Simplify the expression:
(6x - 3) + (5x + 7) and if u can show steps

From the given information, the area of the rectangle is 36√3 cm

From the question, we are to determine the area of the rectangle

From the given information,

The width of the rectangle is 6cm

and

The length of the rectangle is 6√3 cm

From the formula for calculating the area of a rectangle, we have that

Area of rectangle = Length × Width

Area of rectangle = 6√3 cm × 6 cm

Area of rectangle = 6 × 6 √3 cm²

Area of rectangle = 36√3 cm²

Hence, the area is 36√3 cm²

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Answer:

length =  4 width = 4 height = 10

Step-by-step explanation:

8x4x5 = 160

4x4x10 = 160

The first four nonzero terms in the series expansion about x = 0 for a solution to the given equation 25x^2y + 15x^2y + By = 0 are y(x) = a₀ + a₂x^2 + a₄x^4 + a₆x^6 = a₀ - (5B/42)x^4 + (25B/112) x^6 - (245B/1728) x^8.

Using the method of Frobenius and the larger indicial root, the first four nonzero terms for the series expansion about x = 0 for a solution to the equation 25x²y + 15x²y + By = 0 are y(x) = a[1 - (3/7)x² + (15/11)x⁴ + O(x⁶)].

For the equation 16x³y'' + 4x²y + 3y = 0, the coefficients a₀, a₁, and a₂ are 1, 0, and -15/224, respectively, and the first four terms for the solution to the differential equation are y(x) = a₀[1 - (3/16)x² + (15/512)x⁴ + O(x⁶)].

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Answer:

5000 x 0.065 x 3

975 +5000

5975

Answer:

$5975

Step-by-step explanation:

SI = 5000•0.065•3

SI = 975

Total amount = 5000 + 975 = 5975

Answer:

-2.5

Step-by-step explanation:

Surface area of a prism and surface area of a cylinder  involve finding the sum of the areas of all the faces that make up the solid shape.

Finding the surface area of a prism and finding the surface area of a cylinder have similarities and differences.

Similarities:

Both involve finding the sum of the areas of all the faces that make up the solid shape.

Both use basic geometric formulas to calculate the area of individual faces (e.g., rectangles for prisms, circles for cylinders).

Differences:

Faces: A prism has two congruent parallel bases connected by rectangular faces, whereas a cylinder has two circular bases connected by a curved surface.

Formulas: The formulas for finding surface area differ. For a prism, you calculate the sum of the areas of the bases and the lateral faces. The surface area of a rectangular prism is given by 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height, respectively. For a cylinder, you calculate the sum of the areas of the two bases and the lateral surface area. The surface area of a cylinder is given by 2πr² + 2πrh, where r is the radius and h is the height.

Shape: Prisms have flat faces and straight edges, while cylinders have curved surfaces.

While both involve calculating the sum of the areas of the faces, prisms and cylinders differ in terms of their faces, formulas, and overall shape.

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L(t) = (2/3)t + 3, (-1/2)t + 4, t + 2.

The curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 can be found by setting the two equations equal to each other:

x² + y² = y² + z² = 20

The intersection of the two cylinders is a circle.

To determine the radius of this circle, we use either of the two equations and solve for one variable in terms of the other two:

y² + z² = 20y²

= 20 - z²y

= ±sqrt(20 - z²)

If we substitute this expression for y into the equation x² + y² = 25, we can solve for x in terms of z:

x² + (20 - z²)

= 25x²

= 5 + z²x

= ±sqrt(5 + z²)

Thus, the curve of intersection can be expressed parametrically as follows:

r(t) = (x(t), y(t), z(t)) = (sqrt(5 + t²), sqrt(20 - t²), t)for -2sqrt(5) ≤ t ≤ 2sqrt(5)

At the point (3, 4, 2), t = 2.

To find the tangent vector to the curve at this point, we take the derivative of the position vector:

r'(t) = (x'(t), y'(t), z'(t)) = (t/sqrt(5 + t²), -t/sqrt(20 - t²), 1)

at t = 2:r'(2) = (2/sqrt(9), -2/sqrt(16), 1) = (2/3, -1/2, 1)

Finally, we obtain the vector equation of the tangent line by using the point-normal form of the equation of a line:

L(t) = r(2) + t r'(2)L(t)

     = (3, 4, 2) + t (2/3, -1/2, 1)L(t)

     = (2/3)t + 3, (-1/2)t + 4, t + 2

Therefore, a vector equation for the tangent line to the curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 at the point (3, 4, 2) is:

L(t) = (2/3)t + 3, (-1/2)t + 4, t + 2.

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Directed numbers are numbers that have either a positive or negative sign, which can be shown on a number line. Therefore, point F is Fifteen-halves of line segment DE.

A number line is a system that can show the positions of positive or negative numbers. It has its ends ranging from negative infinity to positive infinity. Thus any directed number can be located on the line.

Directed numbers are numbers with either a negative or positive sign, which shows their direction with respect to the number line.

In the given question, the distance between points D and E is 9 units. So that dividing 9 units in the ratio of 5 to 6, we have;

\(\frac{5}{6}\) x 9   = \(\frac{45}{6}\)

          = \(\frac{15}{2}\)

Therefore, the location of point F, which partitions the directed line segment from d to E into a 5:6 ratio is    \(\frac{15}{2}\). Thus the answer is Fifteen-halves.

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Answer:

1/11

Step-by-step explanation:

Got it right on assignment

Answer:

10 miles

Step-by-step explanation:

Answer:

8.49

Step-by-step explanation:

Posted in the image due to lack of proper format.

(a) The initial speed of the projectile - 28.2m/s

(b)The total time interval the projectile was in flight - 4.07s.

a) When a projectile is launched with speed \(v_{i}\) at an angle above the horizontal, the initial velocity components are \(v_{xi}\) = \(v_{i}\) cos\(θ\) and                  \(v_{yi}\)= \(v_{i}\) sin\(θ\) . Neglecting air resistance, the vertical velocity when the projectile returns to the level from which it was launched (in this case, the ground) will be \(v_{y} = - v_{yi}\) .

From this information, the total time of flight is found  \(v_{yf} = v_{yi} + a_{y}\) to be

         \(t_{total} = \frac{v_{yf} - v_{yi} }{a_{y}}\)   = \(\frac{-v_{yi} - v_{yi} }{-g}}\)  = \(\frac{2v_{yi} }{g}\)

         \(t_{total} = \frac{2v_{i}sinθ }{g}\)

Since the velocity of a projectile with no air resistance is constant, the horizontal distance it will travel in this time is given by

R = \(v_{xi} t_{total} = (v_{i} cosθ_{i}) \frac{2v_{i}sinθ }{g}\)  =  \(\frac{v^{2}_{i}}{g}( 2sinθ_{i} cosθ_{i} )\) = \(\frac{v^{2} _{i} (sin2θ_{i} ) }{g}\)

Thus, if the projectile is to have a range of R=81.1m when launched at an angle of \(θ_{i}\)=45.0°, the required initial speed is

\(v_{i} = \sqrt{\frac{81.1 * 9.80}{sin90} }\) = 28.2 m/s

Therefore, the initial speed of the projectile - 28.2m/s

b) With \(v_{i}\)=28.2m/s and \(θ_{i}\) = 45.0°, the total time of flight (as found

above) will be

        \(t_{total} = \frac{2v_{i}sinθ }{g}\)  = \(\frac{2(28.2 m/s) sin45}{9.80m/s^{2}}\) = 4.07s

∴The total time interval the projectile was in flight - was 4.07s.

c) Note that at \(θ_{i}\) =45.0° that sin(2\(θ_{i}\)) will decrease as \(θ_{i}\) is increased above this optimum launch angle. Thus, if the range is to be kept constant while the launch angle is increased above 45.0°, we see from \(v_{i}\) = \(\sqrt{\frac{Rg}{sin2θ_{i}} }\)that the required initial velocity will increase.

Observe that for \(θ_{i}\) <90°, the function sin\(θ_{i}\) increases as \(θ_{i}\) it increased. Thus, increasing the launch angle above 45.0° while keeping the range constant means that both \(v_{i}\) sins will increase. Considering the expression  \(t_{total}\) given above, we see that the total time of flight will increase.

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The correct question is :

The record distance in the sport of throwing cowpats is 81.1m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time interval the projectile was in flight. (c) How would the answers change if the range were the same but the launch angle was greater than 45°? Explain.

Answer:

sup

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x + 3 = 4x - 5

-2x + 3 = -5

-2x = -8

x = 4

Answer: x=4

Step-by-step explanation:

Answer: 120 copies

Step-by-step explanation:

Takes 480 divided by 4 = 120 copies per minute

Answer:

Step-by-step explanation:

1,008/1.8=10,080/18

18)10080(560

     90

    -

   ----------

      108

      108

     -

   ------------

           0

 ---------------

The polynomial 3xA² is a linear monomial having one term and a degree one.

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

There are many types of polynomials according to the number of terms they have.

If a polynomial has one term it is called a monomial, Has two terms called a binomial, and having three makes it a trinomial.

Given, A polynomial 3xA².

Now, The variable is 'x' and raised to the power of 1 so it is linear and consists of only one term so it is a monomial as 3 and A are constants.

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The longest path will have a length of 2n, which is even.

In the complete bipartite graph Km,n with m red nodes and n blue nodes, every red node is connected to every blue node. When m > n, there are more red nodes than blue nodes. To create the longest path in Km,n, we alternate between red and blue nodes, starting with a red node and ending with a blue node.

Since we start and end with different colored nodes, the length of the longest path will be an even number, as it takes two steps to return to the original color (red-blue or blue-red). In this case, the longest path will have a length of 2n, which is even.

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The statement "the algebraic and spreadsheet formulations of a linear programming model both have advantages" is true. (Option 3)

Both algebraic and spreadsheet formulations have their own advantages and disadvantages. Algebraic models allow for a more formal mathematical representation of the problem, making it easier to see relationships between variables and constraints. They also allow for the use of powerful optimization solvers to quickly find optimal solutions.

On the other hand, spreadsheet models allow for more intuitive modeling and visualization of the problem. They also allow for quick and easy scenario analysis and sensitivity testing. Furthermore, they are more accessible to a wider range of users who may not have the technical background to create and solve complex algebraic models.

Therefore, the choice between the two formulations depends on the specific problem and the preferences and expertise of the modeler.

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Complete Question:

which of the following statements about linear programming models is true? multiple choice question.

Answer:

srry if this is wrong but 13!

Answer:

-4/10

Step-by-step explanation:

3/10 + (−7/20)

= 3/10 - 7/10

= -4/10

Answer:

-4/10

Step-by-step explanation:

Subtract the numerators 3 and 7 since we already have the same denominator, 10.

3 - 7 = -4

So, we get -4/10

The probability that a particular death is due to an automobile accident is 4%

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

total deaths in recent years = 1158

automobile accident resulted = 46 accidents

cancer deaths resulted = 226 accidents

heart disease deaths resulted = 388 accidents

the probability that a particular death is due to an automobile accident = 46/1158

                     = 0.04 or 4 % chances

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Answer:

option A is correct answer of this qn

The word which best describes XV is Angle Bisector.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given is a triangle XYZ.

Here a line segment is drawn from the vertex X to the opposite side YZ.

Median is the line segment joining the vertex of a triangle to the mid point of the opposite side.

Here, it is not given that, YV = ZV, so it is not median.

Altitude is the perpendicular line joining the vertex to the opposite side.

Here, it is not given the line is perpendicular. so it is not altitude.

Perpendicular bisector is a line that bisects the opposite line in to right angles. It is also not given.

Angle bisector is a line which divide the angle from which the line is drawn. here it is given that both angles equal to 40°.

So the line is angle bisector.

Hence the correct option is Angel Bisector.

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Answer:

y=1/3x+2

Step-by-step explanation:

y=1/3x+b

3=1/3(3)+b

3=1+b

-1 -1

2=b

Answer:

95

Step-by-step explanation:

180 is a straight line, and it gives u 85, so you subtract 85 from 180 and get 95 which is the answer. If it helped you please give me brainliest

15 liquids that can be found in a kitchen include:

15 solids in a kitchen are:

When it comes to solids in the kitchen, we can mostly find either food ingredients, such as salt, flour, and spices, or actual food that can be prepared such as meat, vegetables, and bread.

As for liquids, these can be anything from drinks such as juice, water and wine, to liquids used for cooking such as oil, soy sauce and vinegar.

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The solution of the equation is ( x - 5 )² +23 = 0.

Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant.

Mathematical symbols can represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping, as well as the order of operations and other features of logical syntax.

Given that the equation is x²-10x = 3. The equation will be solved by completing the square method as below,

x²-10x = 3

x² - 10x - 3 = 0

( x - 5 )² - 3 + 5² = 0

( x - 5 )² - 3 + 25 = 0

( x - 5 )² + 23 = 0

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Answer:

To convert a base-10 pure fraction to a base-n pure fraction (where n is a decimal integer greater than or equal to 2), we use the multiplication method. Here are the conversions for 0.610595703125D to base-2, base-8, and base-16:
1. Conversion to Base-2:
To convert 0.610595703125D to base-2, we need to repeatedly multiply the fractional part by 2, taking the integer part at each step. We stop when the fractional part becomes 0 or when we have obtained the required number of digits after the decimal point.
0.610595703125D * 2 = 1.22119140625D → 1
0.22119140625D * 2 = 0.4423828125D → 0
0.4423828125D * 2 = 0.884765625D → 0
0.884765625D * 2 = 1.76953125D → 1
0.76953125D * 2 = 1.5390625D → 1
0.5390625D * 2 = 1.078125D → 1
0.078125D * 2 = 0.15625D → 0
0.15625D * 2 = 0.3125D → 0
0.3125D * 2 = 0.625D → 0
0.625D * 2 = 1.25D → 1
0.25D * 2 = 0.5D → 0
0.5D * 2 = 1D → 1
Therefore, 0.610595703125D in base-2 is 0.100111000101B.
2. Conversion to Base-8:
To convert 0.610595703125D to base-8, we need to repeatedly multiply the fractional part by 8, taking the integer part at each step. We stop when the fractional part becomes 0 or when we have obtained the required number of digits after the decimal point.
0.610595703125D * 8 = 4.884765625D → 4
0.884765625D * 8 = 7.078125D → 7
0.078125D * 8 = 0.625D → 0
0.625D * 8 = 5D → 5
0D * 8 = 0D → 0
0D * 8 = 0D → 0
0D * 8 = 0D → 0
0D * 8 = 0D → 0
Therefore, 0.610595703125D in base-8 is 0.4715162O.
3. Conversion to Base-16:
To convert 0.610595703125D to base-16, we need to repeatedly multiply the fractional part by 16, taking the integer part at each step. We stop when the fractional part becomes 0 or when we have obtained the required number of digits after the decimal point.
0.610595703125D * 16 = 9.76953125D → 9
0.76953125D * 16 = 12.3125D → C
0.3125D * 16 = 5D → 5
0D * 16 = 0D → 0
0D * 16 = 0D → 0
0D * 16 = 0D → 0
0D * 16 = 0D → 0
0D * 16 = 0D → 0
Therefore, 0.610595703125D in base-16 is 0.9C5.

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The distance between the tennis balls and the cans is 49.46 cubic inches.

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

Given: Each ball has a diameter of three inches.

Three tennis balls are contained in each can, which is how they are sold.

Each can has a cylindrical shape.

We start by determining each tennis ball's volume.

Because of their spherical shape, their volume is determined by

\($V=\frac{4}{3} \pi r^3$\)

Where \($r=\frac{d}{2}=\frac{3 \text { in }}{2}=1.5 i$\) in

Replacing the radius and using \($\pi \approx 3.14$\), we have

\($V=\frac{4}{3}(3.14)(1.5 \mathrm{in})^3=14.13 \mathrm{in}^3$$\)

Therefore, the volume of each tennis ball exists 14.13 cubic inches, approximately.

Assuming that the diameter of each ball exists congruent with the diameter of the can, we contain the volume of a cylinder defined by

\($V=\pi r^2 h$\)

Where, r = 1.5 in and h = 3(3 in)=9 in, because each can has three balls, and the height exists the sum of all three diameters.

\($V=3.14(1.5 i n)^2(9 i n)=63.59 n^3$$\)

Therefore, the volume of each can exists 63.59 cubic inches, approximately.

The complete question is:

Tennis balls with a 3 inch Diameter are sold in cans of three. The can is a cylinder

A)what is the volume of one tennis ball ?

B)what is the volume of the cylinder ?

C)how much space is not occupied by the tennis balls in the can?

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The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.

To convert Decimal into Fraction form:

Do the following Steps:

Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.

Step 2: Remove the decimal places by multiplication.

Step 3: Reduce the fraction.

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Given,

The smallest flowering plant is the flowering aquatic duckweed found in Australia.

And it is 0.0236 inch long and 0.0129 inch wide.

Here we need to write these dimensions as fractions in simplest form.

Rewrite the decimal number as a fraction with 1 in the denominator

So,

=> 0.0236/1 and 0.0129/1

Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.

Then we get,

=> 236/10000 and 129/10000

Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,

=> 59/2500

But the fraction 129/10000 is not reducible.

Therefore, the fraction form is,

=> 59/2500 in. long and 129/10,000 in. wide.

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