Form a polynomial whose real zeros and degree are given. Zeros: - 3,0, 6; degree: 3 Type a polynomial with integer coefficients Make sure it has a leading coefficient of 3. f(x) = (Answer must be written in standard form, multiplied out.)

Answer:

$3

Step-by-step explanation:

Divide 6 from 18 to find the cost per shirt.

18/6=3

3 dollars per shirt.

Hope this helps!

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Answer:

Length = 7   Width = 2

Step-by-step explanation:

L = Length

W = Width

L=9w-11

2L+2W=18

2(9W-11) + 2W = 18

18W - 22 +2W = 18

20W -22 = 18

20W = 40

W = 2

L = 9(2)-11

L=18-11

L=7

The length and width of the rectangle is equals to 7inches and 2inches respectively.

" Rectangle is defined as the quadrilateral whose opposite sides are congruent and parallel to each other , one of the interior angle is of measure 90°."

Formula used

Perimeter of the rectangle = 2 (length + width)

According to the question,

Given,

Perimeter of the rectangle = 18inches

'x' represents the width of the rectangle

As per the condition given,

Length of the rectangle = \(9x -11\)

Substitute the value in the formula we get,

\(2(9x -11 +x)=18\)

⇒\((10x-11)=\frac{18}{2}\)

⇒\(10x= 9+11\)

⇒\(x= 2inches\)

Length of the rectangle = \(9(2)-11\)

                                        = \(18-11\)

                                        = \(7inches\)

Hence,  length and width of the rectangle is equals to 7inches and 2inches respectively.

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Answer:

$938.46

Step-by-step explanation:

862.95 is 100% of the price before tax.

if sales tax is 8.75%, then we need (100 + 8.75)%.

that's one whole + 8.75%.

862.95 X 1.0875 = 938.458.

this is $938.46 to nearest cent

The algebraic expression of the statement is 5 + 3y ≤ z + 14

From the question, we have the following parameters that can be used in our computation:

5 more than the product of 3 and a number y is less than or equal to the sum of another number z and 14

When represented as expression, we have

5 + 3y is less than or equal to z + 14

As an inequality, we have

5 + 3y ≤ z + 14

hence, the expresion si 5 + 3y ≤ z + 14

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a) curl(F) = 0i + 0j + 0k = 0 and The divergence of F is = -2Gm₁m₂(1/x³ + 1/y³ + 1/z³)

b) div(F) = -2(Gm₁m₂/x³) - 2(Gm₁m₂/y³) - 2(Gm₁m₂/z³) = -2Gm₁m₂(1/x³ + 1/y³ + 1/z³)

To calculate the curl and divergence of the vector field F, let's start by expressing F in component form:

F = (Gm₁m₂/x²)i + (Gm₁m₂/y²)j + (Gm₁m₂/z²)k

a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the determinant:

curl(F) = ∇ × F = (dR/dy - dQ/dz)i + (dP/dz - dR/dx)j + (dQ/dx - dP/dy)k

Let's compute the curl of F by taking partial derivatives of its components:

dR/dy = 0

dQ/dz = 0

dP/dz = 0

dR/dx = 0

dQ/dx = 0

dP/dy = 0

Therefore, the curl of F is:

curl(F) = 0i + 0j + 0k = 0

b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the scalar:

div(F) = ∇ · F = dP/dx + dQ/dy + dR/dz

Let's compute the divergence of F by taking partial derivatives of its components:

dP/dx = -2(Gm₁m₂/x³)

dQ/dy = -2(Gm₁m₂/y³)

dR/dz = -2(Gm₁m₂/z³)

Therefore, the divergence of F is:

div(F) = -2(Gm₁m₂/x³) - 2(Gm₁m₂/y³) - 2(Gm₁m₂/z³)

= -2Gm₁m₂(1/x³ + 1/y³ + 1/z³)

Now, let's move on to the second part of your question.

To show that the integral of F · dr is path independent, we need to verify that the line integral of F · dr between two points A and B is the same for all paths connecting them.

Let C be a curve connecting A and B. The line integral of F · dr along C is given by:

∫C F · dr = ∫C (F · T) ds

where T is the unit tangent vector along the curve C, and ds is the differential arc length along C.

We can parametrize the curve C as r(t) = (x(t), y(t), z(t)), where t varies from a to b.

Then, the unit tangent vector T is given by:

T = (dx/ds)i + (dy/ds)j + (dz/ds)k

where ds =√((dx/dt)² + (dy/dt)² + (dz/dt)²) dt.

Now, we can compute F · T and substitute the values to evaluate the line integral.

F · T = (Gm₁m₂/x²)(dx/ds) + (Gm₁m₂/y²)(dy/ds) + (Gm₁m₂/z²)(dz/ds)

Substituting ds and simplifying:

ds =√((dx/dt)² + (dy/dt)² + (dz/dt)²) dt

= √((dx/dt)² + (dy/dt)² + (dz/dt)²) dt / dt

= √((dx/dt)² + (dy/dt)² + (dz/dt)²)

Therefore, the line integral becomes:

∫C F · dr = ∫[a,b] [(Gm₁m₂/x²)(dx/ds) + (Gm₁m₂/y²)(dy/ds) + (Gm₁m₂/z²)(dz/ds)] ds

= ∫[a,b] [(Gm₁m₂/x²)(dx/dt) + (Gm₁m₂/y²)(dy/dt) + (Gm₁m₂/z²)(dz/dt)] √((dx/dt)² + (dy/dt)² + (dz/dt)²) dt

The path independence of this line integral can be shown if this integral is path independent, i.e., it depends only on the endpoints A and B, not on the specific path C chosen.

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Answer:

1) x= 2

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

40/100×25

=10

25-10=15

Answer:

D

Step-by-step explanation:

if you have 37 and however many you eat you subtract from that 37 giving you R

The coordinates of point C are (x, y) = (9, 8).

In this case we need to determine the coordinates of point C based on the dimensions of each block. These dimensions can be determined by solving the following equations:

2 · x - y = 11 - 3

y + 2 · x = 20 - 4

2 · x - 16 + 2 · x = 8

4 · x - 16 = 8

4 · x = 24

x = 6

y = 2 · x - 8

y = 2 · 6 - 8

y = 12 - 8

y = 4

Finally, we determine the coordinates of point C:

X = 3 + x = 9

Y = 4 + y = 8

The point C has the following coordinates: (x, y) = (9, 8).

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Answer: Mean: 17.14                                                                                           Range: 20.

Step-by-step explanation: 12+13+13+15+16+19+32                             25+13+15+16+19+32                                                                                             38+15+16+19+32                                                                                               53+16+19+32                                                                                                         69+19+32                                                                                                               88+32                                                                                                                     120/7                                                                                                                     17.14                                                                                                                                                    

32-12                                                                                                                       20

Answer:

base 3, height 3

Step-by-step explanation:

5-2=3 4-1=3

Answer:

7.4

Step-by-step explanation:

Answer:

Its gotta be (6, 5)

Step-by-step explanation:

If we look at the sequence, the x coordinates are 2, -2, 4, -4. In the first & third x coordinates, there is an increment of 2 i. e. first 2 and then 2+2=4 so the fifth x coordinate should be 4+2=6.

The y coordinates are 3, 5, 4, 5. In the first and third y coordinates, there is an increment of 1 i. e. first 3 and then 3+1=4 so the fifth y coordinate should be 4+1=5.

The sequence goes like this

(2, 3), (-2, 5), (4, 4), (-4, 5), (6, 5), (-6, 5), (8, 6), (-8, 5), and so on

x² + 4x - 5 is the answer...

Answer:

x^2 + 4x - 5

Step-by-step explanation:

(x+5) x (x-1)

Multiply the parentheses

X × X - X + 5x -5

Calculate

x^2 − X + 5x − 5

Collect like terms

Solution:

x^2 + 4x - 5

The x-intercept is (-3,0) and the y-intercept is (0,9).

The x-intercept of a quadratic function is the point where the function intersects with the x-axis. This point represents the value of x for which the function is equal to 0. The x-intercept can be found by setting the function equal to 0 and solving for x.

The y-intercept of a quadratic function is the point where the function intersects with the y-axis. This point represents the value of y for which the function is equal to 0. The y-intercept can be found by setting x equal to 0 and solving for y.

1. The x-intercept of the function is (-3,0) and it represents the point where the function intersects with the x-axis.
2. The y-intercept of the function is (0,9) and it represents the point where the function intersects with the y-axis.

To find the x-intercept, set the function equal to 0 and solve for x:

0 = x^2 + 6x + 9

0 = (x+3)(x+3)

x = -3

To find the y-intercept, set x equal to 0 and solve for y:

y = 0^2 + 6(0) + 9

y = 9

Therefore, the x-intercept is (-3,0) and the y-intercept is (0,9).

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Answer:

2 and 3

Step-by-step explanation:

because they are not in the same from like 1 is in the same from 4 is to but 2 and 3 are roated

Answer:

2

Step-by-step explanation:

1 is not even a rotation it’s a reflection

3 is 2 rotations

4 is dilation

hence your answer is 2 because the shape is rotated once :)

The area covered by the patch is 63.585 cm²

To find the area covered by the circular patch, we can use the formula for the area of a circle:

Area = πr²

Given that the diameter of the patch is 9 centimeters, we can find the radius (r) by dividing the diameter by 2:

r = 9 cm / 2

r = 4.5 cm

Now, substituting the value of the radius into the area formula:

Area = 3.14 × (4.5 cm)²

Area = 3.14 ×20.25 cm²

Area = 63.585 cm²

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The probability that the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35% is approximately 82.38%.

Assuming the sample of 30 Americans is representative of the population, we can calculate the sample proportion as the number of individuals in the sample who agree divided by the total sample size. Let's assume that the sample proportion is p'.

To calculate the probability of the proportion exceeding 35%, we need to find the z-score of the value 0.35 using the formula:

z = (p' - p) / √[p * (1 - p) / n]

where p is the population proportion (which we don't know), and n is the sample size (30 in this case). We can use p' as an estimate of p.

Once we find the z-score, we can use a standard normal distribution table or a calculator to find the probability that the z-score is greater than the value we calculated. This probability is the probability that the proportion of Americans who agree that climate change is an immediate threat to humanity exceeds 35%.

For example, if p' = 0.4, then the z-score is:

z = (0.4 - 0.35) /√ [0.35 * (1 - 0.35) / 30] = 1.03

Using a standard normal distribution table, we can find that the probability of a z-score being greater than 1.03 is approximately 0.8238, or about 82.38%.

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Answer:

360 ft

Step-by-step explanation:

6 x 5 x 4 x 3 = 360

b. 360 ft

Each solid plastic cylinder with a radius of 2.51 cm and length of 5.64 cm has a charge of approximately 282.46 Coulombs.

To find the charge of each cylinder, we need to use the formula for the charge of a uniformly charged solid cylinder, which is given by Q = λ * V, where Q is the charge, λ is the charge density, and V is the volume of the cylinder.

First, we need to calculate the volume of each cylinder. The formula for the volume of a cylinder is V = π * r^2 * h, where r is the radius and h is the height or length of the cylinder.

Using the given values, we have r = 2.51 cm and h = 5.64 cm. Converting these values to meters, we get r = 0.0251 m and h = 0.0564 m.

Calculating the volume of each cylinder:

V = π * (0.0251 m)^2 * (0.0564 m) = 7.0925e-5 m^3

Now, we need to find the charge density λ. The charge density for each cylinder is given by λ = Q / V, where Q is the charge and V is the volume.

Since the radius and length are the same for all four cylinders, the charge density will also be the same. Therefore, we can calculate the charge density using one of the cylinders.

Assuming the charge density is λ, we can rearrange the formula to solve for λ:

λ = Q / V

Given that λ = 2.0 μC/m^3 (microCoulombs per cubic meter), we have:

2.0e-6 C/m^3 = Q / (7.0925e-5 m^3)

Solving for Q:

Q = (2.0e-6 C/m^3) * (7.0925e-5 m^3)

Q = 1.4185e-10 C

Therefore, the charge of each cylinder is 1.4185e-10 C, which is approximately equal to 282.46 Coulombs.

Each solid plastic cylinder with a radius of 2.51 cm and length of 5.64 cm has a charge of approximately 282.46 Coulombs. This calculation is based on the given charge density of 2.0 μC/m^3 and the formula for the charge of a uniformly charged solid cylinder.

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Answer:

144+19= 163

Step-by-step explanation:

hope this helps! Have a great day!

Answer:

163

Step-by-step explanation:

ADD

Given function in the question is,

        g(x) = |x + 1| - 5

Rules to remember for the translation a function,

        g(x) = |x - h|

        h(x) = |x + h|

        k(x) = |x| + k

        p(x) = |x| - k

Using these rules,

Function 'f' will be translated 1 units left and and 5 units down to form the image function 'g'.

       Therefore, Margo made an error to interpret that the function is translated 1 units right.

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Por lo tanto, la cantidad de interés que se pagará en el préstamo de 30,000 pesos durante 3 años con una tasa de interés anual del 17.5% es de 16,691.25 pesos.

para calcular la cantidad de interés que se pagará en un préstamo de 30,000 pesos con una tasa de interés anual del 17.5% durante 3 años, es necesario utilizar la fórmula de interés compuesto. Esta fórmula es: I = P * (1 + r)^n - P, donde I es el interés, P es el principal, r es la tasa de interés anual y n es el número de períodos.

En este caso, el principal es 30,000 pesos, la tasa de interés anual es del 17.5%, y el número de períodos es de 3 años. Entonces, podemos calcular el interés utilizando la fórmula:

I = 30,000 * (1 + 0.175)^3 - 30,000 = 16,691.25 pesos.

Es importante recordar que el interés compuesto aumenta con el tiempo, por lo que es importante considerar esto al planificar préstamos y financiamientos.

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The number of biscuits that can be made with 7 eggs given the ratio of 30 biscuits to 2 eggs is 105 biscuits.

Let

Number of biscuits to be made with 7 eggs = x

Number of biscuits : Number of eggs

30 : 2 = x : 7

30/2 = x/7

cross product

30 × 7 = 2 × x

210 = 2x

divide both sides by 2

x = 210/2

x = 105

Therefore, 105 biscuits can be made from 7 eggs.

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We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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James is (B) 20 meters far from the finish line 9 seconds after the race has started.

To find the distance:

Therefore, James is (B) 20 meters far from the finish line 9 seconds after the race has started.

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The complete question is given below:

James covers a distance of 8 meters in the first second of a 100-meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started?

a. 11

b. 20

c. 28

d. 80

Answer:

0.25

Step-by-step explanation:

:)

Answer: the absolute value of 1/4 is 1

Step-by-step explanation:

Answer:

11/36 = 0,305556 = 30,5556%

Step-by-step explanation:

5/6 * 5/6 = 25/36

36/36 - 25/36 = 11/36