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A partial sum limit is the sum of the series.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.

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In the given Rhombus ABCD, the measure of side AE = 27.85.

Verify that the two diagonals are parallel to one another. The diagonal lines are parallel. A rhombus is what it is. The parallelogram is a rectangle, rhombus, and square since the diagonals are all congruent and perpendicular to one another.

Area can be used to determine the area of a rhombus because it is a parallelogram, and its area can be determined from the length of its base and perpendicular height.

Here, we construct an alternate formula for the area of a rhombus that uses the lengths of its diagonals. Find the length of the other diagonal if one of the diagonals is 8 units long. We already know how to compute the area of a rhombus using its diagonals: Area = (1/2) (diagonal1 diagonal2) 256 = (1/2) (8 diagonal2).

AB = 26

BD = 20

BD/2 = 10

Using Pythagorean theorem:

[tex]AE = \sqrt{26^2 + 10^2}[/tex]

AE = 27.85

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Answer:512

Step-by-step explanation:

Answer:

this is answer ️️️️️️

Answer: we would need 7 bags of fertilizer to cover the area of the triangle.

Step-by-step explanation:

To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle can be found by taking the square root of the semi-perimeter multiplied by the difference of the semi-perimeter and each side length.

The semi-perimeter of the triangle is (2.1+1.8+2.7)/2 = 2.7

The area of the triangle is sqrt(2.7*(2.7-2.1)(2.7-1.8)(2.7-2.7)) = sqrt(2.70.60.9*0) = 1.35

Each bag of fertilizer covers 0.2 square miles, so we need to divide the area of the triangle by the area covered by each bag to find how many bags are needed: 1.35 / 0.2 = 6.75

Rounding up to the nearest whole number, we would need 7 bags of fertilizer to cover the area of the triangle.

Answer:

Step-by-step explanation:

Given similar triangles DEF and GHF, and side lengths DE = 6, EF = 10, GH = 21, FG = 28, you want the lengths of y=FH and x=FD.

Corresponding sides of similar triangles are proportional. This means ...

  DE/GH = EF/HF = FD/FG

  6/21 = 10/y = x/28

We can multiply by 28 to solve for x:

  x = 28(6/21) = 8

Multiplying by 21y/6 will give the value of y:

  y = (21/6)(10) = 35

The values of x and y are 8 and 35, respectively.

__

Additional comment

These are both 3-4-5 right triangles. The smaller is multiplied by 2; the larger is multiplied by 7 to give 6-8-10 and 21-28-35 triangles.

To write algebraic expression for an equivalent expressions, we need to be sure that each side of the equal sign amounts to the same number. An example of an equivalent equation would be:

4x + 2 = 2(2x + 1)

An algebraic expression is a sequence of numbers, variables, mathematical operations, and sometimes exponents. For example, 4x + 3 is a basic algebraic expression. Also see there is no equal sign in the algebraic expression. If so, it can be an equation or set of numbers containing one or more variables.

Equivalent Expressions: Equivalent expressions are expressions that look different but have the same value. Writing the equivalent formula makes it easier to work with and solve. Two Ways to Write the Equivalent Expressions :

1) Write expression using the distributed property:

2) Write equivalent expressions by combining same terms. Same terms are terms that have the same variables raised to the same powers. For example, the list shows several pairs of similar terms, 4t and 5t ; 9k³and 2k³ ; 1.4xy and 6.7xy.

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(0,3) , (4,0) are two solution of equation 3x + 4y = 12.

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts, separated by an equal sign (=), with the expressions on either side representing the same value.

Given Linear equation in two variables:

3x + 4y = 12 ----( 1 )

Substitute x = 0 , in equation ( 1 ) ,

3 × 0 + 4y = 12

=> 4y = 12

=> y = 12/4

y = 3

Therefore ,

( x , y ) = ( 0 , 3 )

Substitute y = 0 in equation ( 1 ) ,

3x + 4 × 0 = 12

=> 3x = 12

=> x = 12/3

x = 4

Therefore,

( x , y ) = ( 4 , 0 )

Required two solutions are ( 0 , 3 ) , ( 4 , 0 )

Therefore, (0,3) , (4,0) are two solution of equation 3x + 4y = 12.

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Answer:

  5) x = 5

  6) x ≈ 51.47

Step-by-step explanation:

It looks like you're being asked to solve for x the equations ...

These are solved in the way any such equation is solved, though you need a calculator to find the values of the trig functions.

Multiply by the denominator:

  x = 10·sin(30°) = 5

Multiply by x, then divide by cos(39°):

  x = 40/cos(39°) ≈ 51.47

hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: [tex]y=4x-9[/tex]

Using the pythagorean theorem: The length of the sides of a 45-45-90 triangle can be easily solved using the pythagorean theorem because it is a right angle triangle.

Recall the formula for the Pythagorean theorem: a 2 + b 2 = c 2; a 2 + b 2 = c2.

To determine the value of (mostly) the hypotenuse in a right triangle, the Pythagorean theorem uses the formula a2+b2=c2. The "non-hypotenuse" sides of the triangle (opposite and adjacent) are a and b.

The well-known geometric theorem known as the Pythagorean theorem states that the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the squares on the legs of a right triangle. This is known as a2 + b2 = c2.

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Work Shown:

[tex]\sqrt{200} \times \sqrt{2}\\\\\sqrt{200 \times 2}\\\\\sqrt{400}\\\\\sqrt{20^2}\\\\20\\\\\text{Therefore, }\sqrt{200} \times \sqrt{2}=20\\\\[/tex]

The rules I used were:

[tex]\sqrt{A}*\sqrt{B} = \sqrt{AB}\\\\\sqrt{A^2} = A \ \ \text{ where } A \ge 0\\\\[/tex]

The expression is simplified to y⁹/12x². Option A

The index form of a number is simply described as a number written as an exponential expression.

It is described as a single number  raised to another number.

Index forms are also described as standard forms and scientific notation.

From the information given, we have;

3x^⁻⁴y⁵/(2x³y⁻⁷)⁻²

Now, expand the bracket of the denominator and multiply the values

3x^⁻⁴y⁵/2x⁶y⁻¹⁴

Divide the expression , we have;

3/-4 (x^⁻⁴y⁵/2x⁶y⁻¹⁴)

To determine the quotient, subtract the exponents of the denominator from the numerators

3× -4(x⁻⁴⁺⁶y⁵⁻¹⁴)

Now, add or subtract the exponential values, we get;

-12 (x⁻²y⁻⁹)

y⁹/12x²

Hence, the value is y⁹/12x²

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Answer:

No

Step-by-step explanation:

Answer:

2 in

Step-by-step explanation:

If im not wrong, each side should be 2 inches, as it would have to be 2x2x2 for a volume of 8 inches cubed

Answer:

OQ = 4

Step-by-step explanation:

the ratios of the segments OP : PQ : QR = 1 : 1 : 3 = x : x : 3x ( x is a multiplier)

then

OP + PQ + QR = OR , that is

x + x + 3x = 10

5x = 10 ( divide both sides by 5 )

x = 2

Then

OQ = OP + PQ

      = x + x

     = 2x

     = 2 × 2

     = 4

Answer:

Solving a system of equations by substitution involves isolating a variable in one equation, then substituting that expression into the other equation. This allows you to solve for the remaining variable in one equation and then substitute it back into the first equation to find the solution for the other variable.

Here is the general process for solving a system of equations by substitution:

Isolate a variable in one of the equations. This is typically done by adding or subtracting one of the variables from both sides of the equation.

Substitute the isolated expression into the other equation by replacing the corresponding variable with the expression you found in step 1.

Solve the new equation for the remaining variable.

Substitute the value you found for the remaining variable back into the first equation and solve for the other variable.

Check your solution by substituting the values you found for the variables back into both equations to make sure they are true statements.

Write your solution in the form of an ordered pair (x, y)

An example of solving a system of equation by substitution :

2x + 3y = 8

4x - 3y = 2

Isolate a variable in one of the equations, for example:

3y = 8 - 2x

Substitute this expression into the other equation:

4x - 3(8 - 2x) = 2

Solve the new equation for the remaining variable:

4x - 24 + 6x = 2

10x = 26

x = 2.6

Substitute the value you found for x back into the first equation and solve for y:

2(2.6) + 3y = 8

5.2 + 3y = 8

3y = 2.8

y = 0.93

Check your solution by substituting the values you found for the variables back into both

Answer:

Step-by-step explanation:

The x -intercept is the point where y = 0 so:

7x - 5(0) = 35

x = 35/7 = 5

x-intercept is at (5, 0)

The y -intercept is the point where x = 0 so:

7(0) - 5y = 35

y = 35/-5 = -7

x-intercept is at (0, -7)

Answer:

x (5, 0)

y (7, 0)

We can find the solution of y = -2x + 6 by graphing the equation by plotting the intercepts of the equation.

Here we can solve the equation by calculating the x and y intercepts of the equation.

This is done by equating the other coordinate to 0 to get the intercept.

For the x-intercept, we will take y to be 0 to get

-2x + 6 = 0

or, 2x = 6

or, x = 3

Hence one intercept will be (3 , 0)

For the y-intercept, we will let x be 0 to get

y = 6

Hence getting the other intercept to be (0 , 6)

Now we can plot the graph by simply plotting these points and drawing a straight line passing through it

To get any unique solution, another equation needs to be plotted and the intersection point of the 2 lines will give us the required answer.

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Complete Question

How do you solve y = -2x + 6?

The sum of a regular polygon's exterior angles will always equal 360 degrees.

Exterior angles are those that are parallel to a polygon's inner angles but are on the outside of it. The sum of two internal opposite angles equals the measure of an exterior angle. The Exterior Angle is the angle formed by any side of a shape and a line drawn from the opposite side. Another example: When we add up the Interior Angle and Exterior Angle we get a Straight Angle (180°), so they are "Supplementary Angles". An exterior angle of the triangle is a nonstraight angle (one that is not just an extension of a side) outside the triangle but adjacent to an interior angle (Figure 1 ).

Here,

The sum of the exterior angles of a regular polygon will always equal 360 degrees.

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Answer:

Step-by-step explanation:

Equiangular triangle

It is means the temperature of the water does not fall below [tex]$10^{\circ} \mathrm{C}$[/tex].

The exponential function, which develops exponentially, is a concept in mathematics. More exactly, it is the function, where e is the irrational Euler's constant, or about 2.71828.

where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

A function that has a positive constant increased to a variable exponent, other than 1, is referred to as an exponential function. A function is assessed by being solved at a certain input value. When the growth rate and initial value are known, an exponential model can be found.

(a) initial temperature: [tex]$30^{\circ} \mathrm{C}$[/tex] it is y-intercept of the graph.

(b) For the first 30 minutes, as time inverses, the temperature decreases.

(c) the horizontal asymptote: y = 10

It is means the temperature of the water does not fall below [tex]$10^{\circ} \mathrm{C}$[/tex].

The complete question is:

Some water is placed in a bottle inside a refrigerator. Suppose the water's temperature [tex]$\left(n^{\circ} \mathrm{C}\right)$[/tex] after minutes can be modeled with an exponential function. The graph of this function is shown below. Use the model to answer the parts to the right.

(a) What is the initial temperature [tex]$\times_6$[/tex] of the water? [tex]$\square^{\circ} C$[/tex] The initial temperature is represented by the (Choose one) of the graph.

(b) For the first so minutes, as time increases, the temperature (Choose one) Temperature

(c) Give the equation of the asymptote. [tex]$y-a l^{\circ} \mathrm{Cl}$[/tex]

Choose the statement that best describes the meaning of the asymptote.

The temperature of the water Time (minutes) does not fall below [tex]$10^{\circ} \mathrm{C}$[/tex].

The water cannot be in the bottle for more than so minutes.

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To write 8 more than a number, we use the mathematical operation of addition and the notation 8+ Number = N+8.

To write 8 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 8 + Number = N+8.

This notation means that we are adding 8 to a number, which results in N+8. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+8.

Another way to write 8 more than a number is to use the phrase "8 plus a number". This phrase indicates that we are adding 8 to a number to get N+8.

Therefore, In short, to write 8 more than a number, we use the mathematical operation of addition and the notation 8 + Number = N+8. This means that we are adding 8 to a number, resulting in N+8. It can also be written as "8 plus N", indicating the same operation.

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The expression that represents the total amount of change she should receive is y = 20 - 3x.

An algebraic expression that uses either a constant or a variable raised to the first power for each term is known as a linear expression. This means that none of the exponents can be greater than 1.

The price of x boxes of cereal $3 each = 3x

Let y be the extra cash she paid

Total cash she paid = $20

Then we have

3x + y = 20

And for expression that represents the total amount of change she should receive

y = 20 - 3x

Thus, The expression that represents the total amount of change she should receive is y = 20 - 3x.

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The logarithmic function is inverse of expontial function that why graph of logarithmic function is draw according to features of expontial function.

The logarithmic function [tex] f(x) = log_{b}(x) [/tex] is the inverse of the exponential function y=bˣ. Clearly, the logarithm function must have domains and limits of (0, ∞) and (−∞,∞). The logarithmic function can be graphed by examining the graph of the exponential function and swapping x and y. Graphs of exponential functions f (x) = bˣ or y = bˣ include the following features:

For example, the graph above represents a logarithmic function, [tex] f(x) = log_{2}(x) [/tex].

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Answer:

y = -3/2 x + 2

Step-by-step explanation:

3x + 2y = 8

2y = -3x + 8

y = -3/2 x + 4

slope of given line = m = -3/2

Parallel lines have equal slopes.

Slope of parallel line through point (-2, 5), m = -3/2.

y = mx + b

m = -3/2

y = -3/2 + b

point: (-2, 5)

5 = (-3/2)(-2) + b

5 = 3 + b

b = 2

Equation: y = -3/2 x + 2

To complete the project in 36 days, the construction manager would need to add at least 8 more workers to his current team of 12 workers.

If 12 workers can complete a building project in 54 days, to determine this we can divide the rate of work by the number of workers by the number of days: 12 workers / 54 days = 0.2222 workers/day.

If the construction manager wants to complete the project in 36 days, he needs to increase the rate of work to complete the project in that shorter timeframe. To do this, he can add more workers or increase the productivity of the current workers.

To determine how many more workers the manager needs, we can use the formula:

(number of workers) = (rate of work) x (number of days)

By plugging in the desired rate of work and number of days, we get:

(number of workers) = (0.2222 workers/day) x (36 days) = 7.999 workers

To complete the project in 36 days, the construction manager would need to add at least 8 more workers to his current team of 12 workers.

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Answer:

Ryan did

Step-by-step explanation:

7/8 is .875 which is about 87

To compare the score of Ryan and Sam, we need to convert the fractions to decimals.

Ryan got 7/8 problems correct, which is equivalent to 0.875 when expressed as a decimal.

Sam got 80% correct, which is equivalent to 0.8 when expressed as a decimal.

So, Ryan got a better score

The rectangular prism's dimensions are 3:2:1 in terms of length, breadth, and height. The prism's length can be computed as 24 cm using its volume, 48 cm3, as input.

Volume = Length × Width × Height

48 cm3 = L × 2 × 1

L = 24 cm

A rectangular prism is a solid 3D object that has six faces, eight vertices and twelve edges. The length, width and height of a rectangular prism can be expressed in a ratio of 3:2:1 respectively. Knowing this ratio and the volume of the prism, which is 48 cm3, it is possible to calculate the length of the prism. To calculate the length of the prism, first the volume of the prism must be expressed in terms of the length. This can be done by using the formula Volume = Length × Width × Height. Therefore, 48 cm3 = L × 2 × 1. Solving this equation for L gives the length of the prism as 24 cm. Therefore, the length of the rectangular prism with a volume of 48 cm3 and a ratio of 3:2:1 is 24 cm.

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