In still water, a boat averages 18 miles per hour (mph). It takes the same amount of time to travel 33 miles downstream (with the current) as it takes to travel 21 miles upstream (against the current). What is the rate of the water's current

Answers

Answer 1

Answer:

The rate of the water current is 4mph

Step-by-step explanation:

Let c= the rate of the current in mph

18+c= the rate of the boat going downstream in mph

18-c= the rate of the boat going upstream in mph

t = time in hrs for both upstream and downstream trips

Going downstream:

33=(18+c)*t (1)

Going upstream

21=(18-c)*t (2)

From (1)

33=(18+c)*t

t=33/1(8+c)

Substitute t=33/(18+c) into (2)

21=(18-c)*t

21=(18-c)*33/(18+c)

Cross product

21(18+c)=33(18-c)

378+21c=594-33c

21c+33c=594-378

54c=216

Divide both sides by 54

54c/54=216/54

c=4

Therefore,

The rate of the water current is 4mph


Related Questions

What is the value of m in the equation
zm = 16, when n = 8?

Answers

Step-by-step explanation:

nm=16

m=16/n

m=16/8

m=2

Which methods could you use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0, -12)?

Answers

Answer:

add the y coordinates of the two lines and divide by 2

Step-by-step explanation:

½[0+(-12)]

½[0-12]

½[-12)

y co-ordinate of the midpoint is -6

Help help help please I need help fast

Answers

The answer would be x =7/5 because you would need to multiply everything by two. Then you would add 4+3 and you would end up with 5x = 7. After that, you need to divided both answers by five

Please Mark brainliest

Answer:

The answer is x=7/5

Step-by-step explanation:

because you have to multiply everything by 2 the add 4+3 and you end up with 5x=7 then divide both sides by 5

HELP ASAP LINEAR EQUATIONS!!

Answers

Answer:

y = 4/3x - 10.

Step-by-step explanation:

3x + 4y = 12

4y = -3x + 12

y = -3/4x + 3

If a line is perpendicular to another, the line has a slope that is the negative reciprocal of the other line. Since the given line has a slope of -3/4, the line perpendicular to that line will have a slope of 4/3.

So far, for the equation of the line, we have an equation of y = 4/3x + b.

To find b, simply substitute the coordinates (6, -2) for x and y.

-2 = 4/3(6) + b

b + 4/3(6) = -2

b + 8 = -2

b = -10

So, the equation of the line will be y = 4/3x - 10.

Check your work...

-2 = (4/3)(6) - 10

-2 = 8 - 10

-2 = -2

Hope this helps!

Answer: C) [tex]y = \frac{4}{3} x-10[/tex]

Step-by-step explanation:

First change this equation into slope-intercept form(y = mx + b).  y = -3/4x + 3.

For a line to be perpendicular to another line, it must have an opposite reciprocal slope.  The opposite reciprocal of -3/4 is 4/3.  Thus, the answer is NOT B.  Then, attempt to plug in 6, -2 into each equation.  The only one where it works is C.

Hope it helps <3

Given the equation y=2x-8, which statement is correct ? A.Y=2(x-4) has a y-intercept of 4 B. Y=2(x-4)has a y-intercept of -4 C. Y=2(x-4) has a x- intercept of 4 D. Y=2(x-4)has a x intercept of -4

Answers

Answer:

Correct option: C -> Y=2(x-4) has a x- intercept of 4

Step-by-step explanation:

To find the y-intercept of the equation y = 2x - 8, we just need to find the value of y when x = 0:

[tex]y = 2*0 - 8 = -8[/tex]

To find the x-intercept of the equation y = 2x - 8, we just need to find the value of x when y = 0:

[tex]0 = 2*x - 8[/tex]

[tex]2x = 8[/tex]

[tex]x = 4[/tex]

So the y-intercept is -8 and the x-intercept is 4.

Correct option: C -> Y=2(x-4) has a x- intercept of 4

What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12? (–6, 0), (2,0) (–2, –16), (0, –12) (–6, 0), (–2, –16), (2, 0) (0, –12), (–6, 0), (2, 0)

Answers

Answer:

(-6, 0) and (2, 0)

Step-by-step explanation:

To find the x-intercepts, we can factor the expression:

f(x) = x² + 4x - 12

2 factors of -12 that add up to 4 are 6 and -2

(x + 6)(x - 2)

Set each factor equal to 0 and solve for x:

x + 6 = 0

x = -6

x - 2 = 0

x = 2

So, the x intercepts are (-6, 0) and (2, 0)

Answer:

It's the first option, (-6, 0) (2, 0)

Step-by-step explanation:

100% on Edge

Simplify 2(x - 3) + 7(x + 2)

Answers

Answer:

9x + 8.

Step-by-step explanation:

2(x - 3) + 7(x + 2)

= 2x - 6 + 7x + 14

= 2x + 7x - 6 + 14

= 9x + 8.

Hope this helps!

Which function represents the following graph?

Answers

Answer:

y = ∛(x+3) + 3

Step-by-step explanation:

I plugged each equation into a graphing calculator.

Alonso is packing a box for shipping. The box contains 3 square ceramic plates with side lengths of 8 inches. He estimates that he will need 102 • 4 – 3(8 • 8 • 1) cubic inches of packing foam. Simplify to find the number of cubic inches of packing foam he will need.

Answers

Answer:

216 cubic inches

Step-by-step explanation:

We want to simplify:

102 * 4 - 3(8 * 8 * 1)

We will apply BODMAS:

Solving the Bracket first:

102 * 4 - 3(64)

102 * 4 - 192

=> 408 - 192

= 216 cubic inches

He will need 216 cubic inches of packing foam.

In his pocket, Hamid has $2.95 in dimes and quarters. If there are 16 coins in total, which system represents the number of dimes and quarters that Hamid has? x + y = 16. 0.10 x + 0.25 y = 2.95. x + y = 16. 0.05 x + 0.25 y = 2.95. x + y = 2.95. 0.10 x + 0.25 y = 16. x + y = 16. 0.01 x + 0.25 y = 2.95.

Answers

Answer: x + y = 16. 0.10 x + 0.25 y = 2.95. x + y = 16.

Step-by-step explanation:

You know that there are 16 coins in all, so x + y has to equal 16 (x being dimes and y being quarters) but you also know that whatever compilation of dimes and quarters is equal to $2.95.

Hope this helped you! Feel free to ask any further questions!

The system of equations which represents the number of dimes and quarters that Hamid has are x+y=16 and 0.10x+0.25y=2.95.

What is equation?

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

How to form equation?

Suppose  the number of dimes be x and the number of quarters be y.

According to question there are 16 coins, so

x+y=16-----1

1 dime=$0.10

1 quarter=$0.25

According to question Hamid has $2,95 ,so

0.10x+0.25y=2.95.

Hence the system which represents the number of dimes and quarters that Hamid has are x+y=16 and 0.10x+0.25y=2.95.

Learn more about equation at https://brainly.com/question/2972832

#SPJ2

A standard fair dice is rolled twice. What is the probability of getting an odd number on the first roll and any number except 4 on the other?

Answers

Answer:

Let,O and P be the events of getting odd number and any other number except 4 respectively.

n(S)=6

O=(1,3,5) so, n(O)=3

P=(1,2,3,5,6) so, n(P)=5

So,probability of getting an odd number and any other number except 4 will be

n(O)/n(S) × n(P)/n(S)

=3/6 × 5/6

=5/12

May be it's the answer I guess. Hope you're clear with it:-)

Type the correct answer in each box, If necessary, use / for the fraction bar(s).
1
-1
The point on the number line shows the opposite of
or the opposite of the opposite of
Reset
Next

Answers

Answer: -1/1

Step-by-step explanation: The fraction, -1/1 or just -1, passes through the transactional point through the slope of the line, y=3x+5.

If 8a^2+ 2b^2= 10 and ab = 2, then what is the value of (2a+b)^2

Answers

Answer:

13

Step-by-step explanation:

We have:

8a^2 + 2b^2 = 10

Dividing both sides by 2,

=> 4a^2 + b^2 = 5

or (2a)^2 + b^2 = 5

We also have ab = 2

=> (2a + b)^2

= (2a)^2 + 2(2a)(b) + b^2

= (2a)^2 + b^2 + 4ab

= 5 + 4(2)

= 5 + 8

= 13

Mabel is comparing the prices of two car rental companies. Company A charges $35 per day and an additional $15 as service charges. Company B charges $42 per day and an additional $10 as service charges. Part A: Write an equation to represent each company's total charges for renting a car for a certain number of days. For both equations (one for Company A and one for Company B), define the variable used. (4 points) Part B: Which company would charge less for renting a car for 6 days? Justify your answer. (3 points) Part C: How much money is saved by using the services of Company A instead of Company B to rent a car for 10 days?

Answers

Answer:

Part A:

Equation for Company A:

x = Number of days renting a car

35x + 15

Equation for Company B:

x = Number of days renting a car

42x + 10

Part B:

Company A will charge $ 37 less than Company B

Part C:

Company A will charge $ 65 less than Company B

Step-by-step explanation:

Part A:

Equation for Company A:

x = Number of days renting a car

35x + 15

Equation for Company B:

x = Number of days renting a car

42x + 10

Part B:

Renting a car for 6 days

Company A:

35 * 6 + 15 = 210 + 15 = $ 225

Company B:

42 * 6 + 10 = 252 + 10 = $ 262

Company A will charge $ 37 less than Company B

Part C:

Renting a car for 10 days

Company A:

35 * 10 + 15 = 350 + 15 = $ 365

Company B:

42 * 10 + 10 = 420 + 10 = $ 430

Company A will charge $ 65 less than Company B

...................​

Answers

Answer:

x = a(c + b)

Step-by-step explanation:

Step 1: Add b to both sides

x/a = c + b

Step 2: Multiply both sides by a

x = a(c + b)

Please help me with this question!!

Answers

Answer: Choice B) The conjecture is valid given the focus is on proportional equivalence of two sectors.

This is another way of saying "the two pie slices are the same percentage in area". By this, I mean the percentage of the entire cake. For instance, the shaded slice could be 20% of the entire circle area, for each circle.

It's probably easier to see this is the angle was 90 degrees (split the cake into 4 equal slices, only shade one slice). Or probably even easier if you cut the cake into two slices and only shade one slice (to form a central angle of 180 degrees). For the first example, the slice would be 25% of the whole area, while the second slice is 50%.

Choice C is close, but the two sectors are not the same area. This is because the bottom circle has a larger radius, and therefore its sector area is larger.

Which expression is equivalent to (–3y – x) – (5y – 8x)?

Answers

Answer:

-8y +7x

Step-by-step explanation:

(–3y – x) – (5y – 8x)Distribute

-3y -x -5y +8x

Combine like terms

-3y-5y -x+8x

-8y +7x

Please answer for brainliest!!!Find the equation of a line that passes through the point (-2,1) and has a gradient of 3. Leave your answer in the form ax+by=c Where a, b and c are integers

Answers

Answer:

3x - y = - 7

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 3 and (a, b) = (- 2, 1) , thus

y - 1 = 3(x + 2) ← distribute

y - 1 = 3x + 6 ( subtract 6 from both sides )

y  - 7 = 3x ( subtract y from both sides )

- 7 = 3x - y, that is

3x - y = - 7 ← in standard form

Write the equation of the line that passes through (2, 3) and is parallel to the line 12x – 5y = 2.

Answers

Answer:

The answer is

5y - 12x = - 9

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

12x - 5y = 2

5y = 12x - 2

Divide both sides by 5

y = 12/5x - 1/5

Comparing with the above formula

Slope / m = 12/5

Since the lines are parallel their slope are also the same.

Slope the parallel line = 12/5

Equation of the line using point (2,3) is

[tex]y - 3 = \frac{12}{5} (x - 2) [/tex]

Multiply through by 5

That's

5y - 15 = 12(x - 2)

5y - 15 = 12x - 24

We have the final answer as

5y - 12x = - 9

Hope this helps you

Which function has real zeros at x = 3 and x = 7?
f(x) = x2 + 4x - 21
Cf(x) = x2 - 4x - 21
Cf(x) = x2 - 10x + 21
f(x) = x2 - 10x - 21

Answers

Answer:

f(x) = x2 – 10x + 21

Step-by-step explanation:

I got it because you substract and add the last part

Please Help me ASAP Just answers please ;)

Answers

Answer:

C

Step-by-step explanation:

< means exclusive, so open hole

≤ means inclusive, so closed dot

also, you can see that the values for y are going down, like 6, 4, 2. That's only in answer C.

Hannah was trying to guess the month of her brother's birthday? She knew that the
month had less than five letters in its name. What is the probability that Hannah guesses
the correct month?
Round to the hundredths place.

Answers

Answer:

1/4 or 0.25

Step-by-step explanation:

1)January

2)February

3)March

4)April

5)May

6)June

7)July

8)August

9)September

10)November

11)October

12)December

Months that have less than five letters in its name

June

July

May

Probability= successful outcome ÷ possible outcone

Successful outcome=3

Possible outcome=12

Probability of Hannah guessing her brother's birthday=3÷12=1/4

Rewrite the expression in the form k x z^n .

Answers

Answer:

(squareroot2^2) times 27 (1/2)

Step-by-step explanation:

Answer:3z^2/9

Step-by-step explanation:

A linear function includes the ordered pairs (0, 3), (3, 9), and (9, n). What is the value of n?

Answers

Answer:

the value of n will be the range

Step-by-step explanation:

lets just give an example of (9,n) and you had to find the value its actually simple

9 is the domain

n is the range

a part of ordered pair function

got it?

PLEASE HELPPP ASAP. I WILL GIVE BRAINLIEST!!!​

Answers

Answer:

Factors: 5x, 3x²y⁵   Not Factor: 10x⁴y³

Step-by-step explanation:

5x is a factor because 15x²y⁶= 5x•3xy⁶

3x²y⁵ is a factor because 15x²y⁶ = 3x²y⁵•5y

10x⁴y³ isn't a factor because 15:10=1.5 isn't integer

Sort each equation according to wnether it has one solution, infinitely many solutions, or no solution
5(x - 2) = 5x - 7
One Solution
Infinitely Many Solutions
No Solution
4x - 2) = 3x - 4
6x+5) = 6x +11​

Answers

Step-by-step explanation:

[tex]5(x - 2) = 5x - 7 \\ 5x - 10 = 5x - 7 \\ 0 = 3[/tex]no solutions

[tex]4x - 2 = 3x - 4 \\ x = - 2[/tex]one solution

[tex]6x + 5 = 6x + 11 \\ 5 = 11[/tex]

no solutions

23. A 340 million square mile forest is how many hectares?

Answers

Answer:

88059595400 hectares

Step-by-step explanation:

Convert 340 million square miles into hectares.

1 square mile = 258.99881 hectares

340,000,000 square miles = 88059595400 hectares

The forest is 88059595400 hectares.

Answer:

[tex]8.80597(10^{10})[/tex] hectares

Step-by-step explanation:

This is unit conversion:

[tex]340,000,000miles(\frac{258.999 hectares}{1 mile} )[/tex]

We then multiply, with our units miles canceling out and leaving us with hectares:

[tex]8.80597(10^{10})[/tex] hectares

or

88059700000 hectares

A server gets an average of $4.50 in tips for each table he serves. In the morning, the server had 12 tables and in the afternoon the server had 13 tables Find his tips

Answers

Answer:

$112.50

Step-by-step explanation:

so the first thing you would do is add 12 to 13 to get

12 + 13 = 25

then multiply 25 by 4.50 to get

25 x 4.50 = 112.50

so the average number of tips the server has received is $112.50


The average (arithmetic mean) of a - 5 and a is x, and the average of a and a + 9 is y. What is the average of x and y?
a + 1
B) a +2
C) 2a + 1
D) 2a + 2

Answers

Answer:

The answer is "Option A"

Step-by-step explanation:

Given:

[tex]\to \frac{(a-5)+a}{2}=x.....(a)\\\\\to \frac{a+(a+9)}{2}=y.....(b)\\\\[/tex]

solve the above equation:

[tex]\to \bold{\frac{(a-5)+a}{2}=x}\\\\\to \frac{a-5+a}{2}=x\\\\\to \frac{2a-5}{2}=x\\\\\to \bold{\frac{a+(a+9)}{2}=y}\\\\\to \frac{a+a+9}{2}=y\\\\\to \frac{2a+9}{2}=y\\\\[/tex]

add both value (x and y):

[tex]\to \bold{x+y}\\\\\to \frac{2a-5}{2}+\frac{2a+9}{2}\\\\\to \frac{2a-5+2a+9}{2}\\\\\to \frac{4a+4}{2}\\\\\to \frac{2(2a+2)}{2}\\\\\to (2a+2)\\[/tex]

average of x and y:

[tex]\to \frac{x+y}{2}\\\\\therefore \bold{x+y= 2a+2}\\\\\to \frac{2(a+1)}{2}\\\\\to \boxed{(a+1)}\\[/tex]

help !!

Evaluate 8 - 50g + 2h when g = 10 and h = 5

Answers

Answer:

The evaluated answer to this equation is -482

Step-by-step explanation:

h = 5

g = 10

Plug in your numbers for the equation.

8 - 50(10) + 2(5)

Multiply -50 by 10 and multiply 2 by 5.

8 - 500 + 10

Subtract 8 by -500.

-492 + 10

Add 10 to -492.

-482

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