If √x-3a+√x-3b=√x-3c then prove that x = (a+b+c) ±2√√a² + b² + c²-ab-bc-ca ​

The given expression can be simplified to x2 - xy = 3.

Expression is a way to communicate ideas, feelings, and thoughts. It can be verbal, physical, and/or written. Expression is the outward manifestation of your inner emotions, which can take many forms. Expression can be used to express joy, sadness, anger, and other emotion. It can also be used to articulate a point of view or opinion. Expression is an important part of communication and is a powerful tool to express oneself and one’s feelings.

This is happening because the addition of 8 to x can be rewritten as x2, and the equal sign can be used to indicate that the two sides of the equation must be equal. Therefore, both sides can be simplified to their original terms. Thus, the expression can be written as x2 - xy = 3.

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The given expression can be simplified to 25 + 5y + 4.

Expression is a way to communicate ideas, feelings, and thoughts. It can be verbal, physical, and/or written. Expression is the outward manifestation of your inner emotions, which can take many forms. Expression can be used to express joy, sadness, anger, and other emotion. It can also be used to articulate a point of view or opinion. Expression is an important part of communication and is a powerful tool to express oneself and one’s feelings.

To simplify the expression x + 8 and = 3, we must first subtract 8 from both sides of the equation to get x = -5. We can then substitute -5 for x in the expression x2 - xy + 4, resulting in (-5)2 - (-5)y + 4.

Simplifying further, we get 25 - (-5)y + 4, or 25 + 5y + 4. Therefore, the simplified expression is 25 + 5y + 4.


This is happening because the addition of 8 to x can be rewritten as x2, and the equal sign can be used to indicate that the two sides of the equation must be equal. Therefore, both sides can be simplified to their original terms. Thus, the expression can be written as 25 + 5y + 4.

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As per the given percentage, the original price to be $180.00.

Let's begin by defining what percentage means. A percentage is a fraction that represents a portion of a whole expressed as a fraction of 100. For example, 25% can be written as 25/100 or 0.25 as a decimal.

Now, let's apply this concept to the problem. We know that the original price increased by 25%, which means the new price is 125% of the original price. We can represent this mathematically as:

New price = Original price + 25% of the original price

125% of the original price = Original price + 25% of the original price

1.25 x Original price = Original price + 0.25 x Original price

1.25 x Original price = 1.25 x Original price

Original price = (225.00 / 1.25)

Therefore, the original price was $180.00.

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[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-4 +3}{2} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{ 1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{1}) \implies y +3 = - \cfrac{ 1 }{ 2 } ( x -1) \\\\\\ y+3=- \cfrac{ 1 }{ 2 }x+\cfrac{1}{2}\implies y=- \cfrac{ 1 }{ 2 }x+\cfrac{1}{2}-3\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 2 }x-\cfrac{5}{2} \end{array}}[/tex]

Answer: First, let's find the slope of the line:

slope = (change in y) / (change in x)

slope = (-4 - (-3)) / (3 - 1)

slope = -1/2

Now, let's choose one of the points, say (1,-3), and use the point-slope formula:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) are the coordinates of the point.

So, substituting in the values we get:

y - (-3) = (-1/2)(x - 1)

Simplifying this equation, we get:

y + 3 = (-1/2)x + 1/2

Subtracting 3 from both sides, we get:

y = (-1/2)x - 5/2

Therefore, the equation of the line that passes through the points (1,-3) and (3,-4) is y = (-1/2)x - 5/2.

Your welcome.

Step-by-step explanation:

Zach has to cut the wooden molding into 9 sections, resulting in a total length of 4 1/2 yards in various numbers.

A measurement of length is the distance between two points on an item. It is one of the essential physical quantities used in physics and a fundamental idea in geometry. Typically, length is expressed in terms of meters, centimeters, feet, inches, or kilometers. Rulers, measuring instruments, and laser rangefinders are just a few of the tools that can be used to determine an object's length. When describing the size of geometric objects like lines, segments, or curves, length is frequently used in mathematics.

given

The overall length of the molding can be calculated by multiplying the length of each piece by the number of pieces, for example, if Zach needs to cut wooden molding into 9 pieces that are each half a yard long:

Total length equals each piece's length times the number of parts.

Overall length is 9 + (1/2 yard)

length overall: 9 2 yards

We can divide 9 by 2 and write the outcome as a mixed number to represent this:

with a residue of 1, 9 2 = 4

Zach has to cut the wooden molding into 9 sections, resulting in a total length of 4 1/2 yards in various numbers.

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(a) Compared to the graph of y = x, the graph of y = x - 4 is shifted downwards by 4 units.

Compared to the graph of y = x, the graph of y = x - 4 intersects the y-axis at the point (0, -4).

(b) Compared to the graph of y = x, the graph of y = 5/2 * x is steeper (has a greater slope).

Compared to the graph of y = x, the graph of y = 5/2 * x intersects the y-axis at the point (0, 0).

(a)

Compared to the graph of y = x, the graph of y = x - 4 is shifted downwards by 4 units. The -4 in the second equation means shifting downward 4 units

Compared to the graph of y = x, the graph of y = x - 4 intersects the y-axis at the point (0, -4). hence the y intercept is -4

(b)

Compared to the graph of y = x, the graph of y = 5/2 * x is steeper (has a greater slope).

Compared to the graph of y = x, the graph of y = 5/2 * x intersects the y-axis at the point (0, 0). In this case both graphs intercepts the y-axis at same point which is at the origin

The graphs are attached

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Answer:

72

Step-by-step explanation:

The measure of the inscribed angle(DEF) is half the measure of its intercepted arc (Arc FD)

The measure of are FD is 144 and half of that is 72.

So the measure of angle DEF is 72 degrees.

Answer:

72°

Step-by-step explanation:

∠DEF is an inscribed angle equal to half the arc on which it rests

∠DEF = 0,5 × 144 = 72°

Answer:

Below

Step-by-step explanation:

For angles whose vertex is inside the circle , the angle measure is the sum of the two arcs subtended divided by 2

 ? = E

E = (55 + 155)/2 = 105°   = ?

The rate of change and initial value are 0.023 and -600 respectively.

The amount he needs to sell to break even is $26,086.96.

The amount he needs to sell in order to make $1000 profit is $69,565.22.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided, a system of equations that models the situation is given by;

-140 = 20,000x + c    ...equation 1.

90 = 10,000x + c       ...equation 2.

By subtracting equation 1 from equation 2, we have:

230 = 10,000x

x = 0.023

For the initial value, we have:

90 = 10,000x + c

c = -140 - 20,000(0.023)

c = -600.

In order to break even, y must be equal to 0;

y = 0.023x - 600

0 = 0.023x - 600

x = 600/0.023

x = $26,086.96.

In order to make $1000 profit, Lanny must sell the following:

y = 0.023x - 600

1,000 = 0.023x - 600

x = 400/0.023

x = $69,565.22.

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It would take them about 8.4 hours to add the special effects if they all work together.

1/T = 1/T1 + 1/T2 + 1/T3 +... + 1/Tn, where T is the time it takes for all n persons to complete the task and T1, T2,..., Tn are the times it takes for each person to do the task individually, is the formula for addressing issues involving work done by several people. This equation is based on the premise that each person's contribution to the activity is inversely proportionate to the time it takes them to do it. In other words, a person contributes more effort to the entire task the faster they work. This method may be used to determine how long it will take all n persons working together to do the assignment in total.

The work done is calculated by:

1/T = 1/T1 + 1/T2 + 1/T3

Here, we have T1 = 20, T2 = 26 and T3 = 32 hours for work done separately.

Substituting the values:

1/T = 1/20 + 1/26 + 1/32

1/T = (32/640) + (24/640) + (20/640)

1/T = 76/640

T = 640/76

T ≈ 8.4 hours

Therefore, it would take them about 8.4 hours to add the special effects if they all work together.

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The total number of voters in favor of Bond Measure A is 3900 voters in favor of Bond Measure A.

First we need to calculate the total number of voters who are registered Democrats and the total number of voters who are not registered Democrats, and then calculate the number of voters in favor of the measure for each group and add them together.

Total number of registered Democrats:

3/4 of 6000 registered voters = 4500 registered Democrats

Number of registered Democrats in favor of Bond Measure A:

2/3 of 4500 registered Democrats = 3000 registered Democrats in favor of the measure

Number of registered Democrats not in favor of Bond Measure A:

4500 - 3000 = 1500 registered Democrats not in favor of the measure

Total number of voters who are not registered Democrats:

6000 - 4500 = 1500 voters who are not registered Democrats

Number of voters who are not registered Democrats and in favor of Bond Measure A:

3/5 of 1500 voters who are not registered Democrats = 900 voters who are not registered Democrats and in favor of the measure

Therefore, the total number of voters in favor of Bond Measure A is:

3000 registered Democrats in favor + 900 other registered voters in favor = 3900 voters in favor of Bond Measure A.

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The statement "using higher order functions, complete the mul by num function. this function should take an argument and return a one argument function that multiplies any value passed to it by the original number" is True. It is possible to complete the `mul_by_num` function using higher order functions. A higher order function is a function that either takes one or more functions as arguments, or returns a function as its result.

In this case, the `mul_by_num` function should take an argument and return a one argument function that multiplies any value passed to it by the original number. Here's how you can do it:

```python
def mul_by_num(num):
   def num_function(val):
       return val * num
   return num_function
```

The `mul_by_num` function takes an argument `num` and returns a one argument function `num_function` that multiplies any value passed to it by the original number `num`. The `num_function` is a higher order function because it is returned by the `mul_by_num` function.

You can use the `mul_by_num` function like this:
```python
mul_by_5 = mul_by_num(5)
print(mul_by_5(10)) # 50
```

The `mul_by_num` function is called with the argument `5` and returns a one argument function `mul_by_5` that multiplies any value passed to it by 5. When the `mul_by_5` function is called with the argument `10`, it returns the result `50`.

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Answer:

Step-by-step explanation:

-10 perecent

because 21-11=10

The list that shows these numbers in order from least to greatest is:

0.009854, 30%, 1.98, V9

The reason for this order is as follows:

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The standard pyramid KO has a volume of roughly 64.88 cubic units.

To find the volume of the given regular pyramid KO, we need to know the area of the base and the height of the pyramid. Since the pyramid is regular, the base is a square. Let the side of the square base be x.

Now, we can use trigonometry to find the height of the pyramid. Draw a line from vertex K to the center O of the base. This line is perpendicular to the base, so it splits the base into two equal parts. Let M be the midpoint of side AB. Then, we have right triangle KMO with hypotenuse KO, and angle MKO equal to half of angle AKO (19 degrees).

We can use the trigonometric function tangent to find the height h of the pyramid:

tan 19 = h/5 (where 5 is half of x, the side length of the base)

h = 5 tan 19 ≈ 1.98

Now, we can use the formula for the volume of a pyramid:

V = (1/3) * area of base * height

Since the base is a square, its area is x². Substituting the known values, we get:

V = (1/3) * x² * h

V = (1/3) * x² * 1.98

V = (0.66) x²

We are given that KO = 10.2, which is the slant height of the pyramid. Using the Pythagorean theorem, we can find x:

x² + (5/2)² = 10.2²

x² = 104.04 - 6.25

x² = 97.79

x ≈ 9.89

Substituting this value for x into the equation for the volume, we get:

V = (0.66) * 9.89²

V ≈ 64.88

Therefore, the volume of the regular pyramid KO is approximately 64.88 cubic units.

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 This function is neither odd nor even. To show this, we can take the algebraic approach.

The definition of an odd function is that for every \( x \), \( f(-x) = -f(x) \).

Therefore, we can substitute \( -x \) for \( x \) and see if this statement is true.

\( f(-x) = 6(-x)^{2}-\frac{4}{-x} \)

\( f(-x) = -6 x^{2}+\frac{4}{x} \)

Since this is not equal to \( -f(x) \), which is \( -6 x^{2}-\frac{4}{x} \), this function is neither odd nor even.

9) The equation of the line that goes through the two points \( (-1,3) \) and \( (2,-4) \) is \( y = \frac{1}{3}x + \frac{17}{3} \).

To find the equation, we can use the point-slope formula. The slope of the line is \( \frac{-7}{3} \), which we can find using the two points.

\( m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-4-3}{2-(-1)} = \frac{-7}{3} \)

The point-slope formula for the equation of the line is \( y - y_{1} = m(x - x_{1}) \). We can substitute in the slope and the point \( (-1,3) \) to get the equation.

\( y - 3 = \frac{-7}{3}(x - (-1)) \)

\( y - 3 = \frac{-7}{3}(x + 1) \)

\( y = \frac{-7}{3}x - \frac{7}{3} + 3 \)

\( y = \frac{1}{3}x + \frac{17}{3} \)

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The axis of rotation is a perpendicular line that passes through the vertex, meaning the lowest point in the graph [tex](4, -3)[/tex].

A vertices is a place on a polygons where two ray or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the lines A, B, C, E, etc E in the aforementioned figures are vertices.

A node of a graph, or one of the vertices from which a graph is formed and that can be connected by graph, is referred to as a "vertex" in computing. Moreover, the words "point," "junction," and "0-simplex" are employed.

To graph the function [tex]f(x) = x^2 - 8x + 13[/tex], we need to find its axis of symmetry, vertex, and a few other points.

Find the axis of symmetry

[tex]x = -b/2a[/tex]

In this case, [tex]a = 1[/tex] and [tex]b = -8[/tex], so the axis of symmetry is [tex]x = -(-8)/(2*1) = 4[/tex].

Find the vertex

[tex]f(4) = 4^2 - 8(4) + 13 = -3[/tex]

So the vertex is [tex](4, -3)[/tex].

To find other points,

When [tex]x = 0, y = 13[/tex]

When [tex]x = 1, y = 6[/tex]

When [tex]x = 2, y = 1[/tex]

When [tex]x = 3, y = -2[/tex]

When [tex]x = 5, y = 2[/tex]

These points cannot be connected on a graph to form a basic picture of the function.

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The domain of the function is positive integers. The function () = 200 + 16 represents the daily cost of production in a factory, where x is the number of complete products manufactured.

Since the production of products cannot be negative or fractional, the domain of the function is restricted to non-negative integers.

Therefore, the domain of the function is the set of positive integers:

{1, 2, 3, 4, ...}

Any value outside this set would not make sense in the context of the problem, as a fraction or a negative number of products cannot be produced.

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The calculated number of additional miles he would run must not exceed 8 miles

The following are symbols for inequalities and their corresponding meanings:

The inequality format that expresses the information in the question is as follows:

Tom's minimum required running distance must be greater than or equal to the sum of the distance he has already run and the distance he plans to run.

Using this inequality, we can derive the equation

30 ≥ 22 + t

Where t represents the distance Tom plans to run.

To determine the value of t, we must simplify the equation by combining similar terms.

We can subtract 22 from both sides, resulting in

8 ≥ t.

Therefore, the maximum distance Tom plans to run is 8 miles.

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The angle measurement between the hands of the clock is 270 degrees. At 9:00, the hour hand points directly to the 9 and the minute hand points directly to the 12.

We know that the hour hand moves 360 degrees in 12 hours (or 30 degrees per hour), and the minute hand moves 360 degrees in 60 minutes (or 6 degrees per minute).

To calculate the angle between the hands, we can use the formula:

angle = |30h - 11m/2|

where h is the hour (9 in this case) and m is the minute (0 in this case). Substituting these values into the formula, we get:

angle = |30(9) - 11(0)/2|

= |270|

= 270

Therefore, the angle between the hands of the clock is 270 degrees.

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Answer:

Step-by-step explanation:

To solve the system of equations algebraically, we need to substitute the second equation into the first equation and solve for x:

y = 4x – 5 (equation 1)

y = -3 (equation 2)

Substitute equation 2 into equation 1:

-3 = 4x – 5

Add 5 to both sides:

2 = 4x

Divide both sides by 4:

x = 1/2

Now, we can substitute this value of x back into either equation to find y:

y = 4(1/2) – 5 = -3

Therefore, the solution to the system of equations is (1/2, -3).

To verify this solution using the graph, we can plot the two equations on the same set of axes:

y = 4x – 5 (red line)

y = -3 (blue line)

The two lines intersect at the point (1/2, -3), confirming our solution.

Therefore, the answer is (B) (1/2, -3).

a. To establish whether the function is concave up or concave down, we must obtain the function's second derivative. F(x) = 2x2 - 12x + 9 F'(x) = 4x - 12 F"(x) = 4x - 12 F"(x) = 4.

The function is concave up because the second derivative has a constant value of 4, which is positive. Since the coefficient of x2 is more than one, the function is narrower than the conventional parabola y = x2. b. The equation x = -b/2a gives the parabola's axis of symmetry, where a and b are the coefficients of the x2 and x terms, respectively.A = 2 and b = -12 for the function F(x) = 2x2 - 12x + 9. As a result, the axis of symmetry is x = -12/(2*2) = 3. c. The point at which The coordinates (h, k) define the parabola, where h = -b/2a and k = f. (h). We already determined that the axis of symmetry for the function F(x) = 2x2 - 12x + 9 is x = 3. So, h = 3. To find k, enter h = 3 into the function: F(3) = 2(3)^2 - 12(3) + 9 = -9 As a result, the vertex is (3, -9). Width: The parabola's width is the distance between the x-intercepts, which may be calculated using the quadratic formula.

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The optimal solution of an objective function does not change when its coefficients are changed within a certain range of values. This range of values for each coefficient depends on the function itself and the value of other coefficients.

For example, if the objective function is 3x + 2y, then the range of values for the coefficient of x (3) can be changed from 2 to 4 without changing the optimal solution. Similarly, the coefficient of y (2) can be changed from 1 to 3 without changing the optimal solution.
Therefore, the ranges of values for each coefficient of the objective function, holding all else constant, can be changed without changing the optimal solution.

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Answer:

This function has no zeroes

Step-by-step explanation:

To understand this problem we need to first understand what the zeroes of a function is; the zeroes of a function is the point at which the y value of a solution is equal to zero. So in this scenario all we need to do is plug 0 in for y:

[tex]0 = x^2 +49[/tex]

Subtract 49 from both sides:

[tex]-49 = x^2[/tex]

Now we can notice that [tex]x^2[/tex] is equal to -49; to our surprise there is no possible value for [tex]x^2[/tex] to be equal to a negative number. Therefore this function has no roots.

Step-by-step explanation:

a zero of a function means what value of x causes a functional value of 0 ?

so,

0 = x² + 49

-49 = x²

x = ±sqrt(-49)

this tells us that there is no solution in real numbers, because no square of any real number can be negative.

but the function still has 2 zeroes. they are numbers of the set of imaginary or complex numbers.

that means they base on the square root of -1, called i.

x = ±sqrt(49×-1) = ±7×sqrt(-1) = ±7i

To classify a quadrilateral by its most specific name, we need to examine its sides and angles.

A quadrilateral is four-sided polygon with four angles. It is closed shape with straight lines that do not cross each other.

Here are the most common types of quadrilaterals and their defining characteristics:

Parallelogram - quadrilateral consist of two pairs of parallel sides.

Rectangle - parallelogram with four right angles.

Rhombus -  parallelogram with four congruent sides.

Square - rectangle and a rhombus, with four right angles and four congruent sides.

Let's consider an example.Suppose we are given a quadrilateral with four sides of equal length and two pairs of opposite parallel sides. This means that it has the characteristics of a parallelogram and a rhombus.

Reasoning: The quadrilateral has four equal sides, which makes it a rhombus. Additionally, it has two pairs of parallel sides, which satisfies the criteria for a parallelogram. However, since a rhombus is a type of parallelogram with additional properties, it is the most specific name for this quadrilateral.

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Andy can set up a maximum of 12 tables, each with 3 servings of tacos and 3 servings of nachos.

Let's assume that there are a limit of n servings per table. We need to get the greatest number of n that divides both 21 and 15 without leaving a remnant because Andy doesn't want any leftover tacos or nachos. In comparison to the factors of 15, which are 1, 3, 5, and 15, the factors of 21 are 1, 3, 7, and 21. Three is the highest number that divides both 21 and 15.

Thus, a maximum of three dishes can be placed on each table. We divide the total servings by the maximum servings per table to get how many tables Andy can set up:

Servings total: 21 + 15 = 36

3 serves maximum per table.

Amount of tables = Total Servings / Maximum Servings Per Table = 36 / 3 = 12

Hence, Andy can only put up a maximum of 12 tables, each with 3 tacos and 3 nachos.

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Thus on the sixth, ninth, twelfth, fifteenth, and eighteenth pages, he reads the same pages.

To tackle proportionality-related mathematical problems, one can apply the unitary method. Finding the value of one unit and then utilising that value to calculate the value of another quantity with a different number of units is what this method entails. Consider the scenario where you are told that an automobile goes 300 miles in 5 hours. The unitary technique can be used as follows to determine how far the car drives in 8 hours: Calculate what an hour is worth: 1 hour is equal to 300/5, or 60 miles. 5 hours equals 1 unit. Use this number to calculate the value of eight hours: 8 hours equals 8/1 units, hence 8 x 60 = 480 miles are covered during that time.

given

Each of them reads roughly one-third of the story's pages when the three of them are reading it together.

As a result, Beth reads the first, fourth, seventh, and cdots pages, Carolyn reads the second, fifth, and eighth, and cdots pages, and George reads the third, sixth, and ninth.

When just Carolyn and George are reading the narrative, Carolyn reads the first page and George reads the second, and so on through the remaining pages.

Thus on the sixth, ninth, twelfth, fifteenth, and eighteenth pages, he reads the same pages.

So, $3+5=8 ($boxed) is the amount of pages that Carolyn and George read that are equal to the amount of pages they would have read if Beth had been present.

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In Linear equation, 196000 cm is the unitless scale of the map in simplest form.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

h = 1/2 t²

here

 g = 980 m/sec²

  t = 20 sec

Therefore, the distance h is: 196000 cm

   h = 1/2 * 980 * 20²  = 196000 cm

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The value of the variable x given the perimeter is 44°.

A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.

Given: radius = 24cm

perimeter (total) of sector = 68cm

Total perimeter of sector=68cm

Radius = 24 cm

24 + x = 68 cm

x =68 - 24

x = 44°

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A diagram shows a sector of a circle of radius 24 cm and perimeter of 68cm. Find the value of x.

Larry's burn rate, which represents the amount of money he spent per unit of time, is $2,600 per month based on the starting balance of $17,300 and the ending balance of $14,700.

Larry's burn rate can be calculated as the amount of money he spent per unit of time, which is usually expressed as a monthly or annual rate. To calculate his burn rate based on the given information, we need to know the time period for which the difference between the starting and ending balances represents.

Assuming that the starting balance of $17,300 represents the beginning of a month or some other specific time period, and that the ending balance of $14,700 represents the end of the same time period, we can calculate Larry's burn rate as follows:

Burn rate = (Starting balance - Ending balance) / Time period

If we assume that the time period is one month, then:

Burn rate = ($17,300 - $14,700) / 1 month = $2,600 per month

Therefore, Larry's burn rate is $2,600 per month. This means that he spent an average of $2,600 per month to run his shoe store during the time period in question.

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Answer:

Yes, they do

Step-by-step explanation:

The more you focus on a concept, the more you get an understanding of it without being taught by another person.

Hard math concepts are hard cause you haven't found an easier way to get an understanding of it.