Classify the following polynomials according to the number of terms. Combine any like terms first.
x²+3x+2x

x³+x+3x²-x

4x³+x+x²-2x

3x²+x-3x*-x

The directional derivative of f(x,y) at the point (2,-3) in the direction of the angle theta = 1/3 pi is 4 + 9sqrt(3).

The directional derivative of a function f(x,y) in the direction of a unit vector u = (cos(theta), sin(theta)) at a point (a,b) is given by:

D_u f(a,b) = ∇f(a,b) · u

where ∇f(a,b) is the gradient vector of f at the point (a,b).

To find the directional derivative of f(x,y) at the point (2,-3) in the direction of the angle theta = 1/3 pi, we first need to find the unit vector u in that direction. We have:

theta = 1/3 pi

cos(theta) = cos(1/3 pi) = 1/2

sin(theta) = sin(1/3 pi) = sqrt(3)/2

Therefore, the unit vector u in the direction of theta is:

u = (cos(theta), sin(theta)) = (1/2, sqrt(3)/2)

Next, we need to find the gradient vector ∇f(2,-3) of the function f(x,y) at the point (2,-3). We have:

f(x,y) = 2x^2 - 3y^2

∂f/∂x = 4x

∂f/∂y = -6y

So, the gradient vector ∇f(x,y) is:

∇f(x,y) = (4x, -6y)

At the point (2,-3), the gradient vector is:

∇f(2,-3) = (8, 18)

Finally, we can calculate the directional derivative of f(x,y) at the point (2,-3) in the direction of u:

D_u f(2,-3) = ∇f(2,-3) · u

= (8, 18) · (1/2, sqrt(3)/2)

= 4 + 9sqrt(3)

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Answer:

\(x > 42\)

Step-by-step explanation:

\(\frac{x}{6} > 7\)

Multiply 6 on both sides. \(6(\frac{x}{6}) > 6(7)\).

Simplify it. \(x > 42\)

Therefore, the answer is \(x > 42\).

Hope this helped! If not, please let me know! <3

In order to find the volume of a composite figure, we will first need to break it down into simpler shapes whose volumes we can calculate and add them together.

We can use this same method to find the volume of a composite figure. For example:Let's say we have a composite figure consisting of a cylinder and a rectangular prism. We can break it down into a cylinder and a rectangular prism, and find the volume of each separately. Once we have done that, we can simply add the volumes together to find the total volume of the composite figure. We will round our final answer to the nearest tenth.

Let's factorize the denominator to solve the given question, 2x³ - 25x⁴ / x² - 2x - 8We need to solve the denominator: x² - 2x - 8Now, let's use the quadratic formula to solve the denominator. x² - 2x - 8  Let's find the roots of the quadratic function x² - 2x - 8.x = (-b ± √(b² - 4ac)) / 2a

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Step-by-step explanation:

5/9 × (x - 32) = 1.8 × x + 32 = 9/5 × x + 32

5×(x - 32) = 9×9/5 × x + 32×9

5×5×(x - 32) = 9×9×x + 32×9×5

25x - 32×25 = 81x + 32×45

32×(-25 - 45) = 56x

4×(-70) = 7x

x = 4×(-10) = -40

-40° is the same temperature in Celsius and in Fahrenheit.

Answer:

One solution

Step-by-step explanation:

-4 + 6n = 7n

you will subtract (6n-6n) which will cancel each other out, than subtract (7n - 6n) which will be (1n)

So now you will have    -4 = 1n

Now you will divide ( -4/1) which is -4

You don't have to divide -4 with 1, because its the same way as multiplying it.

Now you will have -4 = n

Answer:

Neither

because parallel equations often have the same exact slop but different y- intercept and nor is it perpendicular because slop must be flipped over 1 and negative so its not evident there.

Hope it helps:))

Step-by-step explanation:

6.75 cups of cleaner is needed to be mixed with 13.5 gal of water

An equation is an expression used to show the relationship between two or more variables and numbers.

Given that 1/2 cup of cleaner should be mixed with 1 gal of warm water.

Therefore for 13 1/2 (13.5) gal of water:

Amount of cleaner = 13.5 gal of water * 1/2 cup of cleaner per 1 gal of water

Amount of cleaner = 6.75 cups

6.75 cups of cleaner is needed to be mixed with 13.5 gal of water

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To find the symmetric matrix A associated with the given quadratic form 3x^2 - 3xy - y^2, we need to consider the coefficients of the quadratic terms.

The general form of a quadratic form is represented by the equation x^T A x, where x is a column vector of variables and A is the symmetric matrix associated with the quadratic form.

In this case, the given quadratic form is 3x^2 - 3xy - y^2. To find the symmetric matrix A, we need to identify the coefficients of x^2, xy, and y^2.

The coefficients of the quadratic terms are:

Coefficient of x^2: 3

Coefficient of xy: -3

Coefficient of y^2: -1

Now, we can construct the symmetric matrix A:

A = | 3 -3 |

| -3 -1 |

The matrix A is symmetric because it satisfies the property A^T = A, where A^T denotes the transpose of matrix A.

Therefore, the symmetric matrix A associated with the given quadratic form 3x^2 - 3xy - y^2 is:

A = | 3 -3 |

| -3 -1 |

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Answer:

just look that up and walla insta answer

(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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Answer:

2

Step-by-step explanation:

1/4 × 8 = 2

:))))nakajsisj

Answer:

2

Step-by-step explanation:

Answer:

(-4,-3)

Step-by-step explanation:

Answer:

12 feet 11 inches

Step-by-step explanation:

The giraffe is 12 feet 11 inches taller than Jada. Therefore, the correct answer is option C: 12 feet 11 inches.

To find out how much taller the giraffe is than Jada, we need to subtract Jada's height from the giraffe's height.

Jada's height is 3 feet 11 inches, which can be written as 3' 11".

The giraffe's height is 16 feet 10 inches, which can be written as 16' 10".

To perform the subtraction, we need to ensure both measurements are in the same format. We can convert Jada's height to inches:

Jada's height = 3 feet * 12 inches/foot + 11 inches = 36 inches + 11 inches = 47 inches.

Now we can subtract Jada's height from the giraffe's height:

16' 10" - 3' 11" = 16 * 12 + 10 - (3 * 12 + 11) = 192 + 10 - (36 + 11) = 202 - 47 = 155 inches.

Therefore, the giraffe is 155 inches taller than Jada.

To convert this back to feet and inches, we have:

155 inches = 12 feet * 12 inches/foot + 11 inches = 12' 11".

Thus, the giraffe is 12 feet 11 inches taller than Jada. Therefore, the correct answer is option C: 12 feet 11 inches.

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A triangular distribution that has a mode of 0 and a lower limit of -2.45 and an upper limit of 2.45 is similar to a symmetric distribution with finite bounds, such as the uniform distribution.

The triangular distribution is a continuous probability distribution that has a triangular shape, where the maximum occurs at the mode and the distribution is symmetric around the mode.

In this case, since the mode is 0, the distribution is symmetric around 0. The limits of -2.45 and 2.45 create a range of possible values for the distribution, similar to how the bounds of a uniform distribution create a range of possible values.

However, unlike the uniform distribution, the triangular distribution has a higher probability density near the mode, and a lower probability density near the bounds.

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Answer:

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40

Then the greatest common factor is 2.

The greatest common factor of 18 , 24 and 40 is HCF = 2

The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF

Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers

Product of HCF x LCM = product of two numbers

Given data ,

Let the HCF be represented as H

Let the first number be represented as p

Now , the value of p = 18

Let the second number be represented as q

Now , the value of q = 24

Let the third number be represented as r

Now , the value of r = 40

And , the factors of 18 = 1, 2, 3, 6, 9 and 18

The factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24

The factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40

So , the HCF of 18 , 24 and 40 is the number 2

Hence , the HCF is 2

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8×7=56

then subtract it from 100-56=44 so you lost 56 gallons in 8 minutes and there is 44 left.

Answer:

The answer will be 0.062

Step-by-step explanation:

Hope this Helped

Answer:

0.062

Step-by-step explanation:

3.162/ 51 = 0.062

Answer:

Step-by-step explanation:

x + y = −3

y = 2x + 2

Substitute the y value of the second equation into the top equation

x + 2x + 2 = - 3

3x + 2 = - 3

3x = -3 -2

3x = - 5

x = -5/3

x + y = - 3

-5/3 + y = - 3

y = -3 + 5/3

y = -1 1/3

The value of the triple integral is -16.

Triple integral is a mathematical concept used in calculus to calculate the volume of three-dimensional objects. It extends the concept of a single integral to functions of three variables and integrates over a region in three-dimensional space.

The triple integral of a function f(x, y, z) over a region E in three-dimensional space is denoted by:

∭E f(x, y, z) dV

We can set up the triple integral as follows:

∫∫∫ 16y dV

Where the limits of integration are:

0 ≤ x ≤ 2

0 ≤ y ≤ (2- \(x^2\)z)/(2y)

0 ≤ z ≤ 2/\(x^{2y\)

Note that the upper bound of integration for y is not a constant, but depends on both x and z.

Integrating with respect to y first, we get:

∫∫∫ 16y dV = ∫0^2 ∫\(0^(2-x^2z)/(2x)\)∫\(0^(2/x^2y) 16y dz dy dx\)

= ∫\(0^2\) ∫\(0^(2-x^2z)/(2x) 32/x dx dz\)

= ∫\(0^2\) [16(\(2-x^2z)/x^2\)] dz

= ∫\(0^2 (32/x^2 - 16z)\) dz

= 32∫\(0^2 x^-2 dx - 16\)∫\(0^2\)z dz

= 16 - 16(2)

= -16

Therefore, the value of the triple integral is -16.

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Ordered pairs for equations y = -x + 3 , y = (1/2)x - 1 and x + y = 2 are

(-1,4) and (3,0), (-2, -2) and (4,1) and (-3,5) and (3,-1) respectively. Graph is attached below.

A line is a geometry object characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called a straight line.

General equation of line

y = mx + c

where m is slope and c is y - intercept.

Given,

1. y = -x + 3

putting x = -1

y = - -1 + 3

y = 4

Point is (-1 , 4)

Putting x = 3

y = -3 + 3

y = 0

Point is (3 , 0)

1. y = (1/2)x - 1

putting x = -2

y = (1/2)(-2) - 1

y = -2

Point is (-2 , -2)

Putting x = 4

y = (1/2)(4) - 1

y = 1

Point is (4 , 1)

3. x + y = 2

putting x = -3

-3 + y = 2

y = 2 + 3

y = 5

Point is (-3 , 5)

Putting x = 3

3 + y = 2

y = 2 - 3

y = -1

Point is (3 , -1)

Graph of the lines can be drawn as following:

Hence, (-1,4) and (3,0) are ordered pairs for equation 1, , (-2, -2) and (4,1) are ordered pairs for equation 2 and (-3,5) and (3,-1) are ordered pairs for equation 3.

Graph is attached below.

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Answer:

\(45678 = 46000 \\ 98789 = 99000\)

Answer:

It is 9/10 x 3/2= 1 7/20

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

3x+2(-3x+11)=7

Use distributive property:

3x-6x+22=7

Combine like terms:

-3x+22=7

-3x=-15

Then divide:

-3x/3=-15/3 = 5

x=5

By Sarrus' law, the determinant of each matrix:

Case 1: D = 1

Case 2: D = - 134.5

In this problem we must compute the determinant of a matrix, this matrix has three rows and the three columns and its determinant can be found by Sarrus' law, whose statements are summarized below:

Now we find the determinant of each matrix:

Case 1:

D = (- 4) · 0 · 1 + 1 · (- 1) · (- 3) + 2³ - 2 · 0 · (- 3) - 1 · 2 · 1 - (- 4) · (- 1) · 2

D = 0 + 3 + 8 - 0 - 2 - 8

D = 1

Case 2:

D = 0.5 · 2 · 1.5 + 0 · 0 · 3.5 + (- 8) · (- 6) · (- 4) - (- 8) · 2 · 3.5 - 0 · (- 6) · 1.5 - 0.5 · 0 · (- 4)

D = 1.5 + 0 - 192 + 56 - 0 - 0

D = - 134.5

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A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

Function: A(t) = (t+1)/(t-1)For the given function A(t), the following values are to be calculated: A(8), A(-5), A(3/1), and A(-71/1)A(8):We need to substitute t=8 in the function. A(8) = (8+1)/(8-1) = 9/7Therefore, A(8) = 9/7A(-5):We need to substitute t=-5 in the function. A(-5) = (-5+1)/(-5-1) = -1/3Therefore, A(-5) = -1/3A(3/1):We need to substitute t=3/1 in the function. A(3/1) = (3/1+1)/(3/1-1) = (4)/(2/1) = 4*1/2 = 2Therefore, A(3/1) = 2A(-71/1):We need to substitute t=-71/1 in the function. A(-71/1) = (-71/1+1)/(-71/1-1) = (-70/1)/(-72/1) = (-5/36)Therefore, A(-71/1) = -5/36Therefore, the respective answers for the given values of the function A(t) are as follows: A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

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The answer of the given question based on the  arc or angle the answer is the measure of arc BC is 100° degrees.

What is Arc?

In geometry, an arc is  portion of  circle's circumference. It is defined as  curved line that connects two points on circle, called endpoints. An arc is named based on its endpoints.

In the given figure, we see that angle BOC is an inscribed angle and its vertex lies on the center of the circle. By the inscribed angle theorem, the measure of the inscribed angle BOC is equal to one-half the measure of the intercepted arc BC.

Therefore, to find the measure of arc BC, we need to multiply the measure of angle BOC by 2. Since angle BOC is given as 50° degrees, we have:

Measure of arc BC = 2 × Measure of angle BOC

= 2 × 50° degrees

= 100° degrees

Therefore, the measure of arc BC is 100° degrees.

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Answer:The total length of ribbon = 4½ m = 4.5 m. = 4.5 m x (100 cm/1 m). = 450 cm. The number of pieces of ribbon, each 4.5 cm long, that can be cut from a length

Step-by-step explanation:

Answer:

3.333

the three continuous

One water tank can be rented for 160 dollars, according to the provided statement.

The radius of a circular is the separation between its centre and perimeter. Always, the circumference is twice the radius.

The volume of the cylinder-shaped water tank is given by the formula

V = πr²h, where

r is the radius

h is the height.

Substituting the given values, we get:

V = π(4 feet)²(2 feet) = 32π cubic feet

The cost of renting the water tank is given by the product of the volume and the cost per cubic foot:

Cost = 5 dollars/cubic foot × 32π cubic feet

Multiplying these values, we get:

Cost = 160π dollars

Therefore, it costs 160π dollars to rent one water tank.

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Answer:

y - 3y^2 + 4y^2 - 12y

y^2 - 11y

Step-by-step explanation: