero.

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The amount on line 10 (total payments and credits) must be equal to the amount on line 11 (amount you owe) which is C: $4184.

How to calculate difference?

The difference is a mathematical operation used to find the amount by which one number is greater or smaller than another number. It is calculated by subtracting the smaller number from the larger number. The difference can be represented by the symbol "-" or the word "minus"

The dollar amount that could be on line 10 if $4184 is on line 11 and the taxpayer will neither receive a refund nor owe the IRS is $4184.

Line 10 on the 1040EZ form is for the "Total payments and credits" which is the sum of all payments made throughout the year, including any tax payments, estimated tax payments, and any credits the taxpayer is entitled to.

Line 11 is for the "Amount you owe" which is the difference between the total tax liability (calculated on the form) and the total payments and credits.

If the taxpayer will neither receive a refund nor owe the IRS, it means that the total payments and credits are equal to the total tax liability.

Hence, the amount on line 10 (total payments and credits) must be equal to the amount on line 11 (amount you owe) which is $4184.

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