System of Linear Programming:
z=-3x + 5y
x+y> -22
x-y-4
x - y ≤ 2
Minimum value of z:

The expression that represents the cost (in dollars) of renting a paddleboard for h hours is r + xh

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

Cost of rents:

Charging a rental fee plus an hourly rate.

Using the above as a guide, we have the following:

Initial rental fee = r

Hourly rate = x

The cost for h hours can then be represented as

C(h) = Initial rental fee + Hourly rate * Number of hours

Substitute the known values in the above equation, so, we have the following representation

C(h) = r + x * h

Evaluate

C(h) = r + xh

Hence, the expression is r + xh

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the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5). We were then asked to find the number of years elapsed when the trees are at the same height.

In this problem, we were given two different trees, one that is 3 feet tall and growing at a rate of 1 foot per year, and another that is 5 feet tall and growing at a rate of 0.75 feet per year. The ordered pair (3,1) represents the 3-foot tall tree growing at a rate of 1 foot per year and the ordered pair (5,0.75) represents the 5-foot tall tree growing at a rate of 0.75 feet per year.

To find the number of years elapsed when the trees are at the same height, we need to solve the equation:

3 + 1t = 5 + 0.75t

t = (5 - 3)/(1 - 0.75) = 2/0.25 = 8

So the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5).

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Answer:

0

Step-by-step explanation:

h(x) = 3 – 3/x

h(3) = 3 – 3/3

h(3) = 0/3

h(3) = 0

i hope this helped

Answer:

parallelogram

Answer:

The result can be shown in multiple forms.

Point Form: ( 2, − 2 )

Equation Form: x = 2 , y = − 2

Step-by-step explanation:

1. Eliminate the equal sides of each equation and combine them.
2x − 6 = − 5x + 8

2. Solve 2x − 6 = −5x +8 for x.

x = 2

3. Evaluate y when x = 2.

y = − 2

The solution to the system is the complete set of ordered pairs that are valid solutions.

( 2, − 2 )

The result can be shown in multiple forms.

Point Form: ( 2, − 2 )

Equation Form: x = 2 , y = − 2

Answer:

x = 2

y = -2

Step-by-step explanation:

Substitute equation 1 into equation 2 then solve for x:

2x - 6 = -5x + 8

7x = 14

x = 14/7 = 2

Now substitute x=2 into either equation to solve for y:

y = 2(2) - 6 = -2

The slope of the line passing through the equation 4x - 3y = 12 is given by Slope m = -3/4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

4x - 3y = 12   be equation (1)

Now , on simplifying the equation , we get

Adding 3y on both sides of the equation , we get

3y + 12 = 4x

Subtracting 12 on both sides of the equation , we get

3y = 4x - 12

Divide by 3 on both sides of the equation , we get

y = ( 4/3 )x - 4

It is of the form y = mx + b where m is the slope and b is the y-intercept

So , slope m₁ = 4/3

Now , the line is perpendicular to the line y = ( 4/3 )x - 4

So , the product of their slopes is -1

And , m₁ x m₂ = -1

Substituting the values in the equation , we get

m₂ = ( 3/4 ) x -1

m₂ = -3/4

Hence , the slope of the line is -3/4

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The perimeter of a soccer field is 304 meters. The field is 96 meters long. So, its wide becomes: 56 m

The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it. The perimeter of the form is equal to the algebraic sum of each side's length. For the various geometric forms, there are formulae accessible. The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths.

Given that,

The perimeter of a soccer field is 304 m

length of the field is 96 m

wide = ?

As we know,

perimeter = 2 (length + width)

or, 304 = 2 (96 + width)

or, 304 = 192 + 2 width

or, width = 112 /2

or, width = 56 m

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The lessons we get from book that discuss applied regression analysis and other multivariable is that it can be used in real-life problems such as prediction and forecasting.

As a very effective and practical statistical technique, regression analysis has numerous applications to the field of nursing science. It allows scientists to explain, forecast, and quantify the correlations between variables, and form credible conclusions about the underlying causes of any phenomenon under study.

Regression analysis is a reliable way for determining which variables have an impact on a particular topic of interest. The method of doing a regression allows you to safely establish which elements are most important, which factors may be ignored, and how these factors influence each other.

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But to see one’s own face essential that the light emitted by it is either bounced back into our eyes (intimate a mirror - or something very much like it) - or that the light is recorded, captured and then played back into our eyes.

Did you know that shapes have a face? No, this face does not mean a face with two eyes, a nose, and a mouth. I mean a face of a shape, or the flat surface of a shape that you can trace and see. This face is known as a face in math.

Plane shapes in math mean any closed, flat, two-dimensional shape. All plane shapes have a face, because you can trace the shape of all plane shapes.

A triangle has a triangle face.

A rectangle has a rectangle face.

A diamond has a diamond face.

A circle has a circle face.

A square has a square face.

An oval has an oval face.

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Answer:

Step-by-step explanation:

just do - x + = -

- x - = +

so the answer is + i think

Marking of points A and B in 4 cm apart and shaded the region that is closer to B than to A and within 3 cm of B, in the coordinate plane.

The cartesian coordinate system includes a two dimensional plane known as the Cartesian Plane. Rene Descartes created the cartesian plane in the 17th century. The cartesian plane's ability to connect Euclidean geometry and algebra is its most significant characteristic.

Numerical coordinates can be used to describe any point on a cartesian plane. An ordered pair is used to express a point's coordinates on a cartesian plane. These points are also signed, and their distance from two perpendicular lines known as axes is fixed.

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A number line marked with zero, one twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, ten twelfths, eleven twelfths, and one. From the zero point to the three twelfths mark, a red line is painted.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.

Here,

Multiply one times three, and four by three.

It will equal to three out of twelve or 3/12.

=1/4

A number line marked with zero, one twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, ten twelfths, eleven twelfths, and one. From the zero point to the three twelfths mark, a red line is painted.

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Answer:

x = 5, -5, 3, -3

Step-by-step explanation:

First, substitute u = x^2 into the equation, and we have

u^2 - 34u + 225 = 0

u = x^2

Factor u^2 −34u +225 using the AC method, and we get

( u - 25) ( u - 9) = 0

We know If any individual factor on the left side of the equation is equal to

0, the entire expression will be equal to 0, so

u - 25 = 0

u - 9 = 0

Next, we set u - 25 equal to 0  and solve for u, and we get

u = 25

Then set u - 9 equal to 0 and solve for u, and we get

u = 9

The final solution is all the values that make (u−25)(u−9) = 0  true.

u =25,9

Substitute the real value of u=x^2 back into the solved equation.

x^2 = 25

(x^2)^1 = 9

x^2 = 25

x = 5, -5

Now we solve the second equation

(x^2)^1 = 9

x = 3, -3

So, the answers are: 5, -5, 3, -3

Calculating the total VMT or VKT for all road segments during a certain time period by multiplying the daily traffic volume on each segment by its length.

The average automobile is around 15 feet long, so if you multiply 5280 by this number, you get about 350 cars, assuming they are all touching. Just over 284 million automobiles were on the road in the second quarter of 2022 in the United States. Though estimating the overall number of automobiles on the planet is not a precise science, the number is rising quickly.

Given that the ACS estimated there were 150 million workers in 2016, there are at least 115 million automobiles and trucks on American roads every day. Congestion is expected to be so bad during morning and afternoon rush hours. A balance between the demand for using the system and the infrastructure's capabilities can be achieved by creating digital twins of the transportation system and using them to optimise flows.

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r is called as radius in the formula  A=πr^2

A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations.

Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy).

A model is, for example, the method for the area of a circle, πr2.

Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

Α= pi r^2

Divide each side by pi

A / pi = r^2

Take the square root of each side

sqrt( A / pi ) = sqrt(r^2)

sqrt( A / pi ) =r

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B. MLYZ and C. LN = XZ are not true, since these letters do not correspond to any sides or angles in the given triangles.

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." Given the statement "ALMN = AXYZ," we can assume that triangle ALMN is congruent to triangle AXYZ.

With that in mind, the following congruences are true:

A. ZX=ZN (Corresponding parts of congruent triangles)

D. MN = YZ (Corresponding parts of congruent triangles)

E. ZY ZMo (not a valid statement)

F. ZZ = ZL (not a valid statement)

B. MLYZ and C. LN = XZ are not true, since these letters do not correspond to any sides or angles in the given triangles.

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To change the base of an exponential function, we can use the formula:

log_b(a) = log_c(a) / log_c(b).

To change the base of an exponential function, you can use the property that logarithms with different bases are related by the following equation:

log_b(a) = log_e(a) / log_e(b)

Where log_b(a) is the logarithm of a to the base b and log_c(a) is the logarithm of a to the base e.

For example: To change log_3(7) to log_e(x)/log_e(y), we can use the property that logarithms with different bases are related by the following equation:

logb(a) = logc(a) / logc(b)

So log_3(7) = log_e(7) / log_e(3)

To find x and y we can use the logarithm properties and the definition of logarithm:

log_e(x) = log_e(7)

x = 7

log_e(y) = log_e(3)

y = 3

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The three different forms of slope formulas are m=(y-b)÷x, m=(y-y₁)÷(x-x₁), and m=(-A)÷B.

The slope gives the steepness of a straight line. The three different forms of the slope of a linear equation are slope-intercept form, point-slope form, and standard form.

From the equation of slope-intercept form y=mx+b, the slope is calculated using the formula, m=(y-b)÷x. Here, the slope is m and the y-intercept is b.

From the equation of the point-slope form (y-y₁)=m(x-x₁), the slope is calculated using the formula, m=(y-y₁)÷(x-x₁). Here, points on the line are x₁ and y₁.

From the equation of standard form Ax+By=C, the slope is m=(-A)÷B. Here, constants or integers are A, C, and B.

In general, the slope is calculated using the formula, m = (Δy)÷(Δx)= (y₂-y₁)÷(x₂-x₁). Here, in the line, the coordinate of the first point is (x₁, y₁), and the second point is (x₂, y₂).

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⤠is the symbol for the euro, while ⥠is the symbol for the Japanese yen.

The euro, represented by the symbol â¤, is the official currency of 19 of the 28 member states of the European Union. It was introduced in 1999, and is the second-most traded currency in the world after the US dollar. The euro is managed and administered by the European Central Bank and the Eurosystem.

The Japanese yen, represented by the symbol â¥, is the official currency of Japan and is the third most traded currency in the world. It is issued and managed by the Bank of Japan, the country's central bank. The yen is used as a reserve currency by central banks and is often seen as a safe-haven asset during times of economic or political uncertainty.

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The solution of equation: 2y + 8x = 2(y + 4)x.

For the stated equation:

= 2y + 8x

As. 2y and 8x both are divisible by 2 .

So, Taking two common from both.

= 2(y + 4x)

Thus, the solution of the equation becomes: 2(y + 4x).

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It is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm because the sum of two sides are greater than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 25 and 5

25 + 5 > 24

30 > 24

Now we add 25 and 24

25 + 24 > 5

49 > 5

Now we add 5 and 24

5 + 24 > 25

29 > 25

It is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm because the sum of two sides are greater than third sides.

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The required reflection of the points N(-3, 1), G(0, 4), B(-1, 1) across the y-axis are N(3, 1),  G(0, 4), B(1, 1) .

Point (x, y) is reflected across the x-axis as (x, -y). The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse.

We have,

N(-3, 1), G(0, 4), B(-1, 1)

While, find reflected points we are considering y-axis as mirror,

Then,

Reflection of point N(-3, 1) across the y-axis

⇒ N(3, 1)

Reflection of point G(0, 4) across the y-axis

⇒ G(0, 4)

Reflection of point B(-1, 1) across the y-axis

⇒ B(1, 1)

Thus, required reflected points are  N(3, 1),  G(0, 4), B(1, 1) .

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Answer: 75m^3

Step-by-step explanation:

First, find the scale factor:

5/2 = 2.5

Multiply figure A's volume by the scale factor:

2.5 * 30

= 75 m^3

Answer:

2+2%2%5+51%895%+8+81%9+61%+5%+8+%15+%

Answer:

(- 8, - 6 )

Step-by-step explanation:

y = 2x + 10 → (1)

y = x + 2 → (2)

substitute y = 2x + 10 into (2)

2x + 10 = x + 2 ( subtract x from both sides )

x + 10 = 2 ( subtract 10 from both sides )

x = - 8

substitute x = - 8 into either of the 2 equations and evaluate for y

substituting into (2)

y = - 8 + 2 = - 6

solution is (- 8, - 6 )

To calculate how many flowers of each kind Marisol created, use the formulae x+y=96 and x+3y=192. Marisol used 48 tulips in total to produce Garden Delight bouquets on Monday and Tuesday.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Let x be Spring Mix bouquets and y be the Garden Delight bouquets.

x+y=96

x+3y=192

2y=96

y=48

x=48

The system of equations that you can use to find how many bouquets of each type Marisol made is x+y=96 and x+3y=192. The total number of tulips Marisol used to make Garden Delight bouquets on Monday and Tuesday is 48.

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The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left

You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal.  The graph is a diagram that illustrates the statement.

The given inequality is 2(b + 2) > 24

Opening the brackets to get

2b+4≥24

2b≥24-4

This implies that 2b≥20

Making b the subject

b≥20/2

b≥10

Conclusively the graph is a number line with closed point at 10 with arrow pointing left

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Answer:

9 units

Step-by-step explanation:

The y values are the same, this means that this is a horizontal line.  The distance from -5 to 9 is 14 units.

Answer:

14

Step-by-step explanation:

using the distance formula to determine the distance between the two points

Answer:

[tex]\boxed{47.089 \;meters} \\\\[/tex]

Step-by-step explanation:

For any function f(x), the maximum or minimum value can be determined by 1. Finding the first derivative f(x) with respect to x i.e. f'(x)

2. Setting this first derivative to 0, solving for x

3. Substituting for x in the original function to get the maximum/minimum value

[tex]\textrm{The equation for the function f(t) is }\\f(t) = -4.9t^2 + 20.58t + 25.48\\\\[/tex]

[tex]\textrm{The first derivative of this function with respect to t is }\\\\f'(t) = - 2\cdot 49t + 20.58\\= -9.8t + 25.48\\\\[/tex]

[tex]\textrm{Setting this first derivative equal to 0 gives:}\\\\-9.8t + 20.58 = 0\\\\-9.8t = -20.58 \;\;\;\;\;\textrm{(Subtracting 20.58 from both sides)}\\\\9.8t = 20.58 \;\;\;\;\;\; \textrm{ (Multiplying both sides by -1)}[/tex]

[tex]\textrm{Therefore }\\\\t = \dfrac{20.58}{9.8}\\\\t= 2.1 \textrm{ seconds}[/tex]

[tex]\textrm{Therefore, at = 2.1 seconds, the ball will reach its maximum height.}[/tex]

To find what this maximum height is, substitute t = 2.1 in the original equation and solve for h(t)

[tex]h(t)\;at\;t=2.1 \\h(2.1) = 4.9\cdot \:2.1^2+20.58\cdot \:2.1+25.48=47.089 \;meters\\\\[/tex]

[tex]\textrm{ The maximum height the ball achieves before landing is } \boxed{47.089 \;meters} \\\\[/tex]

[tex]\textrm {This occurs 2.1 seconds after launch }[/tex]