Helpp pleasee!!!!!!!!

The critical points and their classifications are:

(0, 1) - saddle point

(0, -1) - saddle point

(6, 1) - local minimum

(6, -1) - local minimum

To find the critical points of the function f(x, y) = x³ + y³ – 9x² – 3y - 6, we need to find the points where the partial derivatives of f with respect to x and y are zero.

∂f/∂x = 3x² - 18x = 3x(x - 6)

∂f/∂y = 3y² - 3 = 3(y² - 1)

Setting these partial derivatives equal to zero and solving for x and y, we get:

x = 0 or x = 6

y = ±1

So the critical points are (0, 1), (0, -1), (6, 1), and (6, -1).

To classify each critical point, we need to compute the second partial derivatives of f:

∂²f/∂x² = 6x - 18

∂²f/∂y² = 6y

∂²f/∂x∂y = 0

At (0, 1):

∂²f/∂x² = -18 < 0 (concave down)

∂²f/∂y² = 6 > 0 (concave up)

So (0, 1) is a saddle point.

At (0, -1):

∂²f/∂x² = -18 < 0 (concave down)

∂²f/∂y² = 6 > 0 (concave up)

So (0, -1) is a saddle point.

At (6, 1):

∂²f/∂x² = 18 > 0 (concave up)

∂²f/∂y² = 6 > 0 (concave up)

So (6, 1) is a local minimum.

At (6, -1):

∂²f/∂x² = 18 > 0 (concave up)

∂²f/∂y² = 6 > 0 (concave up)

So (6, -1) is a local minimum.

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Answer:

8.81

Step-by-step explanation:

Substitute x for 7 and then solve normally

{2(7)^2+7-8}/(7)+4

{(2x49)+7-8}/11

98+7-8/11

97/11

8.81

Using division operation with unit conversions, the length of ribbon that each of the 18 students in Mrs. Hinojosa's class gets is as follows:

a) 4.2 feet.

b) 4 feet and 2 inches

c) 50 inches.

Division and multiplication operations are used in unit conversions.

Unit conversions involve converting measurements from hours to minutes or seconds, centimeters to meters and miles, etc.

The total quantity of ribbon Mrs. Hinojosa had = 75 feet

1 foot = 12 inches

75 feet = 900 inches (75 x 12)

The number of students in the class = 18

The length of ribbon received by each student = 4.167 feet (75 ÷ 18)

The length of ribbon received by each student ≈ 4 feet and 2 inches

The length of ribbon received by each student in inches only = 50 inches (900 ÷ 18)

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Therefore , the solution of the given problem of inequality comes out to be the solutions x = -6 or x = -10 would be acceptable.

Algebra, which lacking a symbol for this difference, can represent it using a pair or group of numbers. Equity usually comes after equilibrium. Inequality is bred by the persistent gap of standards. Equality and disparity are not the same thing. As was my least preferred symbol, notwithstanding knowing that the pieces are often not connected or close to one another. (). No matter how small the variations, they all affect value.

Here,

Finding values of x that cause the left side of the inequality to be bigger than the right side is necessary to make the inequality -2x > 10 true. Divide both sides by -2 and invert the inequality sign to achieve this:

=> -2x > 10

=> x < -5

The inequality is therefore true for any value of x that is less than -5. For instance, the solutions x = -6 or x = -10 would be acceptable.

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From the solution to the question that we have here, the answer is A. There is no solid proof that the number of hours worked dropped after the income rise.

Let μ be the population mean number of hours worked per week by teachers who work part-time jobs, after the salary increase. Here are the alternate and null hypotheses:

H0: μ = 13

H1: μ < 13

n = 400

[tex]\bar{X}=12.5[/tex]

μ = 13

Formula for the t-test statistics is

[tex]t = \frac{\bar{X}-\mu}{s/\sqrt{n} }[/tex]

t = (12.5 - 13)/(6.5/√400)

t = (- 0.5)/(6.5/20)

t = - 10/6.5

= -1.5388

Degree of freedom is 400 -1 = 399

α = 0.05

The p-value is p(t < -1.5385) = 0.062

The p-value exceeds the level of significance. Therefore, we unable to reject the null hypothesis.

Hence, option a is correct.

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To calculate the cost of each tile, we need to first determine the volume of each tile. The length and width of the tile are given as 16 inches, and the thickness is given as 1/4 inches, which can be converted to 0.25 inches. Therefore, the volume of each tile is 16 x 16 x 0.25 = 64 cubic inches.

Next, we need to determine the weight of gold in each tile. Since the density of gold is 11.17 ounces per cubic inch, the weight of gold in each tile is 64 x 11.17 = 715.68 ounces.

Finally, we can calculate the cost of each tile by multiplying the weight of gold by the price of gold per ounce. The price of gold is given as $1,303.80 per ounce, so the cost of each tile is 715.68 x $1,303.80 = $933,526.78. Rounded to the nearest dollar, each tile will cost $933,527.

In summary, each square tile made of solid gold and measuring 16 inches long and 1/4 inches thick will cost approximately $933,527. This cost is based on the density of gold, which is 11.17 ounces per cubic inch, and the price of gold, which is $1,303.80 per ounce.

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The image of ABC under the translation by 1 unit to the right and 4 units up is the triangle with vertices A', B', and C'.

A triangle is a closed two-dimensional geometric shape with three straight sides and three angles. It is one of the basic shapes in geometry and has been studied since ancient times. To translate a figure by a given vector, you need to move each point of the figure by the same amount and in the same direction as the vector. In this case, we want to translate ABC by a vector of (1, 4), which means we need to move each point of ABC one unit to the right and four units up.

Let's say the coordinates of the points of ABC are:

A = [tex]\rm (x_1, y_1)[/tex]

B = [tex]\rm (x_2, y_2)[/tex]

C = [tex]\rm (x_3, y_3)[/tex]

To translate ABC by the vector (1, 4), we add 1 to each x-coordinate and 4 to each y-coordinate:

A' = [tex]\rm (x_1 + 1, y_1 + 4)[/tex]   (x₁ + 1, y₁ + 4)

B' = [tex]\rm (x_2 + 1, y_2 + 4)[/tex]   (x₂ + 1, y₂ + 4)

[tex]\rm C' = (x_3 + 1, y_3 + 4)[/tex]  (x₃ + 1, y₃ + 4)

Therefore, The image of ABC under the translation by 1 unit to the right and 4 units up is the triangle with vertices A', B', and C'.

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Answer:

66.7%

Step-by-step explanation:

Let people asked bye x.

Then, people considering to change = 29% of x

People considering to become vegetarians = 23% of (29% of x)

                                                                          = 23/100 * 29x/100

                                                                          = 667x/10000

Percentage of people considering to become vegetarians = 667x/10

                                                                                                  = 66.7%

The amount of energy the refrigerator uses per day is 3.6 kilowatt-hour (kWh)

The refrigerator energy usage per day in BTU is 12283.704 BTU

The BTU is an acronym for the British Thermal Unit, which is a measure of heat, which is specified in energy units.

The duration the refrigerator fan runs per hour = 30 minutes

The amount of energy the refrigerator uses every hour = 300 watts × 0.5 hour/hour = 150 watts

The amount of energy the refrigerator uses per hour = 150 watt-hour

1 kWh = 3412.14 BTU

Therefore;

The amount of energy in BTU the refrigerator uses per day = 12283.704 BTU

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Selika spends £565.85 on labour costs.

Given, Selika spends money on plants, materials, and labor in the ratio of 1:5:12 and spends a total of £848.75. We have to find how much money she spends on labor costs.

Let the amount of money Selika spends on plants be x. Then, the amount of money she spends on materials is 5x, and the amount of money she spends on labor is 12x.

The total amount of money she spends is £848. 75

x + 5x + 12x = 848.75

18x = 848.75

x = 848.75/18

x = 47.15

She spend on labour 12x = 12 × 47.15

= 565.85

Therefore, Selika spends £565.85 on labour costs.

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The set that includes ONLY rational numbers that are also integers is:

{-3, -2, -1, 0, 1, 2, 3, ...}

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The area of the parallelogram is 300 centimetres squared.

The length of the base is 20 centimetres. The length of the sides is 17 centimetres. The overhang of the base is 8 centimetres long. The angle between the overhang and the height is a right angle.

Therefore,

area of a parallelogram = b × h

where

Therefore, let's use Pythagoras's theorem to find the height of the parallelogram as follows
17² - 8² = h²

289 - 64 = h²

h = √225

h = 15 centimetres

Therefore,

area of the parallelogram = 20 × 15

area of the parallelogram = 300 cm squared

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(a) To find the curl of the vector field F(x, y, z), we first find its component functions:

F(x, y, z) = (5ex sin(y), 9ey sin(z), 2ez sin(x))

Then, we use the formula for the curl of a vector field:

curl F = (∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y)

Plugging in the component functions of F(x, y, z), we get:

curl F = (2ez cos(x), -5ex cos(y), 9ey cos(z))

(b) To find the divergence of the vector field F(x, y, z), we use the formula for the divergence of a vector field:

div F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

Plugging in the component functions of F(x, y, z), we get:

div F = 5e^x sin(y) + 9e^y sin(z) + 2e^z sin(x)
(a) To find the curl of the vector field F(x, y, z) = (5e^x sin(y), 9e^y sin(z), 2e^z sin(x)), we need to compute the cross product of the del operator (∇) and F:

curl F = ∇ x F

curl F = ( (∂/∂y)(2e^z sin(x)) - (∂/∂z)(9e^y sin(z)), (∂/∂z)(5e^x sin(y)) - (∂/∂x)(2e^z sin(x)), (∂/∂x)(9e^y sin(z)) - (∂/∂y)(5e^x sin(y)) )

After computing the partial derivatives, we get:

curl F = ( 0, 5e^x cos(y) - 2e^z cos(x), 9e^y cos(z) - 5e^x cos(y) )

(b) To find the divergence of the vector field F(x, y, z), we need to compute the dot product of the del operator (∇) and F:

div F = ∇ ⋅ F

div F = (∂/∂x)(5e^x sin(y)) + (∂/∂y)(9e^y sin(z)) + (∂/∂z)(2e^z sin(x))

After computing the partial derivatives, we get:

div F = 5e^x sin(y) + 9e^y sin(z) + 2e^z sin(x)

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The equation models the situation described in the problem is 3.50x + 2.25(10) = 3 (x + 10) . The correct answer is C.

To model the situation described in the problem, we need to use an equation that represents the total cost of the flowers in terms of the number of roses (x) and the number of carnations (10). Let's assume that the cost of each flower is proportional to its price, and that the average cost per flower is the total cost divided by the total number of flowers (x + 10).

The cost of x roses at $3.50 each is 3.50x, and the cost of 10 carnations at $2.25 each is 2.25(10) = 22.50. Therefore, the total cost of the bouquet is:

Total cost = 3.50x + 22.50

The average cost per flower is given by:

Average cost = Total cost / (x + 10)

We are told that the average cost per flower is $3.00, so we can set up an equation:

3.00 = (3.50x + 22.50) / (x + 10) or  3.50x + 2.25(10) = 3 (x + 10)

This equation models the situation described in the problem. We can solve for x to find the number of roses needed to make a bouquet that meets the given conditions. The correct answer is C.

Your question is incomplete but most probably your full question attached below

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To find the length of the ladder needed to reach the roof of the shed that is 35 ft from the ground with the base of the ladder 12 ft from the shed, you can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the ladder, in this case) is equal to the sum of the squares of the other two sides (the height and the distance from the shed).

Step 1: Identify the sides of the triangle.
- Height (a): 35 ft (vertical side)
- Distance from the shed (b): 12 ft (horizontal side)
- Ladder length (c): Hypotenuse

Step 2: Apply the Pythagorean theorem.
- a² + b² = c²
- 35² + 12² = c²

Step 3: Calculate the squares and sum them.
- (35 * 35) + (12 * 12) = c²
- 1225 + 144 = c²
- 1369 = c²

Step 4: Find the length of the ladder (c).
- c = √1369
- c = 37

The ladder needs to be 37 ft long to reach the roof of the shed.

Shortening the distance between the ladder and the shed will affect the height of the ladder by making it steeper. This will cause the ladder to be higher above the ground, but it may also make it less stable and more difficult to climb.

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a. To find the probability that there are no cars in the system, we need to use the formula for the steady-state probability distribution of the M/M/1 queue:
P(0) = (1 - λ/μ)
where λ is the arrival rate (2 per hour) and μ is the service rate (3 per hour).
P(0) = (1 - 2/3) = 1/3 or 0.3333
Therefore, the probability that there are no cars in the system is 0.3333.

b. To find the average number of cars in the system, we can use Little's Law:
L = λW
where L is the average number of cars in the system, λ is the arrival rate (2 per hour), and W is the average time spent in the system.
We can solve for W by using the formula:
W = 1/(μ - λ)
W = 1/(3 - 2) = 1 hour
Therefore, the average number of cars in the system is:
L = λW = 2 x 1 = 2 cars

c. To find the average time spent in the system, we already calculated W in part b:
W = 1 hour

d. To find the probability that there are exactly two cars in the system, we need to use the formula for the steady-state probability distribution:
P(n) = P(0) * (λ/μ)^n / n!
where n is the number of cars in the system.
P(2) = P(0) * (λ/μ)^2 / 2!
P(2) = 0.3333 * (2/3)^2 / 2
P(2) = 0.1111 or 11.11%
Therefore, the probability that there are exactly two cars in the system is 11.11%.

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Answer:8

Step-by-step explanation:

Anallency will have $134.46 more money than Alejandro after one year of their respective deposits.

Alejandro and Anallency are depositing money in separate accounts with different interest rates. Alejandro is depositing $1,750 in an account that earns a simple interest rate of 6.5% per year, while Anallency is depositing $1,675 in an account that earns a compounded interest rate of 7.5% per year. After one year of their respective deposits, Anallency will have $134.46 more money than Alejandro.

The difference in interest earned between the two accounts is the reason for the difference in money earned by Alejandro and Anallency. Alejandro's account earns a simple interest rate, which means that he earns 6.5% of his initial deposit every year, regardless of how much interest he has already earned.

On the other hand, Anallency's account earns a compounded interest rate, which means that she earns interest on both her initial deposit and on any interest earned in previous years.

The formula for calculating simple interest is I = Prt, where I is the interest earned, P is the principal (or initial deposit), r is the interest rate, and t is the time in years. Using this formula, we can calculate that Alejandro will earn $113.75 in interest after one year.

The formula for calculating compounded interest is A = P(1 + r/n)^(nt), where A is the amount of money at the end of the time period, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Using this formula, we can calculate that Anallency will have $248.21 more in her account than Alejandro after one year.

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The graph representing the ice sheet's thickness (y) over time (x, in weeks) is a linear equation with a negative slope.

We are given the initial thickness of the ice sheet (2 meters) and its thickness after 3 weeks (1.25 meters). The rate of decrease in thickness is constant.

To find the slope, we can use the formula: (change in y) / (change in x). Here, the change in y is (1.25 - 2) = -0.75 meters, and the change in x is 3 weeks.

Therefore, the slope is -0.75 / 3 = -0.25 meters/week. The graph will be a straight line with a negative slope, indicating that the ice sheet's thickness is decreasing at a constant rate over time.

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Number that produces a rational number when multiplied by 1 is option B, -3.

To determine which number produces a rational number when multiplied by 1,

We need to examine each of the given.

Here, options: A. TI , B. -3, C. T, D. -1.41421356

We know,

A rational number can be expressed as a fraction (a/b) where both a and b are integers and b is not equal to 0. When multiplying by 1, the result remains the same. Option B: -3 multiplied by 1 = -3 which is a rational number because it can be expressed as a fraction (-3/1).

Option D: here given number -1.41421356 multiplied by 1 = -1.41421356 and we cannot be easily expressed as a fraction.

Therefore,it's not a rational number.

Thus, the number that produces a rational number when multiplied by 1 is option B, -3.

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Answer: To find the length of the midsegment of a trapezoid, you need to add the lengths of the two bases together and divide by 2.

The length of the top base is 2n-2 and the length of the bottom base is 4n+6.

Adding the two bases together gives:

(2n-2) + (4n+6) = 6n + 4

Dividing by 2 gives:

(6n + 4) / 2 = 3n + 2

Therefore, the length of the midsegment of the trapezoid is 3n + 2.

A reasonable scale factor that could be applied to Shape 2 to create Shape 1 is 0.5.

When we talk about scaling a shape, we mean changing the size of the shape while maintaining its overall proportions.

This can be done by multiplying all of the dimensions of the shape by the scale factor.

For example, if we wanted to make a shape twice as big, we would multiply all of its dimensions (length, width, and height) by 2. If we wanted to make it half as big, we would multiply all of its dimensions by 0.5.

Looking at the two shapes, we can see that Shape 1 is half the size of Shape 2 in all dimensions.

For example, the height of Shape 1 is half the height of Shape 2, the width of Shape 1 is half the width of Shape 2, and the length of Shape 1 is half the length of Shape 2.

Therefore, to transform Shape 2 into Shape 1, we need to multiply all of its dimensions by 0.5. This will result in a scaled copy of Shape 2 that is identical in shape to Shape 1.

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The cash basis income for Carillo Industries is $41,000 and the accrual basis net income is $35,000.

The cash basis income for Carillo Industries, based on the cash received and paid during the year, is $41,000. The accrual basis net income, based on revenue and expenses earned/incurred during the year, regardless of whether cash was exchanged, is $35,000.

In 2020, Carillo Industries collected $108,000 from customers, of which $25,000 was for services performed in 2019 and $36,000 will not be collected until 2021.

The company paid $72,000 for expenses in 2020, of which $30,000 was for expenses incurred in 2019, and $42,000 of expenses in 2020 will not be paid until 2021. By calculating the cash and accrual basis, Carillo Industries can understand its financial performance from different perspectives.

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Thus, the area of triangle for the given values of height and base is found as:  180 sq. in.

A number of steps are involved in the Unit of Conversion process, which involves multiplying or dividing by a numerical factor. There are numerous ways to measure things like weight, separation, and temperature.

Unit conversion is the process of changing the unit of measurement for a comparable quantity by multiplying or dividing by conversion factors.

Scientific notation is used to express the units, which are then translated into numerical values in accordance with the amounts.

Given data:

We know that,

1 foot  = 12 in.

2 feet = 12*2 = 24 in.

Area of triangle = 1/2 * b * h

Area of triangle = 1/2 * 24 * 15

Area of triangle = 12* 15

Area of triangle = 180 sq. in

Thus, the area of triangle for the given values of height and base is found as:  180 sq. in.

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Waterways Corporation's budget for Q1 2022 involves sales, inventory, materials, labor, overhead, expenses, and financing.

Waterways Corporation is preparing its budget for the first quarter of 2022. The company has gathered information from its managers to begin the budgeting process.

The company expects unit sales to be 112,000 in November 2021, 104,000 in December 2021, and 113,000 in January 2022. The company also expects to keep 10% of next month's unit sales in ending inventory. The company collects 85% of Accounts Receivable in the month of sale and 15% in the month after sale.

Raw materials cost 80 cents per pound, and two pounds of direct materials are required to produce each unit. The company likes to keep 5% of the materials needed for the next month in its ending inventory.

Labor requires 12 minutes per unit, paid at a rate of $9 per hour. The company has variable selling and administrative costs of $1.60 per unit, including advertising, insurance, salaries, and depreciation. The company also plans to make a $480,000 equipment purchase in February.

The company's cash balance on December 31, 2021, was $99,000, but the management wants to maintain a cash balance of at least $700,000 starting on January 31, 2022. The company pays dividends each month at the rate of $2.70 per share for 4,610 shares outstanding.

The company has an open line of credit with Romney's Bank with borrowing terms of $1,000 increments at 9% interest. The company borrows on the first day of the month and repays on the last day of the month.

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We reflect the point (-5, -3) over the x-axis to get (-5, 3), and then translate this point down by 2 units to get the final coordinates of (-5, 1).

To reflect a point over the x-axis, we keep the x-coordinate the same, but negate the y-coordinate. Thus, reflecting the point (-5, -3) over the x-axis gives us the point (-5, 3).

Next, we need to translate the result 2 units down. To do this, we subtract 2 from the y-coordinate of the reflected point. So, subtracting 2 from the y-coordinate of (-5, 3) gives us the final coordinates:

(-5, 3) translated 2 units down is (-5, 1).

In summary, we can reflect a point over the x-axis by negating the y-coordinate, and translate a point down by subtracting a value from its y-coordinate. So, we reflect the point (-5, -3) over the x-axis to get (-5, 3), and then translate this point down by 2 units to get the final coordinates of (-5, 1).

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Answer:

Part 1: 73 periods

Part 2: 73 periods in 1 year - 365/5=73

Part 3: 0.075 periodic interest rate - 180/2400=0.075

Maximum and Minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9.

The maximum value is 3

The minimum value is -3

To find the maximum and minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9, follow these steps:

1. Use the constraint equation (ellipse equation) to solve for one of the variables, either x or y.

Here, let's solve for y:
y² = 9 - 3x²
y = ±√(9 - 3x²)

2. Substitute y in the function f(x, y) with the expressions found in step 1:
f(x, y) = x(±√(9 - 3x²))

3. Differentiate f(x, y) with respect to x to find critical points (maximum or minimum):
f'(x, y) = ±(√(9 - 3x²) - (3x² / √(9 - 3x²)))

4. Set f'(x, y) = 0 and solve for x:
√(9 - 3x²) - (3x² / √(9 - 3x²)) = 0

5. Find the corresponding y values for the x values found in step 4 by substituting x back into the expressions found in step 1.

6. Evaluate f(x, y) at each critical point (x, y) found in steps 4 and 5 to determine the maximum and minimum values.

The maximum value of f(x, y) = xy on the ellipse 3x² + y² = 9 is 3, and the minimum value is -3.

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Answer:

A

Step-by-step explanation:

Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get  2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get  16 = 2x Dividing both sides by 2, we get x=8