Find the value of x. Then tell whether the side lengths for a pythagorean triple

The brace measures 50 inches in length.

The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equals the sum of the squares on the legs of the triangle, a2 + b2 = c2.

The other two sides of the picture frame are its length and width. We thus have:

Length of the hypotenuse (brace)² = Length² of the picture frame + Width² of the picture frame

Let's enter the picture frame's specified dimensions:

Length of the brace² = 30² + 40²

Length of the brace² = 900 + 1600

Length of the brace² = 2500

Taking the square root of both sides, we get:

Length of the brace = √(2500)

Length of the brace = 50

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Answer:

Since alternative angles are equal then

Answer:

[tex]\boxed {\left(-1, -\dfrac{3}{7}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{1}{2}\left|x\:+\:1\right|-\frac{3}{7}}[/tex]

[tex]\boxed{\left(5,\:\frac{2}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{3}{5}\left|x\:-\:5\right|+\:\frac{2}{3}}[/tex]

[tex]\boxed{\left(0,\:-\frac{4}{5}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{1}{2}\left|x\right|\:-\:\frac{4}{5}}[/tex]

[tex]\boxed{\left(\frac{2}{5},\:\frac{5}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{3}{2}\left|x-\frac{2}{5}\right|+\frac{5}{3}}[/tex]

Step-by-step explanation:

The vertex of an absolute function
y = f(x) = a|x - b| + c occurs at x - b = 0 or when x = b

Plugging this  into the original equation will give the value for f(b) which will be f(b) = 0 + c which will be the y-value of the vertex

[tex]\text{Vertex of } f(x) = \dfrac{3}{5} |x - 5| + \dfrac{2}{3}\\\\ \longrightarrow x = 5, y = \dfrac{2}{3} \\\\\longrightarrow \left(5, \dfrac{2}{3} \right)[/tex]

You can do the others in a similar manner.

Here it is easier because the constant in f(x) corresponds to the y-coordinate of the vertex and they are different in the answer choices

The amount of time needed for this capital to triple would be 50 months, the letter "d" being correct. We arrive at this result using simple interest.

Simple interest is a type of financial calculation that is used to calculate the amount of interest on borrowed or invested capital for a given period of time.

In order to find the amount of time required for the principal to be equal to three times the redemption, we have to note that the amount will be equal to three times the principal, using this information in the formula. Calculating, we have:

M = C * (1 + i * t)

3C = C * (1 + 0.04t)

3 = 1 + 0.04t

0.04t = 3 - 1

0.04t = 2

t = 2/0.04

t = 50

On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.

Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. The interest rate on the loan is known as this percentage.

here,

we have

P = 1360;

R = 5.4 ;

T = 12

so, we get,

SI = 1360 X 5.4 X 12 /100

SI =88128/100

= 881.28

Hence, On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.

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Felicia swims 0.43 miles, walks 0.0057 miles and runs 0.57 miles. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often known as "arithmetic operations," are said to adequately describe all real numbers. The mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.

We are given that she swims 15 laps in a pool where each lap is 50 yards.

By using arithmetic operations, we get

Total yards = 15 * 50 = 750 yard

We know that 1 mile = 1760 yards

So,

750 yards = 0.43 miles

She walks 30 feet.

We know that 1 mile = 5280 feet

So,

30 feet = 0.0057 miles

She runs 5 laps around an indoor track that is 600 feet long.

So, total feet she ran = 5 * 600 = 3000 feet

We know that 1 mile = 5280 feet

So,

3000 feet = 0.57 miles

Hence, she swims 0.43 miles, walks 0.0057 miles and runs 0.57 miles.

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The answer to the 1st power mark would be 36 if the 2nd power will be assumed as 3.

What is Power?

How many times a number should be multiplied depends on its power (or exponent).

It appears as a little number above and to the right of the basic number.

So according to the question,

                          3ˣ x ?⁴ = 9²⁰

                           3ˣ  x 3⁴ = 9²⁰(let 2nd variable be 3)

                             3ˣ x 3⁴ = 3²⁰(a^m x a^n=a^(m+n))

                             3⁽ˣ⁺4⁾ = 3²⁰

             So if bases equal powers get equal,

                              X+4=40

                                X=36

The above problem can only be proceeded as assumption because two variables cannot be obtained through one equation.

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It would take approximately 115.38 minutes to drive 125 miles at a rate of 65 miles/hour.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given that, the speed or rate is  65 miles/1 hr, how many minutes will it take to drive 125 miles.

First, we need to find the time it takes to travel 125 miles at a rate of 65 miles/hour.

We can use the formula:

Speed = Distance ÷ time.

time = distance / rate

time = 125 miles / 65 miles/hour

time = 25/13 hours

Now we can convert hours to minutes by multiplying by 60:

= 25/13 hours × 60 minutes/hour

= 115.38 minutes

Therefore, the required time is approximately 115.38 minutes.

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Answer:

12.29 I thin

Step-by-step explanation:

The monthly periodic interest rate is 0.01%.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

APR=14.75%

Now,

The monthly periodic interest rate is the annual interest rate divided by 12 months. According to 1, the formula is:

r = (1 + i/m)^(m/n) - 1

Where:

r = periodic interest rate

i = nominal annual rate

m = number of compounding periods per year

n = number of payments per year

In this case, i = 14.75%, m = 12 and n = 12. Plugging these values into the formula, we get:

r = (1 + 0.1475/12)^(12/12) - 1

r = (1 + 0.012292) - 1

r = 0.012292 or 1.23%

Therefore, by the given APR the interest rate will be 0.01%, rounded to the nearest hundredth of a percent.

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The volume of the capsule is [tex]3052.08 mm^3[/tex]

What is volume of the hemisphere ?

The formula for the volume of a hemisphere is [tex]V = (2/3)\pi r^3[/tex], where r is the radius of the hemisphere.

The volume of a hemisphere is half of the volume of a full sphere with the same radius. This is because a sphere can be divided into two hemispheres of equal size. Therefore, we can use this formula to find the volume of a hemisphere:

[tex]V = (1/2) (4/3)\pi r^3[/tex]

Simplifying this expression, we get:

[tex]V = (2/3)\pi r^3[/tex]

So, the volume of a hemisphere is [tex](2/3)\pi r^3[/tex].

According to the question:
To find the volume of a capsule, we need to break it down into two parts: a cylinder and two hemispherical ends.

The formula for the volume of a cylinder is[tex]Vcylinder = \pi r^2h[/tex], where r is the radius of the cylinder and h is its height.

The formula for the volume of a sphere (or hemisphere) is[tex]Vsphere = (4/3)\pi r^3.[/tex]

Since the capsule is made up of two hemispheres and a cylinder, the total volume of the capsule is the sum of the volumes of these three parts:

[tex]Vcapsule = 2Vsphere + Vcylinder[/tex]

First, let's calculate the volume of the cylinder. We are given that the radius is 3mm and the height is 100mm, so we have:

[tex]Vcylinder = \pi r^2h = 3.14 x 3^2 x 100 = 2826 mm^3[/tex]

Next, let's calculate the volume of the hemispheres. Since the capsule has a radius of 3mm, each hemisphere has a radius of 3mm. So, we have:

[tex]Vsphere = (4/3)\pi r^3 = (4/3) ( 3.14) (3^3 )= 113.04 mm^3[/tex]

Finally, we can calculate the total volume of the capsule by adding the volume of the cylinder and the two hemispheres:

[tex]Vcapsule = 2Vsphere + Vcylinder = 2 *113.04 + 2826 = 3052.08 mm^3[/tex]

Therefore, the volume of the capsule is [tex]3052.08 mm^3[/tex].

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Answer:

you need to learn yo stuff

Step-by-step explanation:

bye

Answer:

Mean is 5.5 and Median is 6.5

Answer:

Z(1.16)

Step-by-step explanation:

Let's start by expressing "Z increased by 16%" using algebra.

Let Z be the original value of some quantity.

To increase Z by 16%, we need to add 16% of Z to Z:

Z + 0.16Z

Simplifying this expression by factoring out Z, we get:

Z(1 + 0.16)

Combining like terms, we have:

Z(1.16)

Therefore, "Z increased by 16%" can be expressed algebraically as:

Z increased by 16% = Z(1.16)

The probability that a randomly selected person actually went on holiday that year is 0.727

Out of the 55 adults surveyed, 25 went abroad and 15 went on holiday in the UK.

Therefore, the total number of people who went on holiday is 25 + 15 = 40

The probability of selecting a person who went on holiday is the number of people who went on holiday divided by the total number of people surveyed:

P(went on holiday) = 40/55

Simplifying the fraction, we get:

P(went on holiday) = 8/11

Rounding to three decimals, we get:

P(went on holiday) = 0.727

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60 adult tickets and 45 children tickets were sold.

Let's use algebra to solve the problem:

Let x be the number of adult tickets sold.

Let y be the number of children tickets sold.

From the problem, we know that:

x + y = 105 (total tickets sold)

10x + 6y = 870 (total amount raised)

We can solve this system of equations by using elimination:

Multiply the first equation by 6: 6x + 6y = 630

Subtract the second equation from the first: 4x = 240

Solve for x: x = 60

Now we can use x to find y:

x + y = 105

60 + y = 105

y = 45

Therefore, 60 adult tickets and 45 children tickets were sold.

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The greatest expected value of 1.2.

a) We multiply the value of each potential outcome by its likelihood, then add the resulting products to determine the expected value at each node.

Beginning with the first node on the right, we have:

"Invest" should return 0.7(2) + 0.3(-2) = 1.2.

Don't invest has an anticipated value of 0.5(0) + 0.5(1.5) = 0.75.

The centre node is next:

"Develop" should be expected to have a value of 0.6(1.2) + 0.4(0.75) = 1.05

"Do not develop" should have a value of 0.4(0) + 0.6(0) = 0.

Lastly, at the node on the left:

Market research should be worth 0.5(1.05) + 0.5(0) = 0.525.

In light of this, the anticipated value at each node is:

Spend: 1.2

1.05 Development

Market research: 0.525

b) Since "Invest" has the highest expected value of 1.2, it is the best course of action.

c) If they are looking for at least $1.2M, "Invest" is still the best course of action because it has the greatest expected value of 1.2, which is already above the desired level.

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Answer:

The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.

In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:

The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.

The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.

The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.

Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).

The solution is B. [tex]y = 200x + 100[/tex] is a linear equation with a slope-intercept form.

When a function is displayed in a graph, a linear function makes a straight line, but a nonlinear function, which is bent in some way, does not. Whereas the slopes of a non - linear function is changing constantly, the slopes of a linear model remains constant.

The graph of a linear function is a direct line. One regression coefficient and one predictor variables make up a linear function. The variables that are both independent and dependent are X and Y, respectively. The y interception, often known as the constant term a.

The slope-intercept form of a linear equation is [tex]y = mx + b[/tex], where m is the slope and b is the y-intercept. Using the given values, we have:

slope [tex]= 200[/tex]

[tex]y-[/tex]intercept [tex]= 100[/tex]

So, the equation of the linear relationship is:

[tex]y = 200x + 100[/tex]

Therefore, the answer is B. [tex]y = 200x + 100[/tex].

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[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}[/tex]

Answer: Ace has 8 apples Christi has 4 and Pudge has 24

Step-by-step explanation:

Ace has 2 twice as much as Christi has, and 4 x 2 is 8. Pudge has 3 times more than Ace has and 8 x 3 is 24. Pudge has 12 more than Christi and Ace combined. 8 + 4 = 12. 12 + 12 = 24. I hope I explained it right.

Answer:

Step-by-step explanation:

sto p cheating ur too bad

(btw its 1d * 4r pi / 28)

Answer: 50% decrease

Step-by-step explanation:

50% of 310 = 155

310-155=155

50% decrease :)

ANSWER: 50% decrease

SOLUTION:

50% of 310 = 155

310-155=155

So in all the answer is.......

50% decrease  :)))))

-XOXOXO:)

In the unitary method,

a) For 75km we need = 15 l

b) cost of 45m cloth is  Rs 564.75

c)  cost of 75 shirts is Rs 16875.

What is the unitary method?

The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.

a) Here using unitary method , we need to find petrol for 1 km.

To travel 125 km we need 25 l pertrol. Then,

for to travel 1 km = [tex]\frac{25}{125} =\frac{1}{5} = 0.2 l[/tex]

Then to travel 75km we need = 0.2×75 = 15 l.

b) Cost of 32m cloth = Rs. 401.60

Then cost of 1m cloth is = [tex]\frac{401.60}{32}=Rs 12.55[/tex]

Now cost of 45m cloth is = 12.55×45 = Rs 564.75

c) Cost of 5 shirts = Rs 1125

Then cost of 1 shirt = [tex]\frac{1125}{5}=Rs 225[/tex]

Now cost of 75 shirts = [tex]225\times75[/tex] = Rs 16875.

Hence using unitary method the answers are,

a) For 75km we need = 15 l

b) cost of 45m cloth is  Rs 564.75

c)  cost of 75 shirts is Rs 16875.

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The perimeter is 14 x 6 = 84 inches .The area is (1/4) x 14 x 6²x cot(π/14) = 153.94 square inches.

Perimeter is a measurement of the total length of the boundary of a two-dimensional shape, such as a polygon or a circle. It is the distance around the outside of a shape, and is usually measured in units such as centimeters, meters, or feet.

Area is a measurement of the amount of space enclosed by a two-dimensional shape, such as a polygon or a circle. It is usually measured in square units such as square centimeters, square meters, or square feet.

In the given question,

We can use the following formulas to find the measure of one interior angle, the perimeter, and the area of a regular polygon:

The measure of one interior angle of a regular polygon with n sides is given by:

(n-2) x 180 / n degrees.

The perimeter of a regular polygon with n sides and side length s is given by: P = n x s.

The area of a regular polygon with n sides and side length s is given by: A = (1/4) x n x s² x cot(π/n), where cot is the cotangent function.

Given that the polygon has 14 sides and one side is equal to 6 inches, we have:

The measure of one interior angle is (14-2) x 180 / 14 = 154.29 degrees (rounded to the nearest whole degree).

The perimeter is 14 x 6 = 84 inches (rounded to the nearest whole number).

The area is (1/4) x 14 x 6² x cot(π/14) = 153.94 square inches (rounded to the nearest hundredths place).

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The absolute value function as a piecewise function f(x) = |- x² - 8x - 7| is

f(x) = { - (x² + 8x + 7) , x ≤ -7 or x ≥ -1    

        { x² + 8x + 7 , -7 < x < -1

What is meant by absolute value?

Absolute value is a mathematical function that gives the distance of a number from zero on a number line. It is denoted by two vertical bars enclosing the number and always returns a non-negative value.

What is meant by piecewise function?

A piecewise function is a function that is defined by different expressions or rules on different parts or intervals of its domain. The domain is divided into pieces, and each piece has its own expression or rule.

According to the given information

When x² + 8x + 7 ≥ 0, we have:

f(x) = |-(x² + 8x + 7)| = -(x² + 8x + 7)

When x² + 8x + 7 < 0, we have:

f(x) = |x² + 8x + 7| = x² + 8x + 7

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The specified central angle is 170 degrees since the figure is 17/36 of a full circle.

A central angle is an angle with endpoints on the perimeter and a vertex in the centre of a circle. An arc is defined by the angle in the centre of a circle.

Since the figure represents 17/36 of a full circle, the central angle that it subtends is also equal to 17/36 of 360 degrees (the measure of a full circle).

We can calculate this as follows:

Central angle = (17/36) x 360 degrees

Central angle = 17 x 10 degrees

Central angle = 170 degrees

Therefore, the measure of the marked central angle is 170 degrees.

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Answer:

Step-by-step explanation:

To find:-

Answer:-

As we know that the measure of complete angle about any point is 360° = 2π rad .

Also we are given that the given circle is 17/36 of full circle. So the angle substended too be will be equal to 17/36 of the complete angle.

So that , we have;

==> Angle = 17/36 * 360°

==> Angle = 170°

Hence the value of central angle is 170° .

The probability of selecting an even integer is 1/2 or 0.5.

What exactly is probability?

Probability is a measure of an event's possibility or chance of occurring. It is a number between 0 and 1, with 0 indicating that the occurrence is improbable and 1 indicating that the event is unavoidable. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide variety of fields, including mathematics, statistics, economics, physics, engineering, and social sciences, to make predictions and informed decisions.

Now,

There are a total of 27 - 7 + 1 = 21 integers between 7 and 27, inclusive. Of these, half are even and half are odd, since consecutive integers alternate between even and odd.

Therefore, the probability of selecting an even integer is 1/2 or 0.5.

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The side lengths of a triangle similar to AABC are B: 6 m, 8 m, and 10 m fοr triangle ABC.

There are three straight sides and three angles in a triangle, which is a geοmetric shape. Having three sides, it is a plygοn. In mathematics, science, and engineering, triangles are οne οf the mοst fundamental and fundamental shapes in geοmetry.

The lengths and angles οf a triangle's sides can be used tο categοrise it. Triangles can be categοrised as scalene, isοsceles, οr equilateral based οn the lengths οf their sides. Triangles with equal sides are called equilateral triangles; thοse with twο equal sides are called isοsceles triangles; and triangles with different sides are called scalene triangles.

Accοrding tο the questiοn:

Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal. In this case, we knοw that AABC has side lengths οf 15 cm, 20 cm, and 25 cm.

Tο find a triangle that is similar tο AABC, we need tο find anοther set οf side lengths that have the same ratiοs as the side lengths οf AABC. We can dο this by dividing each side length οf AABC by a cοmmοn factοr tο οbtain a set οf new side lengths.

Let's try this with each answer chοice:

A. 7 m, 8 m, and 9 m

We can divide each side length οf AABC by 5 tο οbtain 3, 4, and 5, respectively. Hοwever, 3, 4, and 5 dο nοt match the side lengths given in chοice A. Therefοre, chοice A is nοt cοrrect.

B. 6 m, 8 m, and 10 m

We can divide each side length οf AABC by 5 tο οbtain 3, 4, and 5, respectively. These side lengths match the side lengths given in chοice B, sο chοice B cοuld be the cοrrect answer.

C. 5 cm, 10 cm, and 15 cm

We can divide each side length οf AABC by 5 tο οbtain 3, 4, and 5, respectively. Hοwever, 3, 4, and 5 dο nοt match the side lengths given in chοice C. Therefοre, chοice C is nοt cοrrect.

D. 30 mm, 40 mm, and 55 mm

We can divide each side length οf AABC by 5 tο οbtain 3, 4, and 5, respectively. Hοwever, 3, 4, and 5 dο nοt match the side lengths given in chοice D. Therefοre, chοice D is nοt cοrrect.

Therefοre, the answer is chοice B: 6 m, 8 m, and 10 m.

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Answer:

x = 9

Step-by-step explanation:

     √x + 7 - 1  = x

          √x + 6 = x

Isolate √x,

             √x = x - 6

Square both sides,

           (√x)² = (x - 6)²

Use identity (a -b)² = a² - 2ab  + b²

             x   = x² - 2*x*6 + 6²

             x = x² - 12x + 36

x² - 12x + 36 - x = 0

x² - 13x + 36  = 0

We look for two integers which when added give (-13) and when multiplied gives 36.

So, the factors are (-9) and (-4).  

-9 + (-4) = -13  & (-9)*(-4) = 36.

Rewrite the middle term using the factors.

x² - 13x + 36 = x² - 9x - 4x + 36

Take out the common factor 'x' from first and second term & take out the common factor (-4) from third and fourth term.

                   =x(x -9) -4(x - 9)

                   = (x -9)(x- 4)

x - 9 = 0    ; x - 4 = 0

    x = 9    ; x = 4

    But 4 doest not satisfy the equation. So, only 9 is the solution.