boat traveled downstream a distance of 60 mi and then came right back. If the speed of the current was 6 mph and the total trip took 4 hours find the average speed of the boat relative to the water.

Answers

Answer 1

Answer:

7.5mph

Step-by-step explanation:

Let the average speed of the boat to be x mph.

Total Distance = Avg. Speed x Total Time

60 = ((x+6) + (x-6))(4)

60 = (x+6+x-6)(4)

(2x)(4)=60

2x=60/4

2x = 15

x = 15 /2

x = 7.5mph

Answer 2

Answer:

  15 +√261 ≈ 31.155 mph

Step-by-step explanation:

The time for the trip can be found by dividing the distance by the speed.

__

setup

The relation between time, speed, and distance is ...

  time = distance/speed

The speed for the downstream leg was the sum of the boat speed (b) and 6 mph. The speed for the upstream leg was the difference. So the total trip time was ...

  4 = 60/(b +6) +60/(b -6) . . . total  time is the sum of the times for the legs

__

solution

Multiplying by the product of the denominators, we have ...

  4(b +6)(b -6) = 60(b -6) +60(b +6)

  b² -36 = 30b . . . . divide by 4 and simplify

  b² -30b = 36 . . . . put in a form useful for completing the square

  (b -15)² = 36 +15² . . . . . complete the square

  b -15 = √261 . . . . . . . . take the square root (negative root is extraneous)

  b = 15 +√261 ≈ 31.155 . . . . add 15

The average speed of the boat was about 31.155 mph.


Related Questions


Dan sold 40 concert tickets in 5 days.
Each day he sold 3 tickets MORE than the
previous day. The number of tickets he
sold on the third day is?

Answers

Step-by-step explanation:

The number of tickets sold by Dan the first day is x.

Tickets sold on the 2nd day: x+3

on the 3rd day: x+6

on the 4th day: x+9

on the 5th: x+12

Since the total of tickets sold by Dan is 40:

x+(x+3)+(x+6)+(x+9)+(x+12)=40

5x+30=40

5x=10

x=2

number of tickets sold on the third day: 8

If a population of a town is recorded at 1,200 in the year 2000 and the population increases by exactly 50 people each year, what will be the population of the town in 2018? Be careful to treat the year 2000 as the beginning; let x be the number of years since the year 2000.

The answer is not 2,100

Answers

The population at the end of the year 2018 will be 2150.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

If a population of a town is recorded at 1,200 in the year 2000 and the population increases by exactly 50 people each year, what will be the population of the town in 2018.

The population will be calculated as the year 2000 is also considered:-

P = Total years x Increase per year

P = 19 x 50

P = 2150

Therefore the population at the end of the year 2018 will be 2150.

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25) Which graph represents the equation below? ) = w+ 2 A ܠܐ 5 4 (2, 4) 3 2 1 (-2,0) -5 -4 -3 -2 -1 0 -1 x 1 2 3 4 5 -2 -3 -4 -5 8 y​

Answers

The given line equation is y=-1/2x+2

We have given the graph of the line

We have to determine the equation of the line,

We have to points(0,2) and (4,0)

What is the formula for the slope?

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

m=0-2/4-0

m=-2/4

m=-1/2

What is the slope point form?

[tex](y-y_1)=m(x-x_1)[/tex]

[tex]y-0=-1/2(x-4)\\y=-1/2x+2[/tex]

Therefore the second option is correct

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PLEASEEEEEEEEEE HELPPPPPPPPPP!! IM SO CONFUSED HOW TO DO THIS!

Create a word problem that can be represented by this mathematical statement and solve your problem.

12! / 3! 9!

Answers

How many apples would you have if you combined 3 apples and 9 apples?
you would have 12 apples.

Find the average of the numbers 6 4/7, 1 5/56, 9 1/7, 3 5/8. Write the solution as a mixed number or a fraction in lowest terms.

Answers

Answer:

[tex]\frac{187}{112}[/tex]

Step-by-step explanation:

Just add them all up in the calculator and divide by the number of numbers, which in this case is 4

Step-by-step explanation:

follow the steps in the attached

WILL GIVE THE BRAINLIEST!

If r and s are real numbers such that
r>s>0, then

(A) -s>-r> 0.
(B) 0>-r> -s.
(C) 0> -s> -r.
(D) -s>0> -r.
(E) -r> -s > 0.

Answers

Answer:  Choice (C)  0> -s> -r

==========================================================

Explanation:

Let's consider an example. Pick any two positive numbers for r and s, where r is larger than s. I'll go with these:

r = 5s = 2

We see that r > s is true since 5 > 2 is true

Also both are larger than 0 so we can say r > 0 and s > 0

This all combines into r > s > 0 being the case.

If we negate each number, then -r > -s would no longer be true. Use a number line to see that -5 is to the left of -2, so -5 > -2 is not true. Instead it would be -5 < -2

You can think of it like floors on a skyscraper. Positive numbers are above ground, while negative numbers are below ground in the basement levels. See the diagram below.

So -r > -s must be -r < -s instead. Both are smaller than 0

-r < 0 and -s < 0

This combines to -r < -s < 0

Flip everything and swap the outer sides to get 0 > -s > -r which leads us to choice C as the final answer

How much time do you actually save by speeding?

Answers

Is this a genuine question? If so, you would calculate how long it would take for you to reach your destination based on the speed limit. If the speed limit is 40 mph and you need to drive 100 miles, divide the distance by the speed and you find it would take you 2.5 hours. If you speed and go, let’s say 50 mph, divide 100 miles by 50 mph and you will find that it will take 2 hours, saving half an hour of time. Use this strategy to find out how much time you save.
Short answer: if you speed, you go faster. If you go faster you save more time reaching the destination.

find SP when profit loss is given​

Answers

Answer:

the formulas for profit and loss percentage are given below profit percentage p profit cost price into 100 loss percentage l is equal to loss cost price is into 100 SP

Waiting for answer, could u help?

Answers

Answer:

The practical domain of function is , Roscoe can ride his bike only from 10 miles to 30 miles.

Domain of function is defined as the set of input values for which the function is defined i.e.  the set of its possible inputs,

The amount of time it takes for Roscoe to ride his bike m miles is represented by a function.

                     

Where m represent, number of miles he can ride.

Above function is defined for every value of m . But in question it is mention that Roscoe rides his bike at least 10 miles but not more than 30 miles.

Therefore, Domain of function is from 10 miles to 30 miles

Step-by-step explanation:

Given: m∡MXY = m∡KXY

What is the conclusion reached by this proof?

Answers

Answer:

b

Step-by-step explanation:

just took it

Answer:

B. m∠JXY = m∠NXY

Step-by-step explanation:

I got the answer correct

Help I’m stuck on this question! Please help.

Answers

Answer: 20

Step-by-step explanation:

A and B have 57+79-42=94 distinct elements in total.

This means that 114-94=20 elements are in neither A nor B.

question is in the image below please help

Answers

Answer:

p= 80

Step-by-step explanation:

p+8 =  8 x 11

p+8 = 88

p= 88-8

p= 80

P=80 because that’s the answer

Help me please, geometry

Answers

Answer:

x = 19.5 (nearest tenth)

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

[tex]\theta[/tex] is the angle

O is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)

Use the cos ratio to find the measure of the altitude (the perpendicular drawn from the vertex of the triangle to the opposite side):

[tex]\implies \cos(47^{\circ})=\dfrac{a}{18}[/tex]

[tex]\implies a=18\cos(47^{\circ})[/tex]

Now use the sin ratio to the the measure of side x:

[tex]\implies \sin(39^{\circ})=\dfrac{a}{x}[/tex]

[tex]\implies x=\dfrac{a}{\sin(39^{\circ})}[/tex]

[tex]\implies x=\dfrac{18\cos(47^{\circ})}{\sin(39^{\circ})}[/tex]

[tex]\implies x=19.50671018[/tex]

Therefore, x = 19.5 (nearest tenth)

the length of a rectangle is 5 cm less than 3 times its width. The perimeter is 62 cm.
What is the length?

Answers

Answer:

length=22 [cm].

Step-by-step explanation:

1) if the length is 'l' and the width is 'w', then it is possible

2) to write the given perimeter: 62=2(l+w), - this is the 1st equation of system;

3) to write the condition 'the length of a rectangle is 5 cm less than 3 times its width' as 3w-5=l, - this is the 2d equation of the system.

4) using two equations above it is possible to make up the next system:

[tex]\left \{ {{2(w+l)=62} \atop {3w-5=l}} \right. \ = > \ \left \{ {{w+l=31} \atop {3w-l=5}} \right. \ = > \ \left \{ {{l=22} \atop {w=9}} \right.[/tex]

5) finally, the length=22 [cm].

At a soccer game, a vendor sold a combined total of 220 sodas and hot dogs. The number of sodas sold was 46 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.

Answers

Answer:

133 sodas

87 hot dogs

I've completed the work in the photo, just trying to reach the letter count lol

Express cos S as a fraction in simplest terms.

Answers

Answer: Read attachment.

Step-by-step explanation: Attached below is my work. Hope it helps!

Which expressions are equivalent to the given equation. Logarithmic form

Answers

The expression that is equivalent to the given logarithm equation is log₄ 1 / 4  + log₄ x²

How to solve logarithm?

log₄ (1 / 4 x²)

Using logarithm law, the logarithm can be express as follows;

using logarithm law,

Therefore, the expression that is equivalent to the given logarithm equation is as follows:

using addition law for logarithm,

log₄ (1 / 4 x²) = log₄ 1 / 4  + log₄ x²

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In our QR class, 43% live in Massachusetts. Of the Massachusetts residents, 67% live in
Boston. What percentage of the class lives in Boston?

Answers

Answer:

The answer will be 63%.

Step-by-step explanation:

they have all ready mentioned that.

What is the solution to this system of equations
3x+y=17
X+2y=49

Answers

Answer:

x=−3 and y=26

Step-by-step explanation:

Let's solve your system by substitution.

3x+y=17;x+2y=49

Step: Solve 3x+y=17 for y:

3x+y=17

3x+y+−3x=17+−3x(Add -3x to both sides)

y=−3x+17

Step: Substitute−3x+17 for y in x+2y=49:

x+2y=49

x+2(−3x+17)=49

−5x+34=49(Simplify both sides of the equation)

−5x+34+−34=49+−34(Add -34 to both sides)

−5x=15

-5x/5  = 15/-5 (Divide both sides by -5)

x=−3

Step: Substitute −3 for x in y=−3x+17:

y=−3x+17

y=(−3)(−3)+17

y=26(Simplify both sides of the equation)

Answer:

x=−3 and y=26

Which of the following is correct based on this picture?

Answers

B. none of these are correct

Given the function f(x) = -0.5|2x + 2 + 1, for what
values of x is f(x) = 6?
x = 6, x = -5
x = 5, x = -5
x= 7, x=-6
Ono solution
DONE

Answers

Answer:

Step-by-step explanation:

56565656565656565656565

Evaluate.
-|a+b| 2-c when a=1 2/3 b=-1 ,and c= -3 Enter your answer as a simplified fraction in the box.

Answers

Step-by-step explanation:

-| 12/3 - 1| 2-(-3)

-|12-3/3|5

-5|9/3|

-5|3|

-5×3 & -5×-3

-15 & 15

I think it is the answer

The graph of y=x−2−−−−√ is is transformed to become y=x+3−−−−√−2. Which of the following statements best describes the effect this transformation has on the graph of y=x−−√

Answers

Answer:

The graph is translated 5 units left and 2 units down

Step-by-step explanation:

transformation =

initially the equation of graph  [tex]y=\sqrt{x-2} = f(x)[/tex]

after transformation the equation becomes [tex]y = \sqrt{x+3} -2 = g(x)[/tex]

transformation done [tex]f(x) = \sqrt{x-2}[/tex]  → [tex]g(x) = \sqrt{x+3} -2[/tex]

The horizontal shift of graph  

it depends on the value of h. The horizontal shift is described as:

g(x) = f(x + h) - The graph is shifted to the left h units.

g(x) = f(x - h) - The graph is shifted to the right h units.

if h=0,  means that the graph is not shifted to the left or right

the vertical shift of graph

The vertical shift depends on the value of k. The vertical shift is described

as:

g(x) = f(x) +k    - The graph is shifted up k units.

g(x) = f(x)- k     - The graph is shifted down k units.

so here in the question the graph is shifted 5 units left and then 2 units down

you can see the graph of initial equation and transformed equation below.

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what would 41.2 hours converted into minutes?​

Answers

41.2 hours converted to minutes would correctly be stated as : 2472
Answer: 2472 mins

Step-by-Step Explanation:

Time In Hours = 41.2 hrs
No. Of Minutes in an Hour = 60 mins

Therefore,
Time in Minutes = 41.2 * 60 = 2472 mins

need help i don't know what im doing?​

Answers

Answer:

X=5

Step-by-step explanation:

f(1)= -1^2+4(1)+12=15

f(2)= -2^2+4(2)+12=16

f(3)= -3^2+4(3)+12=15

f(4)= -4^2+4(4)+12=12

f(5)= -5^2+4(5)+12=7

g(1)=1+2=3

g(2)=2+2=4

g(3)=3+2=5

g(4)=4+2=6

g(5)=5+2=7

so g(5)=f(5)= X=5

Answer:

Step-by-step explanation:

You're suppose to plug in the values 1, 2, 3, 4, 5, and 6 into f(x) and g(x) to find where they're equal to find the solution to f(x) = g(x) (when the column values are equal).

So for example

f(1) = -(1)^2 + 4(1) + 12

f(1) = -1 + 4 + 12

f(1) = 15

g(1) = 1 + 2

g(1) = 3

put these two values in the table for f(1) and g(1)

f(2) = -(2)^2 + 4(2) + 12

f(2) = -4 + 8 + 12

f(2) = 16

g(2) = 2 + 2

g(2) = 4

f(3) = -(3)^2 + 4(3) + 12

f(3) = -9 + 12 + 12

f(3) = 15

g(3) = 3 + 2

g(3) = 5

f(4) = -(4)^2 + 4(4) + 12

f(4) = -16 + 16 + 12

f(4) = 12

g(4) = 4 + 2

g(4) = 6

f(5) = -(5)^2 + 4(5) + 12

f(5) = -25 + 20 + 12

f(5) = 7

g(5) = 5 + 2

g(5) = 7

f(5) = g(5) so the solution is when x=5

f(6) = -(6)^2 + 4(6) + 12

f(6) = -36 + 24 + 12

f(6) = 0

g(6) = 6 + 2

g(6) = 8

When filling your gas tank, if you pay c dollars for g gallons of gas, you have the following table.


Choose all of the following statements that are true.


a.
The domain is {4, 8, 11, 15}.


b.
An 11 gallon tank would cost $44.00 to fill completely.


c.
A 9.1 gallon fill-up would cost $35.49.


d.
A 12 gallon tank would cost $47.40 to fill completely.

Answers

Option D statement "A 12-gallon tank would cost $47.40 to fill completely" is true.

What is a domain?

The whole of the independent variable's possible values makes up the domain of a function.

For the given data we need to find which of the given statements are true.

From option A:

The domain is {4, 8, 11, 15}.

The domain is all possible x values so this would be 0 to infinity as you can pay for more gallons not just to that certain set of numbers.

Therefore, option A is False.

From option B:

An 11-gallon tank would cost $44.00 to fill completely.

From the given table we can see that 11-gallon tank costs $43.45.

Therefore, option B is False.

From option C:

A 9.1-gallon fill-up would cost $35.49.

To find 9.1 gallons we need to find the cost of 1-gallon.

That is, 15.80/4 = $3.95 (Given in the table)

Now the cost of 9.1 gallon tank is $3.95 x 9.1 = $35.95 not $35.49

Therefore, option C is False.

From option D:

A 12-gallon tank would cost $47.40 to fill completely.

We found that 1 gallon is $3.95.

$3.95 x 12 = $47.40

Therefore, option D is True.

Hence, from the given statements option D is True.

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A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet. What is the height of the tunnel 5 feet from the edge? Round your answer to the hundredths place.

9.99 feet
13.82 feet
24.65 feet
25.01 feet

Answers

The height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

What is an ellipse?

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

A tunnel is constructed with a semi-elliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet.

2a = 60 (width of the tunnel is 60 feet)

a = 30

And the maximum height at the center of the tunnel is 25 feet

b = 25

Let's assume the center of the ellipse is at the origin.

So the equation of the ellipse:

[tex]\rm \dfrac{x^2}{30^2}+\dfrac{y^2}{25^2}=1[/tex]

Now plug x = a - 5 = 30 - 5 = 25

[tex]\rm \dfrac{25^2}{30^2}+\dfrac{y^2}{25^2}=1[/tex]

After solving:

[tex]\rm \dfrac{y^2}{25^2}=1-\dfrac{25}{36}[/tex]

[tex]\rm y^2=\dfrac{6875}{36}[/tex]

y = ±13.819 ≈ ±13.82

Height cannot be negative

y = 13.82 feet

Thus, the height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

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I will give lots of points please help

Answers

Step-by-step explanation:

PART 1:

on the graph you can make a triangle at any point and with any angle measures.

i recommend a smaller right triangle to be easiest.

i recommend the points (0,3) A (3,0) B and (0,0) C

∆ABC angle measurements:

m∠CAB=45°

m∠ABC=45°

m∠ACB=90°

PART 2:

(4,3) D (7,0) E and (4,0) F make an identical right triangle moved 4 squares to the right

m∠FDE=45°

m∠DEF=45°

to find the missing value of the angle EFD we will use subtraction and addition

180-(45+45)

180-90

90

therefore, the m∠EFD=90°

PART 3:

both the angle measures and the shapes of the triangles are the same

PART 4:

i used a 1:1 ratio

sorry for the wait :)

4x² + 24x + 20
common factor =

Answers

The common factor is 4

Please need the answer ASAP for number 3!!!!

Answers

Answer:

second and fourth option

Step-by-step explanation:

the discriminant of a quadratic equation is the easiest way to know how many solutions there will be

(discriminant: b²- 4ac)

{a discriminant of 0 means 1 solution; discriminant < 0 means no real roots, discriminant > 0 means two real roots }

so, we can quickly run b² - 4ac for each equation provided:

(note: ax² + bx + c is the formatting we use to find a, b, and c)

8² - 4(-9)(-8)

64 - 288 = -224

4² - (4)(1)(4)

16 - 16 = 0

-1² - (4)(-10)(-9)

-1 - 360 = -361

-6² - (4)(3)(3)

36 - 36 = 0

So, because the second and fourth options listed have a discriminant of 0, they have 1 real solution

hope this helps!! have a lovely day :)

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One such gift was a codebook from the German ship Magdeburg, a light cruiser that ran aground on an island off of Finland.When Russian ships quickly bore down on the cruiser, the captain of the stranded ship immediately did what all naval officers were taught to do: he ordered his signalman to bring him the ship's codebook so he could throw the book, wrapped in lead covers, into the sea.But before the signalman could deliver the book to his captain, he was killed by Russian guns.When the Russians recovered his body, the sailor was still clutching the codebook in his arms. Translate the following sentences into Spanish.Suddenly we heard a strange (extrao) noise. Which will increase GDP the most: 1 pound of whole apples priced at $1.99/pound, or a16 ounce package of sliced apples priced at $5.99? Explain why. Which of the following molecules Carries genetic information that determines the physical characteristics that organisms inherit? 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If you draw all hearts from a deck of 52 cards,what is the ratio of the remaining cards to thewhole deck? A cylindrical barrel of water has a base radius of 30 cm and is 110 cm high.a) Find its volume in cm.b) Find its capacity in litres( Hint is 1 cm= 1 ml )c) Find the number of bottles of water that can be filled from the barrel if each bottle holds 0.73 litres. Which of these statements is NOT true of the phylogenetic tree? A recent study found that the death rate for people who sleep 6 to 7 hours per night is lower than the death rate for people who sleep 8 or more hours. The 1.1 million observations used for this study came from a random survey of Americans aged 30 to 102. Each survey respondent was tracked for 4 years. The death rate for people sleeping 7 hours was calculated as the ratio of the number of deaths over the span of the study among people sleeping 7 hours to the total number of survey respondents who slept 7 hours. 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