A boat traveled 280 miles downstream and back. The trip downstream took 7 hours. The trip bck took 14 hours. Find the speed of the boat in still water and the speed of the current.

Answers

Answer 1

recall your d = rt, distance = rate * time

bearing in mind that the trip over, upstream, is the same distance as back, 280 miles.

if say, the boat has a speed rate of say "b", and the current has a speed rate of "c", so, when the boat was going upstream, it really wasn't going "b" fast, it was going "b-c" fast, because the stream is subtracting speed from it, because is going against the stream.

And when the boat was going downstream, is not going "b" fast either, is going "b+c" because, since it's going with the current, the current's rate is adding speed to it.

[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Downstream&280&b+c&7\\ Upstream&280&b-c&14 \end{array} \\\\\\ \begin{cases} 280=7(b+c)\implies \frac{280}{7}=b+c\\ 40=b+c\implies 40-c=\boxed{b}\\ -------------\\ 280=14(b-c)\implies \frac{280}{14}=b-c\\ 20=b-c\\ ----------\\ 20=\left( \boxed{40-c} \right)-c \end{cases} \\\\\\ 20=40-2c\implies 2c=40-20\implies c=\cfrac{20}{2}[/tex]

what's the speed of the boat? well, 40 - c = b.

Related Questions

If a couple has two children, what is the probability that both are boys? assume that it is equally likely that a child is a boy or girl.

Answers

this is the answer check it out

The stage manager of a school play creates a rectangular acting area of 42 square yards. String lights will outline the acting area. To the nearest whole number, how many yards of string lights does the manager need to enclose this area?

Answers

In this item, we cannot be fully sure of the dimensions of the rectangle because we are not given its properties and the type. For the sake of showing the solution to this item, we assume the rectangle to be square such that the area can be calculated through the equation,
s² = 42
where s is the length of the side. From the equation, the value of the s is 6.48 yards.

The perimeter of the rectangle is calculated through the equation,
P = 2L + 2W
Substituting the known values,
P = 2(6.48) + 2(6.48)
P = 25.92
Thus, answer is 25.92 yards.

Is the correct answer E)1 ?

Answers

It's either B C or D, the question asks which "values", meaning there are multiple values.

The correct answer is A

This is because its asking for which x-values would the y's be be constant. This would be the numbers greater than 2 because the line is constant.

the price of a pack of gum today is 63 cents. this is 3 cents more than three times the price ten years ago. what was the price ten years ago?

Answers

the answer would be .43

20, you subtract the three leaving 60 then divide

seven less than the quotient of a number, x, and twelve is five times the number. which answer represents this situation? x/12−7 5x 7−x/12=5x 7−x/12 5x x/12−7=5x

Answers

Quotient is basically the answer you get when you divide two numbers. For example, the quotient of 6 and 3 is 2 because when I divide 6 by 3, I get 2.

Quotient of a number x and 12 = [tex] \frac{x}{12} [/tex]

7 less than quotient of a number x and 12 = [tex]\frac{x}{12} - 7[/tex]

5 times the number = 5*x = 5x

Hence, the equation is;

[tex]\frac{x}{12} - 7 = 5x[/tex]

[tex] \frac{x-(7*12)}{12} = 5x[/tex]

[tex]x-84 = 5x*12[/tex]

[tex]x - 84 = 60x[/tex]

[tex]x - 60x = 84[/tex]

[tex]-59x = 84[/tex]

x = [tex] \frac{84}{-59} = - \frac{84}{59} [/tex]

= -1.423728813559322 ≈ 1.42

Hence, the answer is A.

Which operator is best to determine whether x contains a value in the range of 10 through 57?

Answers

to answer your question the choice is use "and"

Bella's score on a spelling test is a function of the number of hours she studies. Which expression represents Bella's score on a spelling test if she studies for 3 hours?

A. 3(score)
B. Score(3)
C. Score + 3
D. 3 - score

Answers

The correct answer is C

Answer:

B. Score(3)

Step-by-step explanation:

Given,

Bella's score on a spelling test is a function of the number of hours she studies.

Let x represents the number of hours and S represents her score after x hours,

Thus, her scoring after x hours = S( x )

If she studies for 3 hours,

That is, x = 3,

Then her score would be S(3) or we can say that score(3).

Hence, option 'B' is correct.

What constant would be added to the expression x2−7xx2−7x in order to make it a perfect square?

Answers

ok

assuming ya mean [tex]x^2-7x[/tex]
since the quadratic coefient is 1, take 1/2 of the liner coeficient and square it
the linear coefient is -7
half of that is -7/2
squared we get 49/4
add that to get
[tex]x^2-7x+\frac{49}{4}[/tex]
it factors to
[tex](x-\frac{7}{2})(x-\frac{7}{2})[/tex] or [tex](x-\frac{7}{2})^2[/tex]

you must add [tex]\frac{49}{4}[/tex] to make it a perfect square

What is the equation of the following graph? Write it in both slope-intercept form and standard form.

Answers

x-intercept : (-2,0) and y-intercept (0,3)

slope = (3-0)/(0+2) = 3/2 = 1.5
b = 3

equation in slope-intercept form
y = 1.5x + 3

equation in standard form
1.5x - y = -3

Final answer:

The equation of the graph is y = 3x + 9 in slope-intercept form and 3x - y = -9 in standard form.

Explanation:

The equation of the graph can be written in slope-intercept form (y = mx + b) and standard form (ax + by = c).

Slope-intercept form: y = mx + bGiven slope (m) = 3 and y-intercept (b) = 9Substituting the values, the equation becomes: y = 3x + 9Standard form: ax + by = cRearranging the equation from slope-intercept form, we get: 3x - y = -9

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what is 4 less than three sevenths of y written as an algebraic expression

Answers

IT means that u need to subtract 4 from 3/7 of y i.e
3/7 of y = 3Y/7
subtract 4 from it we get
{(3Y/7)- 4}

hope this helps, Gastondekota! :-)

Final answer:

The algebraic expression for 'four less than three sevenths of y' is (3/7)y - 4. This involves finding three sevenths of y and then subtracting four.

Explanation:

The phrase 'four less than three sevenths of y' is asking us to first find three sevenths of y, and then subtract four from that number. In algebra, this is represented as (3/7)y - 4. The expression (3/7)y means 'three sevenths of y', and the '- 4' indicates we are finding 'four less than' this quantity.

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Solve for x, given the equation Square root of x minus 5 + 7 = 11

Answers

sqrt (x-5) + 7 = 11
sqrt (x-5) = 11 -7
sqrt (x-5) = 4
x - 5 = 4^2
x - 5 = 16
x = 16 + 5
x = 21

The value of x will be equal to 21.

What is an expression?

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

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression will be solved as below:-

√(x-5) + 7 = 11

√(x-5) = 11 -7

√(x-5) = 4

x - 5 = 4^2

x - 5 = 16

x = 16 + 5

x = 21

Therefore, the value of x will be equal to 21.

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Use substitution. 2x + 3y = 5 4x - y = 17 Use linear combinations: 2x + 3y = 5 4x - y = 17

Answers

I'll help you get started. To use substitution on the first pair of equations, we want to solve for one of the variables in one of the two equations. It looks like it would be easiest to solve for y in the second equation:
[tex]4x-y=17[/tex]
[tex]4x=17+y[/tex]
[tex]4x-17=y[/tex]

Now we want to substitute this alternate version of y into the first equation:
[tex]2x+3(4x-17)=5[/tex].

I'll let you finish off that first one. The second problem asks to solve the two equations using linear combination. This means we want to add the two equations together and cancel out one of the variables. Again, it's easiest to cancel out the y since one is negative. First we want to take the second equation and multiply by 3 on both sides:
[tex]3(4x-y)=3(17)[/tex]
[tex]12x-3y=51[/tex]

Now we want to add both equations together. Add the left sides and the right sides on their respective sides of the equals sign:
[tex](2x+3y)+(12x-3y)=5+51[/tex]

You can finish that one as well. Your answers for both methods will be the same if you do everything right! Let me know if you have more questions

A recipe calls for of a cup of milk for 11 cookies. How many cups of milk are needed to make 99 cookies?

Answers

9 cups of milk would be needed to make 99 cookies
If 1 cup = 11 cookies then...
99 (cookies we need to make) divided by 11 (cookies each cup) we get 9.

I hope this helps!

9 cups of milk

1 cup for 11 cookies
9 cups for 99 cookies

Mr. Weber drives to a landscape supply center to buy sand and gravel. He needs at least 2 lb of sand. The amount of gravel he will buy will be at least twice the amount of sand he will buy. The center has 6 lb of sand and 13 lb of gravel in stock.

The graph shows the feasible region, where x represents the number of pounds of sand and y represents the number of pounds of gravel.

Which ordered pairs meet all the constraints and make sense in the context of the situation?

Select each correct answer.

(2 1/2, 10)

(3, 12)

(4,6)

(5, 8 1/2)

Answers

Answer:

This is correct! answer is (2 1/2, 10) and (3/12)

Step-by-step explanation:

Two more than 4 times a number is -18

Answers

4x + 2 = -18
4x = -20
x = -5

2+4x=-18
4x=-20
x=-
those are all the steps needed

Jerome earns $200 per month plus $12 for each bike he sells at the bike shop. This month, he wants to earn at least $400. What is the least amount of bikes that Jerome can sell to reach his goal

Answers

weird problem lol but you multiply 400 times 12 and divide by 200 which tells you he needs to sell at least 24 bikes

he needs to sell at least 17 bikes

he already has 200 per month
he needs 200 more

$12×17(bikes)= $204
( any number less than 17 will not equal $200)

200+204=$404

Write a quadratic equation having the given solutions -8

Answers

Answer:

[tex]y=x^2+16x+64[/tex]

Step-by-step explanation:

A quadratic needs 2 solutions, but since you only have 1, I am to assume that x = -8 twice (or multiplicity of 2). If x = -8, then in factor form, it's (x + 8). Muliplying that by itself twice:

(x + 8)(x + 8):

[tex]x^2+8x+8x+64=0[/tex]

Simplifying gives you:

[tex]x^2+16x+64=y[/tex]

If it takes about 20 minutes to grade a student paper how long in hours does it take to grade palers for a class of 25 people

Answers

20X25=500mins
500/60 (mins in a hour)=8.33 hours

Final answer:

It takes about 20 minutes to grade one student's paper, so for a class of 25 students, it would take a total of 500 minutes, which is approximately 8.33 hours to grade all the papers.

Explanation:

If it takes about 20 minutes to grade a student paper, to find out how long it takes to grade papers for a class of 25 students, we need to multiply the number of students by the time taken to grade each paper.

Step-by-Step Calculation:

Multiply the number of students (25) by the minutes per paper (20 minutes): 25 students * 20 minutes per student = 500 minutes.

Convert minutes to hours. Since there are 60 minutes in an hour, we'll divide the total minutes by 60: 500 minutes ÷ 60 minutes per hour = 8.33 hours.

Therefore, it takes approximately 8.33 hours to grade papers for a class of 25 students. Please note that this is an ideal situation without any breaks or interruptions accounted for.

Solve each inequality
3t-2<5
-6<5b-4

Answers

For the first one, we add 2 to both sides by get 3t<7. Dividing both sides by 3, we get t<7/3

I challenge you to do the second one based off of how I did the first one! Remember that if you multiply or divide by a negative number, you have to switch the sign around!

Question #12 assessment progress 30 percent suppose that the functions r and s are defined for all real numbers x as follows. =rx4x2 =sx2x

Answers

uwixdybuyxbdsugvdcadugfcvsd djhcbk sduhkccbdsyiobfcdyifcbdsyicfds sdfchibsdcioydsbcfisdhfcbdsuyfcdsoufcs douhfcw dgc csduoh cdusdoycfvds cqgv yvchv dsh csdcdscbj k adc iyvdaoiyc vaduvc adsugkc ouysd c ozdyibc odsiydcbyadoidcdadcbeqdc

Lori purchases a new set of watercolor paints and some canvases to create art for her next exhibit. The watercolor paint set costs $15 and the canvases are $24.50 each. If Lori buys 6 canvases, what is the total amount of money she spends for her next exhibit?
A $211.00
B $162.00
C $237.00
D $147.00

Answers

Starting with the paints, we have 15$ as our base value. Next, since we add $24.50 for each new canvas bought, 24.5*x=the amount of money for x canvases. Therefore, since 15 is our base value, we have 15+24.5*6=162

The answer is B.) $162.00

Each interior angle of a regular polygon measures 120°. what is the name of the polygon?

Answers

the total angel of any polygons is (n as the totap side of the polygon)
(n - 2) x 180°

now we can substitute 120° into this formula
(n - 2) x 180° / n = 120° (because we're calculating each angle from the polygon, so we need to divide the equation by n)
(180n - 360) = 120n
180n - 120n = 360
60n = 360
n = 6
a 6 side polygon is hexagon.

If every pair of consecutive angles of a quadrilateral are supplementary, then the quadrilateral must be parallelogram? True or False?

Answers

The answer to your question above is true

It's true If every pair of consecutive angles of a quadrilateral are supplementary, then the quadrilateral must be a parallelogram.

What are the four types of parallelograms?

Rectangles, rhombus, and squares are parallelograms. A trapezoid has as a minimum one pair of parallel facets. The parallel aspects are referred to as the bases and the non-parallel sides are called the legs. There are three kinds of trapezoid - isosceles, right-angled, and scalene trapezoids.

How do you discover a parallelogram?

To identify a parallelogram, the shape has to fulfill one of the following standards:

It has two pairs of parallel contrary aspects.It has pairs of the same opposite angles.It has two pairs of equal and parallel contrary facets.Its diagonals bisect each other.

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Dahlia is simplifying (3t)^4 using these steps:

(3t)^4= 3t*3t*3t*3t=3*3*3*3*t*t*t*t

Although Dahlia is correct so far, which step could she have used instead to simplify the expression ?

A. 3t^4=3t^4
B.3^4t=81t
C. 4(3t)=12t
D.3^4t^4=81t^4

Answers

Dahlia could have raised both the coefficient and variable to the power of 4

Simplifying exponential functions

Given the exponential expression as shown below;

(3t)^4

This shows that we are to multiply 3t in 4 places to have;

(3t)^4 = (3t) * 3t * 3t * 3t

(3t)^4 = 3^4 * t^4

(3t)^4 = 81t^4

This shows that Dahlia could have raised both the coefficient and variable to the power of 4

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Solve the equation a+b-c=180 for c

Answers

We need to make sure c is on one side:

a + b - c = 180

So let’s subtract a and b from both sides:

-c = -a -b + 180

Now, multiply both sides by -1:

c = a + b - 180

Hope this helps!

Answer:

Step-by-step explanation:

we are given the equation a+b-c=180

Now to solve it for c we need to isolate the c

first step can be addition of c to both side

a+b-c+c=180+c

a+b=180+c

now in second step we subtract 180 from both sides to get

a+b-180=180+c-180

a+b-180 = c

c= a+b-180

Suppose you start with at least $82 in your savings account and deposit $32 each week. Write, solve, and graph an inequality to describe how much money, m, you have after 10 weeks, w.

Answers

32 x 10= 320 + 82=402

Answer:

m ≥ 82 + 32w

m ≥ 402

Step-by-step explanation:

Here, w represents the number of weeks and m represents the total amount in the account after w weeks,

The amount of money saved in each week = $ 32,

So, the total amount saved after weeks = 32w dollars,

Since, the original amount in the account = $ 82

The total amount in the account = 82 + 32w

Thus, the required inequality would be,

m ≥ 82 + 32w

If w = 10,

The amount in the account after 10 weeks = 82 + 32(10) = 82 + 320 = $ 402

⇒ m ≥ 402

That is, the closed circle on 402 and shaded right in the number line ( shown below )

Sunny earns $12 per hour delivering cupcakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did sunny earn this week?

Answers

Answer: [tex]12x-15[/tex]

Step-by-step explanation:

Given: Sunny earns $12 per hour delivering cupcakes. She worked for x hours this week.

The total earning for this week = [tex]12x[/tex]

Also, she was charged $15 for a late delivery on Tuesday.

It means, The total earning for this week =[tex]12x-15[/tex]

So if Sunny earns $12 per hour delivering cupcakes. She worked for x hours this week and was charged $15 for a late delivery on Tuesday then her earning for this week = 12x-15

Convert 4 radians to degrees.

Answers

Hello!

To convert radians to degrees, we have to multiply them by [tex]180/ \pi [/tex].
Let's multiply.
[tex]4*180/ \pi [/tex]
≈ 229.18311805

Please note that since we are using [tex] \pi [/tex], we need to use the approximation sign.

4 radians ≈ 229.18311805°

You can feel free to let me know if you have any questions regarding this!
Thanks!

- TetraFish

four more than the product of one and a number x

Answers

(X times 1) + 4 will be your answer

hope this helps

Hi there! I don't know if you want the answer or the equation, but I'll put both. :)

The equation would be "4 more" than 1*x. This would be (1 * x) + 4.

The answer to this expression would be x + 4.

Harvey collects rare marbles. He has 112 marbles in his collection. If he uses Seven Trees to hold all of the marbles, how many marbles will he display on three trays? Is tray hold an equal number of marbles answers at brainly.com

Answers

three trays will hold 48 marbles because each treat will be able too hold 16 marbles.

Final answer:

Harvey has 112 marbles distributed equally across seven trays. Each tray holds 16 marbles, therefore, on three trays, Harvey will display a total of 48 marbles.

Explanation:

Harvey has 112 marbles in his collection and uses seven trays to hold all of the marbles. To find out how many marbles Harvey will display on three trays, we need to divide the total number of marbles by the total number of trays to find out how many marbles each tray holds.

First, divide 112 marbles by 7 trays to find out how many marbles go on each tray. The calculation is as follows:

112 marbles ÷ 7 trays = 16 marbles per tray

Now that we know each tray holds 16 marbles, to find out how many marbles are displayed on three trays, we multiple the number of marbles per tray by the number of trays:

16 marbles per tray × 3 trays = 48 marbles

Therefore, Harvey will display 48 marbles on three trays.

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