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Let x represent the speed of of boat.

We have been given that the river current is 3 miles per hour.  

The speed of boat upstream will be [tex]x-3[/tex].

The speed of boat downstream would be [tex]x+3[/tex].

[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]

We have been given that you travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to a dock.

We can represent this information in an equation as:

[tex]\text{Time}=\frac{2}{x+3}+\frac{3}{x-3}[/tex]

Since the speed of the boat is 18 miles per hour, so we will substitute [tex]x=18[/tex] in above equation and solve for time.

[tex]\text{Time}=\frac{2}{18+3}+\frac{3}{18-3}[/tex]

[tex]\text{Time}=\frac{2}{21}+\frac{3}{15}[/tex]

[tex]\text{Time}=\frac{2}{21}+\frac{1}{5}[/tex]

[tex]\text{Time}=\frac{2\cdot 5}{21\cdot 5}+\frac{1\cdot 21}{5\cdot 21}[/tex]

[tex]\text{Time}=\frac{10}{105}+\frac{21}{105}[/tex]

[tex]\text{Time}=\frac{31}{105}[/tex]

[tex]\text{Time}=0.295238095[/tex]

Since time is in hours, so let us convert our given time in minutes.

1 hour = 60 minutes.

[tex]\text{Time}=0.295238095\times 60\text{ minutes}[/tex]

[tex]\text{Time}=17.7142857\text{ minutes}[/tex]

Rounding to nearest tenth of minute.

[tex]\text{Time}\approx 17.7\text{ minutes}[/tex]

Therefore, it will take approximately 17.7 minutes for the boat to take the trip.

Answer:

74

Step-by-step explanation:

you find the volume of each one by doing length * width * height and once you find the volume of all of them which is 36, 2, 36 you add them all together and you get 74

Answer:

74 ft

Step-by-step explanation:

Volume = length x width x height

For the 1st square - 3 x 3 x 4

For the rectangle in the middle - 1 x 1 x 2

For the last big square - 3 x 3 x 4

___________________________________

3 x 3 x 4 = 36

3 x 3 x 4 = 36

1 x 1 x 2 = 2

___________________________________

36 + 36 + 2 = 74

___________________________________

The volume of this figure is 74 ft

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Answer:67

Step-by-step explanation:

Answer:

C. The sum of the measures of the interior angles

Step-by-step explanation:

An exterior ∠ is equal to the addition of the two Δ angles not right next to it.The 2 exterior angles at each vertex are = in measure because they are vertical angles.

• The exterior angles (taken one at a vertex) always total 360º

Answer:

x =83

Step-by-step explanation:

supplementary angles add to 180 degrees

x+y = 180

We know y is 97

x+97= 180

Subtract 97 from each side

x+97-97= 180-97

x =83

Answer:

It is 83

Step-by-step explanation:

Supplementary is 180 degrees

180-97=83

Answer:

Exactly 1 solution

Step-by-step explanation:

First we must disrupte3y+27=12y+13

Next we switch one number to the other side27=9y+13

Now we must switch the other number14=9y

Now we must solve by dividing 14 by 9y=1.555

This is one solution, so we now have our answer.

The equation has only one solution. Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equations are given below.

3y = -6x + 9

y = -2x + 3       ...1

y = -6x + 9      ...2

From equations 1 and 2, then we have

-2x + 3 = -6x + 9

4x = 6

x = 6/4

x = 1.5

Then the value of the variable 'y' is calculated as,

y = -2x + 3

y = -2(1.5) + 3

y = - 3 + 3

y = 0

The solution of the equation y = -2x + 3 and y = -6x + 9 will be (1.5, 0). Then the equation has only one solution. Then the correct option is A.

More about the solution of the equation link is given below.

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Answer:

Original side of triangle = 6 units

Step-by-step explanation:

Given:

Perimeter = 45 units

Scale factor = 2.5 (Increase)

Find:

Original side of triangle = ?

Computation:

Original Perimeter = Perimeter / Scale factor

Original Perimeter = 45 units / 2.5

Original Perimeter = 18 units

Perimeter of an equilateral triangle = 3 (Side)

18 units = 3 (Side)

Side = 6 units

Original side of triangle = 6 units

Answer:

45

Step-by-step explanation:

Because this is an isosceles triangle, two of the angles must be equal. Since the third angle is 90 degrees, the other two must be 90/2=45 degrees. Hope this helps!

Answer:

The area of the base is 14.5π in²

Step-by-step explanation:

The volume of a cylinder is given by

Volume =base\:area \times height

Or

V=Bh

It was given that the volume of the cylinder is 174π in³.

The height was given as 12 inches.

We substitute to get,

174π=12B

Divide both sides by 12 to get:

B=14.5π in²

Hence the area of the base is 14.5π in²

Answer:

area of base =  14.5π in²

Step-by-step explanation:

the area of the base of a cylinder with a volume of 174π in^3 and a height of 12 inches is found by applying the formula for the volume of a cylinder:

V = πr²h

Here  the area of the base of a cylinder with a volume of 174π in³ and a height of 12 inches, and so:

V = πr²(12 in) = 174 π in³

Dividing both sides by 12 in isolates πr², which is the area of the base:

                                   174π in³

area of base = πr² = --------------- = 14.5π in²

                                     12 in

Answer:

Dilation

Step-by-step explanation:

The transformation maps the large triangle onto the small triangle will be dilation. Then the correct option is A.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Dilation does not change the shape, but changes the size of the geometry.

2 right triangles have identical angle measures but different side lengths.

The first triangle has side lengths of 6, 10, 8 and the second triangle has side lengths of 3, 5, 4.

The transformation maps the large triangle onto the small triangle will be

6 / 3 = 10 / 5 = 8 / 4 = 2

Then the small triangle is dilated by 2.

Then the correct option is A.

More about the transformation of geometry link is given below.

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The numerical expression shows the amount of video games Alina has left after selling half will be (4 + 8 + 6):2. Then the expression C is correct.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Alina has been collecting video games for a year. The table below shows how many games she has received over the year.

                          Amount of video games

Birthday                             4

Holidays                            8

School trades                    6

Then the total number of the video games will be

⇒ 4 + 8 + 6

At the end of the year, she went to a store and sold half of her video games.

⇒ (4 + 8 + 6) / 2

⇒ (4 + 8 + 6) : 2

Then the expression C is correct.

More about the Algebra link is given below.

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Answer:

Do u have like a worksheet for the problem because that kinda confusing , but I would love to help if you could screens shot or post the pic.

Step-by-step explanation:

Answer:

Step-by-step explanation:

But there is not a question?

Answer: The roots are -5 and 5

Step-by-step explanation:

5^2=25

5^-2=25

Answer:-5 and 5

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

12 +10x  = 81 + 31

Combine like terms

12 +10x = 112

Subtract 12 from each side

12-12+10x = 112-12

10x= 100

Divide each side by 10

10x/10 = 100/10

x = 10

Answer:

10

Step-by-step explanation:

Exterior angle = sum of interior angles

12 + 10x = 81 + 31

12 + 10x = 112

10x = 100

x = 10

7500(1+0.032)5=

1.032 to the power of 5= 1.171

7500x 1.171=8,782

Answer:

A (first graph)

Step-by-step explanation:

Since the equation is negative, the graph will be opening down, and since it is -1, turned into +1, it will shift to the right by one unit.

mutlak değerden + veya- çıkar.

|X-4|<3

-3 <x-4 <3

-3+4 <x <3+4

1 <x <7

The solution to the inequality |x-4| < 3 is x> 1 or x<7

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

|x-4| < 3.

Simplifying,

-3 < x - 4 < 3

Adding 4 to all sides,

1 < x < 7

Therefore, the solution is 1 < x < 7.

To learn more about the inequality;

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Answer:

1 is the out lier

Step-by-step explanation:

if you put them in order: 1, 4, 4, 4, 5, 5, 5, 6, 7, 7, 8, 9, 9

They are in order exept for the one.

To solve this system of equations, we have to cancel out a variable:

12x-4y+28=0

16y-110=48x

Reorder:

12x-4y=-28

-48x+16y=110

Multiply first equation by 4:

4(12x-4y=-28)

-48x+16y=110

=>

48x-16y=-112

-48x+16y=110

0x+0y=-2

0=-2

This can never be true, therefore there are NO SOLUTIONS

Answer:

No Solutions

Answer:

$61.11

Step-by-step explanation:

When the price of something has a certain percent added to it, you can first convert that percentage to a decimal and then add 1, since 1 is the original price. Therefore, we can set up the following equation:

48.50*1.05*1.20=$61.11

Hope this helps!

Answer:

The length and width of the field are 68ft and 32ft respectively

Step-by-step explanation:

Given:

Rectangular Playing Field

Perimeter. P = 200 ft

Required

The dimension of the field (Length and Width)

Let L and W represent the length and the width of the field.

From the question, L is 4 more than twice of W.

This means

L = 4 + 2W

Provided that the playing field is rectangular in shape;

We need to make use of the formula of perimeter of a rectangle.

P = 2(L + W)

Substitute 200 for P

200 = 2(L + W)

Divide through by 2

[tex]\frac{200}{2} = \frac{2(L + W)}{2}[/tex]

100 = L + W

Recall that L = 4 + 2W

Substitute 4 + 2W for L

100 = L + W becomes

100 = 4 + 2W + W

100 = 4 + 3W

Subtract 4 form both sides

100 - 4 = 4 + 3W - 4

96 = 3W

Divide both sided by 3

[tex]\frac{96}{3} = \frac{3W}{3}[/tex]

32 = W

W = 32

Recall that L = 4 + 2W

Substitute 32 for W

L = 4 + 2(32)

L = 4 + 64

L = 68

Hence the length and width of the field are 68ft anf 32ft respectively

Answer:

First one:

4 x minus 5 y = negative 5 and 3 x + 10 y = negative 20

Step-by-step explanation:

4 x - 5 y = -5 (1)

3 x + 10 y = -20 (2)

Multiply (1) by 2 and add to (×)

8x - 10y = -10

3x + 10y = -20

11x = -30

x = -30/11 = -2.727272

x = -2.7

4(-30/11) - 5y = -5

5y = -65/11

y = -13/11 = -1.18181818

y = -1.2

Answer:

4 x - 5 y = - 5 and 3 x + 10 y = - 20

Step-by-step explanation:

4 x - 5 y = -5 (1)

3 x + 10 y = -20 (2)

Multiply (1) by 2 and add to (×)

8x - 10y = -10

3x + 10y = -20

11x = -30

x = -30/11 = -2.727272

x = -2.7

4(-30/11) - 5y = -5

5y = -65/11

y = -13/11 = -1.18181818

y = -1.2

hope this helps..

Answer:

V = 2210.56

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = pi (8)^2 11

V = pi 704

Letting pi = 3.14

V = 2210.56

Answer:

x ≈ 2.34373881

Step-by-step explanation:

Answer:

Area is: 1,728 inches

Perimeter is: 168 inches

Step-by-step explanation:

Area= Length times width

Perimeter= length plus length plus width plus width.

Answer:

1.728 is the perimeter. the area is 84.

Step-by-step explanation:

all you do multiply for perimeter and add for area.

Answer:

x+2

Step-by-step explanation:

6x2 + 30x+ 36

Factor out the greatest common factor

6 (x^2 +5x+6)

Factor inside the parentheses

That 2 numbers multiply to 6 and add to 5

2*3 = 6

2+3 = 5

6(x+3)(x+2)

Answer:

a

Step-by-step explanation:

i think it is a

but I am not sure

Answer:

B. Congruent - SAS

Answer:

2 2/4 or 2 1/2

Step-by-step explanation:

since its like denominators,

3 minus 1= 2

then you move onto fractions

3/4 minus 1/4= 2/4

and if you wanted to simplify 2/4= 1/2