A boat covers 25 km upstream and 44 km downstream in t hours. Also, it covers 15 km upstream and 22 km downstream in 5 hours. Find the speed of the boat in still water and that of the stream.​

Answers

Answer 1

9514 1404 393

Answer:

  boat speed: (7t -95)/(6t² -110t +500)

  stream speed: (37t -345)/(6t² -110t +500)

Step-by-step explanation:

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

  time = distance/speed

The boat speed (b) is added to the stream speed (s) going downstream. The stream speed is subtracted going upstream. The given relations tell us ...

  25/(b-s) +44/(b+s) = t

  15/(b-s) +22/(b+s) = 5

This gives us 2 equations in 3 unknowns, so we can only provide a solution in terms of one of the unknowns. Since we are asked for the speeds, they will be provided in terms of t.

Subtracting the first equation from 2 times the second gives ...

  2(15/(b-s) +22/(b+s)) -(25/(b-s) +44/(b+s)) = 2(5) -(t)

  5/(b-s) = 10 -t

  5/(10 -t) = b -s

Substituting for b-s in the second equation gives ...

  15/(5/(10-t)) +22/(b+s) = 5

  30 -3t +22/(b+s) = 5

  22/(b+s) = 3t -25

  22/(3t -25) = b+s

Adding the equations for the sum and difference of speeds, we get ...

  (b-s) +(b+s) = 5/(10-t) +22/(3t -25)

  2b = (5(3t -25) +22(10 -t))/((10-t)(3t-25)) = (95 -7t)/((10-t)(3t-25))

  b = (7t -95)/(6t² -110t +500)

Subtracting the equations for sum and difference of speeds, we get ...

  (b+s) -(b-s) = 22/(3t -25) -5/(10 -t)

  2s = (22(10-t) -5(3t -25))/((10-t)(3t-25))

 s = (37t -345)/(6t² -110t +500)

__

The speed of the boat in still water is (7t -95)/(6t² -110t +500) km/h.

The speed of the stream is (37t -345)/(6t² -110t +500) km/h.

__

Note that these solutions only make sense for values of t between 25/3 and 345/37, approximately 8.33 < t < 9.32. For t=9 hours, the boat speed is 8 km/h and the stream speed is 3 km/h.


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Step-by-step explanation:

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Step-by-step explanation:

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• Then multiply it with the derivative of the term inside the bracket

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the square of a negative number increased by 6 times the number is 72. Find the number.

Answers

Answer:

y = 6

Step-by-step explanation:

(y + 6) × y = 72

y = negative number²

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(6 + 6) × 6 = 72

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Percy wrote a total of 15 pages over 5 hours. After spending 6 hours writing this week, how many pages will Percy have written in total? Assume the relationship is directly proportional. pages

Answers

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Calculate the surface area of the square pyramid below.





yd2

Answers

Answer:

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Step-by-step explanation:

A rectangular prism has a length of 4 inches, a height of 5 inches, and a width of 19 inches. What is its volume, in cubic inches?

Answers

Answer:

380 cubic inches

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Since the scale used by Bruce in the drawing that she made is:

1 milimeter = 10 meters

If the restaurant kitchen is 3 milimeters long in the drawing, the length of the actual kitchen will then be:

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Therefore, the actual length is 30 meters.

Please Help me out I just need the answers and pls make sure they are right idrc for an explantion​

Answers

1. 215.10

2. 57.60

3. 16.11

4. 8.24

5. 89.40

6. 149.10

7. 476

8. 48

9. 59.50

10. 13.49

100 POINTS AND BRAINLIEST

What is the common difference of the arithmetic sequence? −17, −13, −9, −5, −1

A) -17
B) -13
C) 4
D) -4

Answers

Answer:

The common difference is 4 or C on your test

Step-by-step explanation:

-17+4= -13

-13+4= -9

And so on...

Solve for x. Give explanation

Answers

Answer:

x =  47 degrees.

Step-by-step explanation:

The angles in a triangle add up to 180 degrees, therefore:

x + 43 + 90 = 180

x = 180 - 43 - 90

x = 180 - 133

= 47 degrees.

what is the geometric mean between 7 and 12

Answers

Answer:

Geometric Mean = 9.17

Step-by-step explanation:

Here,

a = 7

b = 12

Geometric mean = root(ab)

= root( 7 x 12)

= root(84)

= 9.17

9.5 is the geometric mean of any 2 numbers.

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Answers

Step-by-step explanation:

(x-2) is not a factor

x = -3 is not a zero

Please mark my answer as the brainliest for further answers :)

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Answers

Answer:

s = 4

Step-by-step explanation:

Note that the triangle has 2 congruent base angles, both 45°

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Step-by-step explanation:

Express each of the following as a fraction in its simplest form
if u answer for points,
I will take revenge by doing the same on your questions.

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

Given

[tex]\frac{y}{3}[/tex] + [tex]\frac{y+3}{5}[/tex]

The common denominator is 15 ( the LCM of 3 and 5 )

Multiply numerator/ denominator of first fraction by 5

Multiply the numerator/ denominator of second fraction by 3

= [tex]\frac{5y}{15}[/tex] + [tex]\frac{3y+9}{15}[/tex] ← add numerators , leaving denominator of 15

= [tex]\frac{5y+3y+9}{15}[/tex]

= [tex]\frac{8y+9}{15}[/tex]

(b)

Given

[tex]\frac{3x}{8}[/tex] - [tex]\frac{x+5}{4}[/tex]

The common denominator is 8 ( the LCM of 8 and 4 )

Multiply numerator/ denominator of second fraction by 2

= [tex]\frac{3x}{8}[/tex] - [tex]\frac{2(x+5)}{8}[/tex] ← simplify numerators leaving denominator of 8

= [tex]\frac{3x-2x-10}{8}[/tex]

= [tex]\frac{x-10}{8}[/tex]

Answer:

a) (8y + 9)/15.

b) (5x + 10)/8.

Step-by-step explanation:

(a)  y/3 + (y + 3)/5

     The LCD of 3 and 5  is 15 so we have:

     5y/15 + 3(y + 3)/15

      = (5y + 3(y + 3)) / 15

     = (5y + 3y + 9)/15

     = (8y + 9)/15.

b)  3x/8 + (x + 5)/4

     The LCD of 4 and 8  is 8 so we have:

     3x/8 + 2(x + 5)/8

      = (3x + 2x + 10) / 8

      = (5x + 10)/8.

     

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Answers

Answer:

2*x^(3/8)

Step-by-step explanation:

Answer:

2*x^(3/8)

Step-by-step explanation:

khan

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Answers

Answer:

How about this: There's always an implicit 1 in the expansion:

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21=2⋅1=2

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Answers

Step-by-step explanation:

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[tex](f \: o \: g)(x)[/tex]

means we put the function g(x) into f(x) so that means it looks like

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[tex]x - 4[/tex]

So that expression above is the answer.

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This means for our function to work we can use any numbers as long as it greater than -4.

So we would represent that as x is all real numbers as long as x is greater than or equal to -4

In interval notation this would be

[-4,+ infintiy)

10th term of 4, 7, 10, 13........ (Please enter number only)

Hint
Use a+(n-1)d

Answers

Answer:

31

Step-by-step explanation:

a + (n-1)d  where a = first term;  n = which number we want;  d = common difference.

=> 4 + (10 - 1)3

=> 4 + (9)*3

=> 4 + 27

=> 31

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Answers

12+11x=17x11x+12=17x
(both sides of the equation)
11x+12−17x=17x−17x
(Subtract 17x from both sides)
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(Subtract 12 from both sides)
−6x=−12−6x−6=−12−6
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x=2
Check answers. (Plug them in to make sure they work.)
x=2
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Answers

Answer:

C

Step-by-step explanation:

So what you gotta do is count the lines. You don't count the one with one on it, but you count all the way through to 2. That gets you eight, so each line is 1/8. 1-2 in 1/8 intervals. 1 1/4 multiply 2 on the numerator and denominator gets 1 2/8, 1 1/2 multiply 4 on the numerator and denominator gets you 1 4/8. Counting the lines, each of those matches up. The first interval is 1 1/8.

1. Find the probability that you will roll a six and then a five when you roll a die twice
2. A bag contains 3 red, 4 blue, and 6 yellow marbles. One Marble is selected at a time, and once a marble is selected, it is replaced, find each probability.

Answers

1/36 for the first need the questions for the second

33/q = 8/12 q=?
What is q

Answers

Answer:

q= 49.5

Step-by-step explanation:

[tex] \frac{33}{q} = \frac{8}{12} [/tex]

Cross multiply:

8q= 33(12)

8q= 396

Divide by 8 on both sides:

q= 396 ÷8

q= 49.5

After winning a soccer game, the coach took the team out for ice cream cones. He spent $21 on 12 single-scoop ice cream cones. If all the ice cream cones cost the same amount, what was the cost of one ice cream cone?

Answers

Answer:

Unitary cost= $1.75

Step-by-step explanation:

Giving the following information:

He spent $21 on 12 single-scoop ice cream cones.

To calculate the unitary cost, we need to use the following formula:

Total cost= number of units*unitary cost

Unitary cost= total cost / number of units

Unitary cost= 21 / 12

Unitary cost= $1.75

There are 120 pieces of candy in a bag. Fill in the table below to determine the number of pieces of each color

Answers

Answer:

Blue = 30

Green = 24

Red = 54

Orange = 12

Step-by-step explanation:

hahahshahhahahahahahauehfudbrog f ghg

**EASY**

Determine the intercepts of the line -

2x + 5y = -6


Y-intercept: (_ , _)

X-intercept: (_ , _)

Answers

The answer is
X intercept : -3,0
Y intercept: 0, -6/5
The answer is y-intercept: (0, -6/5) and X-intercept: (-3, 0)

up
Write an equation for the translation of x2 + y2 = 49 by 3 units left and 4 units
O(x + 3)2 + (y + 4)2 = 49
O(x + 3)2 + (y – 4)2 = 49
O(x – 3)2 + (y – 4)2 = 49
O(x – 3)2 + (y + 4)2 = 49

Answers

Answer: (x+3)^2+(y-4)^2=49

The answer is b :)

Step-by-step explanation:

Of the last 10 contestants on a game show, 8 won a prize. Considering this data, how many of the next 20 contestants would you expect to win a prize? contestants Submit Type the answer please or don't do it​

Answers

8/10 to find the probability of winning.
8/10 = 0.8
then multiply this by the number of contestants
0.8 * 20
this gives 16

Help me out here plz

Answers

Answer:

I think that it would be [tex]28^{2}[/tex] cm

Step-by-step explanation:

8 x 7 = 56

56/2 = 28

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