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The slope is 2/6 because the rise is 2 while the run is 6

rise             2

-------    =    -------

run              6

The dimensions of the rectangle for the most economical fence are length, L = 50 feet and width, W = 25 feet

Given: Area =  1250 square feet, , cost of material along three sides = $6 per foot, cost of material for fourth sides = $18 per foot

In order to calculate the dimension of the fence

Let L and W represent the length and width of the fence respectively

Thus, the area of the fence can be represented as:

A = L × W = 1250  ---- (1)

L = 1250/W

Let the total cost to construct the fence be 'C' can be obtained if we construct the shorter side with material with a cost of $18 per foot

C = 6×(2W + L) + 18×L

C = 12W + 24L  ---- (2)

Substituting the value of L from equation 1 into equation 2 we have:

C = 12W + 24×(1250/W)

To minimize the cost we differentiate both sides with respect to W and equate the result to zero:

C = 12W + 24×(1250/W)

dC/dW = d/dW (12W + 30000/W)

0 = 12 - 30000/W²

12W² = 30000

W² = 2500

W = 50 feet

Since L = 1250/W

L = 1250/50

L = 25 feet

Therefore, the dimensions of the rectangle are length of 25 feet and width of 50 feet

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Actually 20 is the answer

The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Also an equation is a set of variables that are constrained through a situation or case.

Given that the 1 gallon is $3.70

x gallons = $3.70x

So, C = 3.70x

This will be the cost of x gallons

Hence "The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x".

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The instantaneous rate of change of power with respect to velocity is 1.6 W/mph.

What is the rate of change function?

The pace at which one quantity changes in relation to another is known as the rate of change function.

Given, P = 0.015[tex]V^{3}[/tex]

Differentiating P with respect to V:

P′=(0.015)(3)[tex]V^{2}[/tex]

At V = 5.9 mph, then

P′=(0.015)(3)[tex]5.9^{2}[/tex] = 1.6 W/mph

Hence, the instantaneous rate of change of power is 1.6 W/mph.

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Answer:

22

Step-by-step explanation:

12 + 19 + 7 + _?_ = 15

38 + _?_ = 15

-38             -38

-----------------------

? = 23

12 + 19 + 7 + 23 = 61

                    -1

12 + 19 + 7 + 22 = 60

60 ÷ 4 = 15

I hope this helps!

Answer:

17

Step-by-step explanation: ..

The length and width of the rectangle is 16 ft and 13 ft respectively.

The perimeter of a rectangle = 2(length + width)

The perimeter of a rectangle = 2(length + width)

58 = 2{(w + 3) + w}

58 = 2(w + 3 + w)

58 = 2(3 + 2w)

open parenthesis

58 = 6 + 4w

subtract 6 from both sides

58 - 6 = 4w

52 = 4w

divide both sides by 4

w = 52/4

w = 13

Hence,

Width of the rectangle = w ft

= 13 ft

Length of the rectangle = (w + 3) ft

= 13 + 3

= 16 ft

Therefore, the dimensions of the rectangle is given by 16 ft and 13 ft respectively

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Answer:

58 members of the House of Representatives, and 28 members of the senate.

Step-by-step explanation:

We can find the answer to this by simply subtracting:

86 - 58 = 28

So, there are 58 members of the House of Representatives, and 28 members of the senate.

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24 units is the area of the shaded region if the "frame" is 2 units wide.

The area of Rectangle is length times of width

We know that the frame is 2 units wide, and the measure of the rectangle and the frame are:

width = 7 units

length = 12 units

Now, if we remove the frame, we will remove 2×2 units = 4 units for each measure (because for each measure we have the frame in both sides).

So the measures for the shaded rectangle are:

width = 7 units - 4 units = 3 units

length = 12 units - 4 units = 8 units.

And the area of a rectangle is given by the product between the width and length, then we have:

A = (3 units)*(8 units) = 24 square units.

Hence, 24 units is the area of the shaded region if the "frame" is 2 units wide.

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Answer:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.

Step-by-step explanation:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.

hope it helps

:)

Answer:

2/7

Step-by-step explanation:

2 parallel lines have the same slope

we just need to find the slope of the line with the point’s connecting O and P

We use y2-y1/x2-x1 to find slope

3-1/2-(-5)

2/7

2/7 is the slope

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The class width of the distribution is 4

Class width is the difference between the Upper class limit and the Lower class limit of a class interval.

Class Width = Upper Class Limit − Lower Class Limit. For example: For a class interval, 163−175, Class Width =175−163=12.

Similarly for a class interval of 75-79, the class width is 79-75= 4.

The upper class limit is 79 and the lower class limit is 75.

The class limit for all the frequency distribution is constant.

Therefore the class width of the distribution is 4

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Answer:

Step-by-step explanation:

If the equation is going off of what is the traditional, and correct way to tip, the tip would be based off the total BEFORE tax.

Therefore, the expression for the total cost would be: x + .23x +.08x, which, simplified, would be 1.33x.

Answer:

$33.25

1 package is $4.75

Step-by-step explanation:

9.5 divided by 2 is 4.75, that is how much one package costs.

4.75 times 7 is 33.25, that's seven packages worth.

The length is 7.25 feet

Here the detail

The formula for rectangled-shaped area is multiply length and width

Area = Length x Width

In this case, we know that the area is 36.25 ft2 and the width is 5 feet

so we can divided the area and the width to solve the length

Area = Length x Width

36.25 = Length x 5

Length = 36.25 : 5

Length = 7.25 feet

Hence the length of the rectangular floor is 7.25 feet

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Answer:

Please look at the attached image, thank you so much! Hope this helps! :D

Step-by-step explanation:

Answer:

6.92820323028, rounded would be 6.92. Even more rounded would be 7.

Step-by-step explanation:

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Answer: -16.66

Reason: 10*-5/3=−16.66666667 or −50/3​

The volume of the jewelry box will be;

⇒ 343 inch³

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The volume of a cube with side s = s³

And, Edna bought a cube-shaped jewelry box that has 7-inch sides.

Now,

Since,  Edna bought a cube-shaped jewelry box that has 7-inch sides.

Hence, The volume of the jewelry box = 7³

                                                           = 7 x 7 x 7

                                                           = 343 inch³

Thus, The volume of the jewelry box will be;

⇒ 343 inch³

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In the given triangle, the length of side t is 87.7 cm

From the question, we are to determine the length of t.

From the given information,

r = 71 cm

∠T = 48°

∠R = 37°

From the law of sines, we can write that

t / sin T = r / sin R

t / sin 48° = 71/sin 37°

t = (71 × sin 48°)/sin 37°

t = 87.6736

t ≈ 87.7 cm

Hence, the length of t is 87.7 cm

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The combination of beads that the student will use to make a model of  magnesium hydroxide, Mg(OH)₂ is

Molecule models depict the positions of the various atoms, roughly to scale, and typically with color coding, as well as how they are joined together.

These models are helpful tools for visualizing the structures and shapes of groupings of atoms, which is vital for understanding the behavior of molecules

Over the course of the development of contemporary atomic theory, models have been employed to represent atom configurations.

The model of magnesium hydroxide, Mg(OH)₂ will require the atoms in the ratio:

Magnesium : Oxygen : Hydrogen = 1 : 2 : 2

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The cost of each chair is $2.25.

The cost of each table is $8.25.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x + 4 = 5 is an equation.

We have,

Cost of each chair = x

Cost of each table = y

Now,

2x + 6y = 54 _____(1)

5x + 3y = 36 ______(2)

From (1) we get,

2x = 54 - 6y

x = (54 - 6y)/2 ______(3)

Now,

Putting (3) in (2) we get,

5(54 - 6y)/2 + 3y = 36

270/2 - 30y/2 + 3y = 36

135 - 15y + 3y = 36

99 = 12y

y = 99/12

y = 8.25 ______(4)

Now,

Putting 4 in (3) we get,

x = (54 - 6 x 8.25) / 2

x = 4.5/2

x = 2.25

Thus,

The cost of each chair is $2.25.

The cost of each table is $8.25.

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Answer: 70%

Step-by-step explanation:

0.7
----- x 100% = 70%

 1

Answer:

70%

Step-by-step explanation:

When turning a decimal into a percent always bring the decimal point two places to the right.

0.7.0.

070%

70%

The graph of the equation y = 30x + 20 is shown below.

It would cost $380 for 12 hours.

The equation of a graph can be written as y = mx + b, if we know the slope of the graph (m) and the y-intercept (b) which is the point on the y-axis that the line will intercept.

Therefore:

Slope/unit rate (m) =  $30 per hour

Rental service charges is the y-intercept (b) = $20

To write the equation, substitute m = 30 and b = 20 into y = mx + b:

y = 30x + 20

See the attachment below for the graph of the equation.

Substitute x = 12 into the equation y = 30x + 20 to find the cost of renting canoe for 12 hours:

y = 30(12) + 20

y = $380

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The solution is Option D.

The equation of the line is y = 28x

What is an Equation of a line?

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 total distance traveled by the car y = 476 miles

Let the total amount of gasoline x = 17 gallons

So , the equation of line is given by

y = mx + c

where m is the slope

Slope m = y /x

Substituting the value for y and x in the equation , we get

Slope m = 476 / 17

              = 28

Therefore , the equation of line is y = 28x  and the graph is given below

Hence , The equation of the line is y = 28x

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Answer:

1,406

Step-by-step explanation:

Answer: Yes.

Step-by-step explanation:

Answer:

yes, it is because the right side is the bigger side.

Step-by-step explanation:

See in a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse.

As several differences are there between them and is differentiated below.

A list of numbers in a specific order is called a sequence. The terms of the sequence are the various numbers that appear in it.

Let a sequence's terms be a1, a2, a3,..., an,..., etc.

The term's position is indicated by the subscripts. That implies,

Initial phrase = a1

term two = a2

term three Equals a3

….

The nth term, indicated by an, is the number that appears in the sequence at the nth place. This phrase is also known as the sequence's general phrase.

Geometric Sequence:

Arithmetic Sequence:

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Answer: 7.5

Step-by-step explanation:

the tank is 15 gallons and you can get 13 percent ethanol or 69 percent ethanol, so you simply just get 7.5gallons of 69 percent and then 7.5 gallons of 13 percent

.69 divided by 15 is .046

.13 divided by 15 is .008

The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.

Given is that a car has a 15 gallon tank and can run on fuel with added

ethanol. The fuel contains either 13 percent ethanol or 69 percent

ethanol.

The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is given by -

{x} = 69% of 15 - {40% of 15}

{x} = (69/100 x 15) - (40/100 x 15)

{x} = 10.35 - 6

{x} = 4.35

Therefore, the amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.

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