A motorboat travels 464 kilometers in 8 hours going upstream and 540 kilometers in 6 hours going downstream. What is the rate of the bot in still water and what is the rate of the current?

Answers

Answer 1

Answer:

rate 72 mph; current 16 mph

Step-by-step explanation:

to find the rate of the boat and the current we can model the equation like this

let r = rate

let c = current

8(r - c) = 464

6(r + c) = 540

8r - 8c = 464

6r + 6c = 540

r - c = 58

r + c = 90

then you could use elimination to find r

2r = 148

r = 74

the rate is 74 mph

then plug it in

the current is 16 mph


Related Questions

please help. on zearn find the coordinates of each shape​

Answers

Answer:

   ◯ ( 3, [tex]\frac{1}{2}[/tex] )  ,   ⬛(  [tex]1\frac{1}{2}[/tex]  ,[tex]2\frac{1}{2}[/tex]) ,   △( 0, [tex]4\frac{1}{2}[/tex] )

Step-by-step explanation:

             x-coordinate                    y-coordinate

◯ ---            3                                           [tex]\frac{1}{2}[/tex]

⬛ ---           [tex]1\frac{1}{2}[/tex]                                         [tex]2\frac{1}{2}[/tex]

△  ---             0                                         [tex]4\frac{1}{2}[/tex]

Measure the unit grids on the graph, x and y, that's the x and y coordinate.

75 POINTS
Provide the missing reasons for the proof.

Answers

Answer:

1. Given

2. definition of vertical angles

3. SAS triangle similarity theorem

Step-by-step explanation:

1. Given simply means the problem directly tells you it is true

2. Vertical angles are angles that share 2 lines and are congruent.

3. SAS triangle similarity theorem is the theorem that proves 2 triangles with a similar side, angle, and side (in that order) are similar.

Annika needs to sell at least 25 boxes of Girl Scout cookies to get a new badge she has already sold 4 boxes how many more does she need to sell

one step inequality word problems ​

Answers

(post deleted by author)

Four eighth graders solve the equation
x
3

150
=
66.
x3−150=66. The table shows the students’ answers.



Which statement is true?


Student
1
1 is correct because
72
3

150
=
66.
723−150=66.Student 1 is correct because 72 cubed minus 150 is equal to 66 point

Student
2
2 is correct because
6
3

150
=
66.
63−150=66.Student 2 is correct because 6 cubed minus 150 is equal to 66 point

Student
3
3 is correct because
18
3

150
=
66.
183−150=66.Student 3 is correct because 18 cubed minus 150 is equal to 66 point

Student
4
4 is correct because
7
3

150
=
66.
73−150=66.Student 4 is correct because 7 cubed minus 150 is equal to 66 point

Answers

Answer:

Student 2 is correct because 6 cubed minus 150 is equal to 66

Step-by-step explanation:

[tex]x^3-150=66[/tex]

[tex]\implies x^3=66+150=216[/tex]

[tex]\implies x=\sqrt[3]{216} =6[/tex]

Add and subtract polynomials of degree one and degree two What is the value of 3s3t−2 for s = 2 and t =−3 Method 1 Simplify first.

Ava cannot spend more than $100 on food for a party. The lemonade will cost $19 and she wants to spend the rest on pizza. Each pizza costs $7.


How many pizzas can she buy?


Enter your answer in the box.


___ pizzas

Answers

Answer and Step-by-step explanation:

So for this question, we need to create an equation. We will use one of the most common forms of equations of math, which would be the linear equation of y=mx+b. The only difference is, we need to change the = to a ≥ symbol, meaning greater than or equal to, because the 100 dollars needs to be more or equal to the amount spent. But we cannot solve this problem until we know where everything goes.

So, the 100 is all she can spend, so this is where the ≤ comes in handy. She can use less than or equal to the amount of 100 dollars for the food for this party. And because she started out with 19 dollars, that can be added into the problem. So far we have:

100 ≥ __x + 19.

Now we need to find what the missing part of the equation is. But first let's change the x to p in this equation so that it is easier to understand. The p stands for the amount of pizzas purchased. Each pizza costs 7 dollars, so the equation should look like this:

100 ≥ 7p + 19. Now we solve for p.

-19           - 19 Subtract 19 from both sides to cancel out the positive 19 (+ 19).

81 ≥ 7p           Divide 7 into 81 to single out p.

7      7            So p = 81/7. But we can't have 81/7 of a pizza, so we convert this to a decimal then round. So: 11.57142857… is the decimal form.

Now we need to round, because that is way too big. So, we round to the nearest whole number. So we look at the placement behind it (The tenths placement in this situation). Because the placement behind it (5) is on the 5 - 9 scale, the placement before it gets rounded up.

So, Ava can buy 12 pizzas.

I hope that this helps.

Answer:

12

Step-by-step explanation:

I Took The Test

3 3/8 divided by 2 1/4 ILL GIVE BRAINLEIST

Answers

Answer:

I missed the part where that's my problem

Answer:

1 1/2

Step-by-step explanation:

Divide

3 and 3 over 83

3

8

÷ 2 and 1 over 42

1

4

= 108 over 72

108

72

solve 2x +5y =-24 2x+ y =-8

Answers

Answer:

[tex]x=-2, y=-4[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}2 * \frac{-24 - 5y}{2}+ y= -8\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-24-4y=-8\end{array}\right][/tex]

[tex]x=\frac{-24-5(-4)}{2}[/tex]

[tex]x=-2, y=-4[/tex]

Answer:

[tex]{x,y} = {-2,-4}[/tex]

Step-by-step explanation:

[tex]2x + 5y = -24 \\ 2x + y = -8[/tex] <---------- Linear equations given

Graphic Representation of the Equations : PICTURE

[tex]5y + 2x = -24 \\ y + 2x = -8[/tex]

Solve by Substitution :

// Solve equation [2] for the variable  y

[tex][2] y = -2x - 8[/tex]

// Plug this in for variable  y  in equation [1]

[tex][1] 2x + 5*(-2x-8) = -24\\ [1] -8x = 16[/tex]

/ Solve equation [1] for the variable  x

[tex][1] 8x = - 16 [1] x = - 2[/tex]

// By now we know this much :

[tex]x = -2 \\ y = -2x-8[/tex]

// Use the  x  value to solve for  y

[tex]y = -2(-2)-8 = -4[/tex]

Solution :

[tex]{x,y} = {-2,-4}[/tex]

Remi plans on spending at most $75 at the mall. She wants to buy a $30 hoodie and some t-shirts that cost $9. Write and solve an inequality to find how many t-shirts Remi can purchase.
Please help! :(

Answers

Answer: 6 t-shirts
Explanation:
1. 30+9x less or equal to 75
2. 9x less or equal to 55
3. x less or equal to 55/9
4. she can by 6 t-shirts

Answer:

T-shirts= 5

Step-by-step explanation:

Remi plans on spending 75$ and she already bought a hoodie that cost $30.

x= how many hoodies you buy.  

Inequality- $75= 30+75+x

Next- 75-30= $45

Finally- 45/9= 5 t-shirts that you can buy.

Hope that helped! :)

Please help me simplify both of these.

Answers

Answer:

A is 3/y, B is 4y

Step-by-step explanation:

please help me ..............................................................................

Answers

Hiyaaa! I'm Nat and I'm gonna help you~♡

Thermo means heat! So. Thermosphere has to relate to hot and warm things.

Meso meaning middle,or intermediate.

,

Thermosphere = is very hot,satellites travel here,reached out into space

Mesosphere= Directly under the stratosphere,is very cold,acts has a barrier

Hope this helps!!

Brainliest?

-Nat

Is everything to the power of 0 = 1?

examples:
[tex]1^{0}, 2^{0}, 3^{0} .....[/tex]

Answers

Hey there!

Any numbers that is to the power of 0 is 1 because it’s just like the product just without any numbers that are given. Therefore, to answer your question: YES

Good luck on your assignment and enjoy your day!


~Amphitrite1040:)

find the equation of the line tangent to the graph of f at (1,4), where f is given by f(x)=2x^3-3x^2+5

Answers

Answer:

[tex]y = 4[/tex]

Step-by-step explanation:

First, find the derivative of f:

[tex]\displaystyle \begin{aligned} f'(x) & = \frac{d}{dx}\left[ 2x^3 - 3x^2 + 5\right] \\ \\ & = 6x^2 - 6x \\ \\ & = 6x(x-1)\end{aligned}[/tex]

Find the instantaneous slope at x = 1:

[tex]\displaystyle \begin{aligned} f'(1) & = 6(1)((1)-1) \\ \\ &= 0 \end{aligned}[/tex]

From the point-slope form, find the equation of the line:
[tex]\displaystyle \begin{aligned}y - y_1 & = m(x-x_1) \\ \\ y - (4) & =(0)(x-(1)) \\ \\ y & = 4 \end{aligned}[/tex]

In conclusion, the equation of the tangent line is y = 4.

Answer number 1 please.​

Answers

[tex] \sf {a}^{2} = {13}^{2} - {5}^{2} [/tex]

Formula :

Base²= Hypotenuse² - Perpendicular ²

[tex] \\ \\ [/tex]

[tex] \hookrightarrow\sf {a}^{2} = {13}^{2} - {5}^{2} [/tex]

[tex] \\ \\ [/tex]

[tex] \hookrightarrow\sf {a}^{2} =169 - 25[/tex]

[tex] \\ \\ [/tex]

[tex] \hookrightarrow\sf {a}^{2} =144[/tex]

[tex] \\ \\ [/tex]

[tex] \hookrightarrow\sf {a} = \sqrt{144} [/tex]

[tex] \\ \\ [/tex]

[tex] \hookrightarrow\sf {a} = \sqrt{12 \times 12} [/tex]

[tex] \\ \\ [/tex]

[tex] \hookrightarrow\sf {a} = 12[/tex]

Remember the a² in formula has nothing to do with the a we have to find. :)

[tex]\bold{\huge{\pink{\underline{ Solution }}}}[/tex]

[tex]\bold{\underline{ Given :-}}[/tex]

We have a right angled triangle whose two sides that is perpendicular and hypotenuse are 5 units and 12 units

[tex]\bold{\underline{ Let's\: Begin:-}}[/tex]

According to the Pythagoras theorem,

Pythagoras theorem states that the sum of squares of two small sides that is perpendicular height and base are equal to the square of longest side that is hypotenuse

That is,

[tex]\sf{\red{ ( Base)² + ( Perpendicular )² = ( Hypotenuse)²}}[/tex]

[tex]\sf{ ( a )² + ( b )² = ( c )²}[/tex]

Subsitute the required values,

[tex]\sf{ ( a )² + ( 5 )² = ( 13)²}[/tex]

[tex]\sf{ a² + 25 = 169}[/tex]

[tex]\sf{ a² = 169 - 25 }[/tex]

[tex]\sf{ a² = 144}[/tex]

[tex]\sf{ a = √144}[/tex]

[tex]\sf{ a = 12}[/tex]

[tex]\sf{\blue{ Hence,\: Length \:of \:a\: is \:12 units }}[/tex]

Find the measure of angle

Answers

Answer:

It can be any measure

Step-by-step explanati

A bucket can hold 5 gallons of water. About how many liters of water can the bucket hold? Round to the nearest tenth.

Answers

22.7 liters
EXPLANATION : just did it

what's up? 5 gallons ≈ 19 liters  (THIS IS U.S. GALLON, THE OTHER ANSWER HAS IMPERIAL GALLON IF THAT IS WHAT YOU NEED)

best of luck with your studies

The sum of two integers is 46. The larger is 16 more than four times the smaller. Find
the two integers.

Answers

Answer:

40 and 6

Step-by-step explanation:

The length of a rectangle is 3 metern .
more than triple the width

Answers

It is 9 because you need to triple 3 so 3x3 is 9

One half of a number is subtracted from 25 the answer is 10. What is the number

Answers

Answer:

The answer is 30

Step-by-step explanation:

30÷2=15

25-15=10

Answer:

30

Step-by-step explanation:

25-30/2 = 25-15 = 10 Hope this helps!

Earning Commission
Sales Commision Rate Commission
$450
6%
?
The commission is ?

Answers

Answer:6%

Step-by-step explanation:

This is pretty much asking what the percentage is!

Help Me what is 2,267,742,732,288 in scientific notation for 20 pts

Answers

Answer:

2.267742732288 × 1012

Step-by-step explanation:

6h + 16 = 46
Evaluate the equation

Answers

Answer:

h=5

Step-by-step explanation:

Answer:

6h +16 =46

6h +16-16

6h =30 6h ÷6 =30÷6

h =5

Santino fires a paintball 3 meters from the ground such that the initial trajectory is perfectly horizontal. Assume the paintball does not hit anything in the ground is level. When will the paintball hit the ground?


A. About 3 seconds
B. About 0.78 seconds
C. About 0.52 seconds
D. About 1 second


Answer: B

Answers

The correct answer is B

bernice buys 5 VHS tapes. each VHS tape cost $9. if bernice receives a $2 discount on each vhs, what is the total amount of money she spends? write an expression that matches the words.

Answers

Answer: bernice buys 5 VHS tapes. each VHS tape cost $9. if bernice receives a $2 discount on each vhs, what is the total amount of money she spends? write an expression that matches the words.

the answer is $11

Step-by-step explanation: 9+2=11

The table represents the number of medals won by each member of the Academic Bowl Team. What is the ratio of the number of medals won by Josephine to the total number of medals won by the team?
A) 1/13
B) 1/4
C) 1/3
D) 2/5

Answers

1. Ratio of medals won by Josephine to the total number won by the team: 1/13 (A)

2. Ratio of medals won by Jacob to medals won by Antonio: 2/1 (D)

What is Ratio?

Ratio can be described as a quantitative relation that compares how many times a value is contained in another.

1. Ratio of medals won by Josephine to the total number won by the team:

Total won by the team = 26

Medals won by Josephine = 2

Ratio = 2:26 = 2/26

= 1/13 (A)

2. Ratio of medals won by Jacob to medals won by Antonio:

Jacob = 8

Antonio = 4

Ratio = 8:4 = 8/4

= 2/1 (D)

Learn more about ratios on:

https://brainly.com/question/13513438

In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle. The left side of the figure is 18 ft, the bottom side of the figure is 21 ft, the right side of the figure is 8 ft, and the top part of the horizontal rectangle to the right of the vertical rectangle is 12 ft PLEASE HURRY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The area of the L shaped figure is 258 ft²

Area

Area is the amount of space occupied by a two dimensional figure.

The area of a rectangle is given by:

Area = length * breadth

From the diagram, the area is:

Area = [18 * (21 - 12)] + (12 * 8) = 258 ft²

The area of the L shaped figure is 258 ft²

Find out more on Area at: https://brainly.com/question/25292087

♪Answer : 21ft - 12ft = 9ft

Total Area = Area 1 + Area 2

Total Area = (18ft*9ft) + (21ft*8ft)

Total Area = 330ft²

I hope this helps!

PLZ HELP ILL MARK AS BRAINLEIST

Answers

Answer:

c

Step-by-step explanation:

A=2πrh+2πr2=2·π·3·20+2·π·32≈433.53979

433 ft^2

{Answer the surface area of the cylinder is 433 ft^2}

(-3x+5)(2x+4) in standard form step by step

Answers

Answer:

[tex]- 6 {x}^{2} -2x + 20[/tex]

[tex]( - 3x + 5)(2x + 4) \\ \\ = - 3x(2x + 4) + 5(2x + 4) \\ \\ = - 3x(2x) - 3x(4) + 5(2x) + 5(4) \\ \\ = - 6 {x}^{2} - { 12x} + {10x} + 20 \\ \\ = - 6 {x}^{2}-2x + 20[/tex]

Solution:

To simplify this expression, multiply the terms together....

(-3x + 5)(2x + 4)=> (-3x × 2x) + (-3x × 4) + (2x × 5) + (5 × 4)=> -6x² - 12x + 10x + 20=> -6x² - 2x + 20

Hence, the simplified expression is -6x² - 2x + 20.

Hoped this helped!

The solutions to a certain quadratic equation are x= -4 and X = 3. Write the equation in standard form below.
[blank] +x [blank] [blank] = 0

Answers

Answer:

x² + x - 12 = 0

Step-by-step explanation:

If x = -4 and x = 3 are solutions to a quadratic equation, then

(x + 4)(x - 3) = 0

Expand the brackets:  x² - 3x + 4x - 12 = 0

Combine like terms:  x² + x - 12 = 0

What visualization is most appropriate to see if there is an association between birth and death rates during a given time interval

Answers

Bar chart visualization should be used if there is an association between birth and death rates during a given time interval.

Bar chart

A bar chart is a chart that is used to represent data using rectangular bars with heights proportional to the values that they represent. Bar charts can either be vertically or horizontally.

Bar graphs are usually used when comparing two or more different things as well as their respective changes over time.

Bar chart visualization should be used if there is an association between birth and death rates during a given time interval.

Find out more on Bar chart at: https://brainly.com/question/24741444

8(2x – 10) = 28
What is the steps to complete?

Answers

Answer:

6.75

Step-by-step explanation:

first let's simplify whatever is inside the parantheses

8(2x-10)=28

8*2(x-5)=28

16(x-5)=28

now we divide both sides by 16 to get rid 16

x-5 = 28/16

now move -5 to the right side

x = 28/16 + 5

x = 28/16 + 80/16 = 108/16 = 6.75

First, distribute eight

16x - 80 = 28


Then, get x to be the only value on its side

16x = 108


Next, divide

x = 108/16


Finally, simplify

x = 27/4
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