Algebraically, the point (1, -5) satisfies the first inequality, but it does not satisfy the second inequality because -5 is not greater than -5. Graphically, the point (1, -5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore (1, -5) is not a solution to the given system of inequalities.

Using the sine rule and triangle ABC,   the height  is 14.43375ft. BAC=40° and ABC=30°

if C is 20° and  A is 50°

ABC=50°-20°=30°

BCA=20°+90°=110°

ABC+BCA+BAC=180°

30°+110°+BAC=180°

BAC=180°-140°=40°

Using the sine rule and triangle ABC,

opposite=x

adjacent =25 m.

tanθ =x/25

Multiplying both sides by 25 gives

x=25* tan 30° =25* 0.57735.=14.43375

To put it another way, there is only one plane that contains all of the triangles. All triangles are enclosed in a single plane on the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless otherwise specified, this article deals with triangles in Euclidean geometry, specifically the Euclidean plane.

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Answer:

volume

Step-by-step explanation:

Answer:

1.5 in

Step-by-step explanation:

To find the missing dimension (length), we can use the formula for the volume of a prism:

Volume = Base Area x Height

We know that the volume of the prism is 60 in³ and the height is 4 in. We also know that the base of the prism is a rectangle with a width of 2.5 in.

Base Area = Length x Width

We can rearrange the formula for volume to solve for the missing dimension:

Length = Volume / (Base Area x Height)

Base Area = Width x Length

Plugging in the given values, we get:

Base Area = 2.5 in x Length

Base Area x Height = 10 in²

Length = 60 in³ / (10 in² x 4 in)

Length = 1.5 in

Therefore, the missing dimension (length) of the prism is 1.5 inches.

Answer:

[tex]\theta = 60^\circ \;and\; \theta = 300^\circ[/tex]

Step-by-step explanation:

Given

[tex]\sin \left(2\theta\right)=\sin \left(\theta\right)[/tex]

Use the identity: [tex]\sin(2\theta) = 2 \sin(\theta)\cos(\theta)[/tex]

=> [tex]2 \sin(\theta)\cos(\theta) = \sin(\theta)[/tex]

Divide both sides by [tex]\sin(\theta)[/tex]

=> [tex]2 \cos(\theta) = 1[/tex]

[tex]= > \cos(\theta) = \dfrac{1}{2}[/tex]

[tex]= > \,\theta=\cos^{-1}\left(\dfrac{1}{2}\right)[/tex]

[tex]\cos^{-1}\left(\dfrac{1}{2}\right) \;is\: \dfrac{\pi}{3}} \text{ in the first quadrant and $\dfrac{5\pi}{3}$ in the fourth quadrant}}[/tex]

In degrees this corresponds to
[tex]\dfrac{\pi}{3} = \dfrac{\pi}{3} \times \dfrac{180^\circ}{\pi} = 60^\circ\\\\and\\\\\dfrac{5\pi}{3} = \dfrac{5\pi}{3} \times \dfrac{180^\circ}{\pi} = 300^\circ\\[/tex]

Answer
[tex]\theta = 60^\circ \;and\; \theta = 300^\circ[/tex]

The general solution to a 2nd order derivative for f(x) with real coefficients can be obtained by finding the other root of the auxiliary equation and then using those roots to write the general solution.

Since one of the roots of the auxiliary equation is 3 + 7i, the other root must be the conjugate of this root, which is 3 - 7i. This is because the coefficients of the auxiliary equation are real, so the roots must come in conjugate pairs.

Now that we have both roots, we can write the general solution to the 2nd order derivative as:

f(x) = e^(3x)(C1*cos(7x) + C2*sin(7x))

where C1 and C2 are arbitrary constants.

This is the general solution to the 2nd order derivative for f(x) with real coefficients when one of the roots of the auxiliary equation is 3 + 7i.

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Answer:

Mai is correct. We can use exponential notation to represent the number of coins each day. Let's call the number of coins on the first day "1". Then the number of coins on each subsequent day is twice the number of coins on the previous day. So we have:

Day 1: 1

Day 2: 2 = 2^1

Day 3: 4 = 2^2

Day 4: 8 = 2^3

...

Day n: 2^(n-1)

To find the number of coins Mai has on the 6th day, we substitute n = 6 into the formula for the number of coins:

Day 6: 2^(6-1) = 2^5 = 32

So Mai has 32 coins on the 6th day. Writing out the product of 2's (1.2.2.2.2.2.2) is equivalent to writing 2^6 = 32.

To find out how many coins Mai has after 28 days, we substitute n = 28 into the formula for the number of coins:

Day 28: 2^(28-1) = 2^27 = 134,217,728

So after 28 days, Mai has 134,217,728 coins.

The vector AC can be expressed in terms of vector AB and vector BC as follows:

In Euclidean geometry, a parallelogram is described as a simple quadrilateral with two pairs of parallel sides.

We have that  ABCD is a parallelogram, vector AC is equivalent to vector BD, which can be expressed in terms of vector AB and vector BC as follows:

Vector BD = Vector AB + Vector BC

We can substitute BD for AC in the above equation because  vector AC is equivalent to vector BD, we obtain the following:

Vector AC = Vector AB + Vector BC

In conclusion, vector AC can be expressed in terms of vector AB and vector BC as the sum of vector AB and vector BC.

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For the logarithmic function y = log (5x+6), the domain is (-6/5, [infinity]).

The domain of a logarithmic function is the set of all values for which the function is defined. In the case of y = log(5x+6), the function is only defined for values of x that make the expression inside the logarithm, 5x+6, greater than zero. This is because the logarithm of a negative number or zero is not defined.

To find the domain analytically, we need to solve the inequality 5x+6 > 0 for x:

5x+6 > 0

5x > -6

x > -6/5

This means that the domain of the function is all values of x greater than -6/5. In interval notation, this can be written as (-6/5, infinity).

So the domain of the logarithmic function y = log(5x+6) is (-6/5, infinity).

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The evaluated expressions are 2, -7, -2, -12, -8, and 7.

To evaluate the expressions without using a calculator, we need to substitute the given values of the variables into the expressions and simplify.

a. Substitutex=4into the expressionx−2

=4-2

=2

b. SubstituteB=−5into the expressionB−2

=-5-2

=-7

c. Substitutew=−2into the expression−w−4

=-(-2)-4

=2-4

=-2

d. Substitutey=−3into the expression(y)4

=(-3)4

=-12

e. Substitutet=4into the expression−t2

=-(4)2

=-8

f. SubstituteR=−10into the expression−R−3

=-(-10)-3

=10-3

=7

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The surface area of the solids are listed below:

In this problem we find three cases of unfolded solids, whose surface area must be determined. The surface area is the sum of the areas of all faces of the solid. The area formulas for the triangle and the rectangle are, respectively:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the surface area of the solids are listed below:

Case 1

A = (9 in)² + 0.5 · (9 in)²

A = 81 in² + 40.5 in²

A = 121.5 in²

Case 2

A = 4 · (10 cm) · (2 cm) + (2 cm)²

A = 80 cm² + 4 cm²

A = 84 cm²

Case 3

A = 3 · (8 ft) · (10 ft) + 2 · (8 ft) · (5 ft)

A = 240 ft² + 80 ft²

A = 320 ft²

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If Ella is 15 meters away from Mary and 9 meters away from Dante, then distance between Dante and Mary are 12 meters away from each other.

It is given that Ella is 9 meter away from Dante and in the Dante is in south of Ella. This means that if we consider a plane ground and mark the directions as north, south, east and west, Ella and Dante will be in north and south direction respectively. Since Mary is in the east direction of Dante, this means She will be in the South East direction of Ella and about 15 meters away from her. This creates a triangular connection between them.

Hence by applying the Pythagoras theorem, we get following equation:

ED^2 + DM^2 = EM^2

where,

ED = Distance between Ella and Dante

DM = Distance between Dante and Mary

EM = Distance between Ella and Mary

9^2 + DM^2 = 15^2

81 + DM^2 = 225

DM^2 = 144

DM = 12

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Answer:

That is true.

Answer: True

Step-by-step explanation:

due to the fact that its 2 and every time you multiply by the factor itll equal a even number

A permutation matrix is a square matrix that has exactly one entry of 1 in each row and each column, and all other entries are 0. When a permutation matrix is multiplied with another matrix, it rearranges the rows of the other matrix.

For matrix A = \begin{bmatrix}-1 & 2 & -2\\ 2 & 3 & 5\\ 1 & 2 & 2\end{bmatrix}

(a) A permutation matrix P that allows for an LU decomposition of PA is P = \begin{bmatrix}0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1\end{bmatrix}

When we multiply P and A, we get PA = \begin{bmatrix}0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1\end{bmatrix}\begin{bmatrix}-1 & 2 & -2\\ 2 & 3 & 5\\ 1 & 2 & 2\end{bmatrix} = \begin{bmatrix}2 & 3 & 5\\ -1 & 2 & -2\\ 1 & 2 & 2\end{bmatrix}

(b) An LU decomposition of PA is L = \begin{bmatrix}1 & 0 & 0\\ -0.5 & 1 & 0\\ 0.5 & 0 & 1\end{bmatrix} and U = \begin{bmatrix}2 & 3 & 5\\ 0 & 3.5 & 4.5\\ 0 & 0 & -0.5\end{bmatrix}

So, PA = LU = \begin{bmatrix}1 & 0 & 0\\ -0.5 & 1 & 0\\ 0.5 & 0 & 1\end{bmatrix}\begin{bmatrix}2 & 3 & 5\\ 0 & 3.5 & 4.5\\ 0 & 0 & -0.5\end{bmatrix} = \begin{bmatrix}2 & 3 & 5\\ -1 & 2 & -2\\ 1 & 2 & 2\end{bmatrix}

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To find out how many of each product Derrick can buy, we can use algebra. Let's call the number of headphones x and the number of cell phone cases y. We can set up an equation to represent the situation:

26x + 14y = 150

Now we can solve for one of the variables in terms of the other. Let's solve for y:

14y = 150 - 26x

y = (150 - 26x)/14

Now we can plug in different values for x and see what values of y will result in a total cost of at least $150. For example, if x = 1, then y = (150 - 26)/14 = 8.86. This means that Derrick could buy 1 pair of headphones and 8 cell phone cases for a total cost of $150.

Similarly, if x = 2, then y = (150 - 52)/14 = 7. This means that Derrick could buy 2 pairs of headphones and 7 cell phone cases for a total cost of $150.

We can continue plugging in different values for x until we find a combination of products that will cost at least $150. Alternatively, we could use a graphing calculator or an online graphing tool to graph the equation and find the intersection points with the line y = 150. These intersection points will represent the combinations of products that will cost at least $150.

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Answer: Your welcome!

Step-by-step explanation:

The ratio of 24kg is 3:5, which means 3 parts of 24kg is 3 times the 5th part of 24kg.

Therefore, 3 parts of the 24kg is 18kg and 5 parts of the 24kg is 6kg.

The correct option is B, The area of the figure will be the sum of the area of the rectangle and half the area of the circle is 220 cm².

The rectangle has a length of 22 cm and a width of 10 cm, so its area is:

A_rectangle = length × width = 22 cm × 10 cm = 220 cm²

A rectangle is a four-sided polygon with opposite sides parallel and equal in length. The area of a rectangle is the measure of the space that it occupies and is given by the product of its length and width.

To find the area of a rectangle, one needs to multiply the length of the rectangle by its width. For example, if the length of the rectangle is 5 meters and its width is 3 meters, the area would be 15 square meters. This is because 5 multiplied by 3 is equal to 15. In general, the formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width. The units of the area will depend on the units of the length and width.

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Complete Question: -

The drawing is composed of a rectangle and a semicircle Find the area of the figure to the nearest unit:

Not drawn to scale.

a. 41 cm^2

b. 220 cm^2

c. 410 cm^2

d. 820 cm2

Ben's ball lands approximately 2.5 seconds after Andrew's ball.

Since the value of parameter a is -5 for both balls, the height of each ball follows the equation:

h(t) = -5t² + vt + h0

where;

Let's assume that Andrew's ball is hit with an initial velocity of v1, and Ben's ball is hit with an initial velocity of v₂. We also know that Ben's ball reaches a maximum height 50% greater than Andrew's, which means that:

h_max2 = 1.5h_max1

At the maximum height, the velocity of the ball is zero, so we can find the time it takes for each ball to reach the maximum height by setting v = 0 in the equation for h(t):

t_max1 = v₁ / (2 x 5)

t_max2 = v₂ / (2 x 5)

Since Ben's ball reaches a maximum height that is 50% greater than Andrew's, we can write:

h_max2 = 1.5h_max1

-5(t_max2)² + v₂t_max2 + h0 = 1.5(-5(t_max1)² + v1 * t_max1 + h0)

Simplifying this equation, we get:

-5(t_max2)² + v₂t_max2 = -7.5(t_max1)² + 1.5v₁t_max1

We also know that Andrew's ball lands after 4 seconds, which means that h(4) = 0:

h(4) = -5(4)² + v1 * 4 = 0

-80 + 4v1 = 0

v1 = 80/4

v1 = 20 m/s

Solving these equations for t_max2 and v2, we get:

t_max1 = v1 / (2 x 5)

t_max1 = 20 / (2 x 5)  = 2 s

t_max2 = 1.5 * t_max1 = 3 s

v2 = 1.5 * v1 = 30 m/s

To find the time it takes for Ben's ball to land, we need to find the time t2 when h(t2) = 0.

We can use the equation for h(t) with v = v2, h0 = 0, and solve for t:

-5t² + v₂t = 0

-5t² + 30 = 0

5t² = 30

t² = 30/5

t² = 6

t = √6

t = 2.5 s

Therefore, Ben's ball lands approximately 2.5 seconds after Andrew's ball.

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The scale factor of the preimage to image is 3. Then the correct option is C.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The picture rectangle has points on coordinates (0, 0), (0, 8), (9, 8), and (9, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).

The scale factor is given as,

SF = 9 / 3

SF = 3

The scale factor of the preimage to image is 3. Then the correct option is C.

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The complete question is given below.

What is the scale factor in the dilation?

On a coordinate plane, the image rectangle has points (0, 0), (0, 8), (9, 8), and (8, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).

a) One-sixth

b) One-third

c) 3

d) 6

Answer:

Step-by-step explanation: C  !!!!!! / 3

Edge 2023

1/6

1/3

3   <--------------- correct

6

The target is 4125 feet away from the bullet.

To find the distance between the target and the bullet, we need to use the formula distance = speed × time. We have two distances to find: the distance the bullet travels and the distance the sound travels. Let's call the distance between the target and the bullet d.

The distance the bullet travels is given by:
d = 3300 × t

The distance the sound travels is given by:
d = 1100 × (t - 2.5)

Since the two distances are equal, we can set the two equations equal to each other and solve for t:

3300 × t = 1100 × (t - 2.5)
3300t = 1100t - 2750
2200t = 2750
t = 1.25

Now that we have the time, we can plug it back into one of the equations to find the distance:

d = 3300 × 1.25
d = 4125 feet

So the target is 4125 feet away from the bullet.

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The length of TS is 30.

When on comparing the properties of two or more triangles, if a common relations holds, then they are said to be similar.

Note that similarity is NOT congruency.

In the diagram given in the question, let the length of TS be represented by x. So that;

TS/ QS = SU/ SR

But, we have;

TS = x

SU = TS - 6 = x - 6

So that;

x/ 55 = (x - 6)/ 44

44x = 55(x - 6)

      = 55x - 330

330 = 55x - 44x

330 = 11x

x = 330/ 11

 = 30

x = 30

Therefore, the length of TS is 30.

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1) Cannot be determined.

2) Surface area of the cylinder with radius 4 inches and height 3 inches is 100.48 square inches.

3) Exact surface area of the cylinder with radius 1 and three-fourths centimeters and height 3 and one-fourth centimeters is 35 and seven-eighths times pi square centimeters.

4) The area of icing needed for one red velvet cake with a radius of 13 centimeters and a height of 15 centimeters is approximately 459 square centimeters.

What is the surface area of the cylinder?

The surface area of a cylinder is the total area of all its curved and flat surfaces. It is given by the formula:

Surface Area = 2πr² + 2πrh

To answer these questions, we need to use the formula for the surface area of a cylinder:

Surface Area = 2πr² + 2πrh

where r is the radius of the circular base of the cylinder, h is the height of the cylinder, and π is the mathematical constant pi.

We are given that the container was covered in plastic wrap during manufacturing. We are not given the dimensions of the container, but we can assume it is a cylinder. Therefore, we need to calculate the surface area of the cylinder. We are not given the values of r and h, so we cannot calculate the surface area directly. Therefore, we cannot determine the answer to this question.

We are given the net of a cylinder with a labeled radius of 4 inches and a labeled height of 3 inches. To find the surface area of the cylinder, we need to use the formula:

Surface Area = 2πr² + 2πrh

Substituting r = 4 and h = 3, and using π ≈ 3.14, we get:

Surface Area = 2(3.14)(4²) + 2(3.14)(4)(3) = 100.48 in²

Therefore, the surface area of the cylinder is 100.48 in².

We are given a cylinder with a labeled radius of 1 and three-fourths centimeters and a labeled height of 3 and one-fourth centimeters. To find the surface area of the cylinder, we need to use the formula:

Surface Area = 2πr² + 2πrh

Substituting r = 1.75 and h = 3.25, we get:

Surface Area = 2(3.14)(1.75²) + 2(3.14)(1.75)(3.25) = 35.875π cm²

Therefore, the exact surface area of the cylinder in terms of π is 35 and seven-eighths times pi square centimeters.

We are given a red velvet cake with a radius of 13 centimeters and a height of 15 centimeters. We need to find the area of the circular top of the cake, which is the same as the surface area of a cylinder with radius 13 and height 0. We can use the formula:

Surface Area = 2πr² + 2πrh

Substituting r = 13 and h = 0, we get:

Surface Area = 2(3.14)(13²) + 2(3.14)(13)(0) = 1061.76 cm²

We need to subtract this from the surface area of the whole cylinder (the cake) to find the area of the icing. Using the formula again with r = 13 and h = 15, we get:

Surface Area = 2(3.14)(13²) + 2(3.14)(13)(15) = 1520.6 cm²

Therefore, the area of icing needed for one cake is:

1520.6 - 1061.76 = 458.84 cm²

Rounding this to the nearest square centimeter, we get:

459 cm²

Therefore, approximately 459 square centimeters of icing is needed for one cake.

Hence,

1) Cannot be determined.

2) Surface area of the cylinder with radius 4 inches and height 3 inches is 100.48 square inches.

3) Exact surface area of the cylinder with radius 1 and three-fourths centimeters and height 3 and one-fourth centimeters is 35 and seven-eighths times pi square centimeters.

4) The area of icing needed for one red velvet cake with a radius of 13 centimeters and a height of 15 centimeters is approximately 459 square centimeters.

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The property illustrated in "√2+√8 is a real number" is the closure property of addition,

The property illustrated in the given statement is the closure property of addition, which states that the sum of two real numbers is also a real number.

The closure property of addition states that the sum of any two real numbers is also a real number. In the given statement, √2 and √8 are both real numbers, and therefore their sum √2+√8 is also a real number.

This property applies to all real numbers, and it is an important property of the number system. which states that the sum of two real numbers is also a real number.

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By answering the above question, we may infer that The input value 0 equation represents the height at sea level, making it an inappropriate value for this function.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

For the predicament, the following input values would be suitable:

B) 1

C) 2

D) 3

E) 4

As the temperature drops by around 5°F for every 1,000 feet of height, we must utilise altitude numbers in thousands of feet to obtain the function's proper input values. Hence, we would utilise a value of 1 as an input for every 1,000 feet of height rise. Consequently, 1, 2, 3, and 4 would be the proper input values, which correspond to altitudes of 1,000, 2,000, 3,000, and 4,000 feet, respectively. The input value 0 represents the height at sea level, making it an inappropriate value for this function.

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The both triangles are not similar.

Similar triangles are triangles that have the same shape but may have different sizes. Two triangles are considered similar if their corresponding angles are equal, and their corresponding sides are in proportion or have the same ratio.

In other words, if two triangles have the same angles, then they are similar. The ratio of the lengths of the corresponding sides of similar triangles is the same, and this ratio is called the scale factor.

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The equation of y=x^(2) can be translated 8 units to the left and then 6 units downward by modifying the equation as follows:

y=(x+8)^(2)-6

This equation represents the same parabola as y=x^(2), but it has been shifted 8 units to the left and 6 units downward.

The translation of a function can be represented by modifying the equation in the form y=f(x-h)+k, where h is the horizontal shift and k is the vertical shift. In this case, h=-8 and k=-6, so the equation becomes:

y=f(x-(-8))+(-6)
y=f(x+8)-6

Substituting the original function f(x)=x^(2) into this equation gives:

y=(x+8)^(2)-6

Therefore, the equation of y=x^(2) when it is translated 8 units to the left and then 6 units downward is y=(x+8)^(2)-6.

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pls edit yours and i will give an answer

Step-by-step explanation:

Answer:

I can't order the numbers without knowing the numbers sorry

Answer:

I think 2nd option..........

Answer:

A, I and III

Step-by-step explanation:

The origin is the point in the center of a graph, where the x- and y-axes intersect. This point is also (0,0).

The product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form is (4/3)x^2 + (13/9)x + (10/9).

To express the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form, we need to multiply the two binomials using the distributive property.

First, we will multiply the first term of the first binomial by each term of the second binomial:
(2/3)x * 2x = (4/3)x^2
(2/3)x * (5/6) = (10/18)x = (5/9)x

Next, we will multiply the second term of the first binomial by each term of the second binomial:
(4/3) * 2x = (8/3)x
(4/3) * (5/6) = (20/18) = (10/9)

Now we will combine like terms:
(4/3)x^2 + (5/9)x + (8/3)x + (10/9) = (4/3)x^2 + (13/9)x + (10/9)

Therefore, the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form is (4/3)x^2 + (13/9)x + (10/9).

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