the speed of the boat is 5.418 km/h and the speed of the stream is 2.167 km/h
Let's define the variables:
B = speed of the boat in still water.
S = speed of the stream.
When the boat travels downstream, the total speed of the boat will be equal to the sum of the speed of the stream and the speed of the boat in still water:
speed = B + S
When the boat goes downstream, the speed will be:
speed = B - S
Now, also remember the relation:
speed*time = distance.
The given information is:
In 8 hours the boat can:
go 12 km upstream and 40km downstream.
We now need to define another variable, T, as the time that the boat travels upstream.
Then we can write this as:
12km = (B - S)*T
If the boat travels T hours upstream, and travels for a total of 8 hours, then the amount of time that travels downstream is 8h - T, then we can write:
40km = (S + B)*(8h - T)
Similarly, when we have:
"it can go 16 km upstream and 32 km downstream in the same time."
we can define a new variable T', and write:
16km = (B - S)*T'
32km = (S + B)*(8h - T')
Then we have a system of 4 equations:
16km = (B - S)*T'
32km = (S + B)*(8h - T')
40km = (S + B)*(8h - T)
12km = (B - S)*T
And we need to solve this for S and B.
To do it, we need to isolate one of the variables in one of the equations.
Let's isolate T in the last equation:
T = 12km/(B - S)
now we can replace that in the third equation to get:
40km = (S + B)*(8h - 12km/(B - S))
So now we have 3 equations:
16km = (B - S)*T'
32km = (S + B)*(8h - T')
40km = (S + B)*(8h - 12km/(S - B))
Now we need to do the same thing, this time let's isolate T' in the first equation and replace it in the second one:
T' = 16km/(B - S)
Replacing it in the second equation we get:
32km = (S + B)*(8h - T')
32km = (S + B)*(8h - 16km/(B - S))
So now we have two equations:
40km = (S + B)*(8h - 12km/(B - S))
32km = (S + B)*(8h - 16km/(B - S))
Let's simplify these:
40km = 8h*(S + B) - 12km*(S + B)/(B - S)
32km = 8h*(S + B) - 16km*(S+ B)/(B - S)
Now we can multiply both equations by (B - S) to get:
40km*(S - B) = 8h*(S + B)*(B - S) - 12km*(S + B)
32km*(S - B) = 8h*(S + B)*(B - S) - 16km*(S+ B)
Let's keep simplifying this:
40km*(B - S) + 12km*(S + B) = 8h*(S + B)*(B - S)
32km*(B - S) + 16km*(S+ B) = 8h*(S + B)*(B - S)
Now we get:
52km*B - 28km*S = 8h*(S^2 + B^2)
48km*B - 16km*S = 8h*(S^2 + B^2)
Notice that the right side of these equations is the same thing, then we can write:
52km*B - 28km*S = 48km*B - 16km*S
(52km - 48km)*B = (28km - 18km)*S
4km*B = 10km*S
B = (10/4)*S
B = (5/2)*S
Now we can replace this in one of our two equations, let's use the first one:
48km*B - 16km*S = 8h*(S^2 + B^2)
48km*(5/2)*S - 16km*S = 8h*( S^2 + ( (5/2)*S)^2)
Now we can solve this for S
104km*S = 8h*( S^2 + 25/4*S^2)
104km*S = 8h*(29/4*S^2) = 48h*S^2
104km*S = 48h*S^2
dividing at both sides by S we get:
104km = 48h*S
104km/48h = S = 2.167 km/h
And using B = (5/2)*S
We can find the speed of the boat:
B = (5/2)*2.167 km/h = 5.418 km/h
Then:
the speed of the boat is 5.418 km/h and the speed of the stream is 2.167 km/h
If you want to learn more about this topic, you can read:
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Please help
Solve the system of equations shown below.
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
2x - 6y = - 12 → (1)
x + 2y = 14 → (2)
Multiplying (2) by - 2 and adding to (1) will eliminate x
- 2x - 4y = - 28 → (3)
Add (1) and (3) term by term to eliminate x
- 10y = - 40 ( divide both sides by - 10 )
y = 4
Substitute y = 4 into either of the 2 equations and solve for x
Substituting into (1)
2x - 6(4) = - 12
2x - 24 = - 12 ( add 24 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6
solution is (6, 4 )
Mr.Swanson drove 150 miles in 4 hours how many miles will he drive in 1 hour
Answer:
37.5 miles
Step-by-step explanation:
Distance covered in 4 hours = 150 miles
Distance covered in 1 hour = 150/4 = 37.5 miles
lf y 1/4 · when x=5, find y when x=7. given that y varies directly with x.
y=
Answer:
y= 0.35
Step-by-step explanation:
y 1/4
when x=5,
find y=? when x=7.
given that y varies directly with x.
y = kx
Where k is the constant of proportionality
k= y/x
k= (1/4)÷ 5
k= 0.05
y= kx
y= (0.05)(7)
y= 0.35
I Hope this will helpful...
Write 1.61 as a mixed number and as an improper fraction.
Do not try to simplify your answers.
mixed number:
improper fraction: |
Answer:
the answers would be 1 61/100 and 161/100
2x+6=3x+9-3 solve for x
Answer:
x=0
Step-by-step explanation:
2x-3x=9-3-6
-x=0
x=0
Answer:
x = 0
Step-by-step explanation:
Given
2x + 6 = 3x + 9 - 3 , that is
2x + 6 = 3x + 6 ( subtract 2x from both sides )
6 = x + 6 ( subtract 6 from both sides )
0 = x
Rewrite the expression using positive exponents
1. 1/9x^-2y^-1
2. a^-5*a^-8
Answer:
Property : a^-b = 1/a^b
Using this property, we can rewrite the expression using positive exponents :
[tex]1. \frac{1}{9}*x^{-2} *y^{-1} =\frac{1}{9}\frac{1}{x^{2} } \frac{1}{y} =\frac{1}{9x^{2} y} \\2. a^{-5} a^{-8} =\frac{1}{a^{5}a^{8} } =\frac{1}{a^{13} }[/tex]
The system of linear equations x – y + 2 = 0 and 2x + y -14 = 0
Answer:
(4, 6 )
Step-by-step explanation:
Given the equations
x - y + 2 = 0 ( subtract - y + 2 from both sides )
x = y - 2 → (1)
2x + y - 14 = 0 → (2)
Substitute x = y - 2 into (2)
2(y - 2) + y - 14 = 0 ← distribute and simplify left side
2y - 4 + y - 14 = 0
3y - 18 = 0 ( add 18 to both sides )
3y = 18 ( divide both sides by 3 )
y = 6
Substitute y = 6 into (1) for corresponding value of x
x = 6 - 2 = 4
solution is (4, 6 )
Which figure is described below?
The locus of points in a plane
equidistant between
(-5, -6) and (-5, 7).
Answer:
A.Line
Step-by-step explanation:
The locus of points in a plane equidistant between (-5, -6) and (-5, 7) is describe by the Line. so option A is correct.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
We know that the graph of x = 5 is the vertical line through 5 on the x-axis. Two points on this line are (-5, -6) and (-5, 7).
We form a horizontal line through (0,1) and (1,1). This is the locus of points equidistant between (-5, -6) and (-5, 7)
We have parallel lines like this, the locus of points equidistant from the two lines is always one single line, and it's the middle line as described above.
This applies to diagonal parallel lines as well, and vertical parallel lines.
Hence, The locus of points in a plane equidistant between (-5, -6) and (-5, 7) is describe by the Line. so option A is correct.
Learn more about a point dividing a line segment in a ratio here:
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if you have 500 dollars and spend 20 every week then what would be the slope explain
Answer:
y=-20m+500
Step-by-step explanation:
express the ratio 7day to 6weeks as a decimal fraction
Answer:
6 weeks=6*7 days=42days
7/42 =1/6 =0.16667
OR
7 days=1 week
therefore 1/6=0.16667
Note that both must be in the same unit.
PLEASE HELPP!!!!
Find the area.
A.530in²
B. 779in²
C.390in²
D.1060in²
Answer:
530in²
Step-by-step explanation:
Area of triangle(a)=1/2bh=1/2*40*26.5=530
a b c or d? pls help out thx
Answer: I'm very sure the answer is B
Step-by-step explanation:
If the rocket is going straight up and it's measuring the height and time in seconds it should be at a slight curve but maintaining it's straight curve up making it a linear.
The divisibility rule for 7 says 10a + b is a multiple of 7 if only and only if a - 2b is a multiple of 7
Explain.
Answer:
Step-by-step explanation:
Well I can show you by example. Try 28
a = 2
b = 8
2 - 2*8 = 2 - 16 = -14
- 14 is divisible by 7. You get - 2.
That means that 28 is also divisible by 8
We'll try one more. Try 56
a = 5
b = 6
5 - 2*6 = 5 - 12 = - 7
- 7 is divisible by 7 so 56 must be as well. What I'm wondering is if the rule in some form works for 735 and if it does how?
a = 73
b = 5
73 - 10 = 63
63 is divisible by 7 (giving 9)
so 10*73 + b is divisible by 7.
Try something a bit harder.
115444
a = 11544
b = 4
a - 2*4
11544 - 8
11536 / 7
1648 which works perfectly.
115444 is divisible by 28 which is a multiple of 7
Really amazing! Thanks for posting.
If third term of G.P. is 3, the product of its first five terms is
a) 1024 b) 243 c) 3125 d) 32
Convert the following as a. 2 hours to second
1. First convert hrs into min by multiplying 60
= 2 *60=120min
2. Then multiply 60 in 120 to convert it into seconds
120*60=7200 sec
MARK AS BRANLIEST.Find the equation of the circle whose center and radius are given.
center ( 7, -3), radius = √7
Answer:
(x-7)^2 + (y+3)^2 = 7
Step-by-step explanation:
The equation of a circle is
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x-7)^2 + (y- -3)^2 = (sqrt(7))^2
(x-7)^2 + (y+3)^2 = 7
HELP ILL GIVE U BRAINLIEST
Answer:
-6 33/40
Step-by-step explanation:
[tex]2\frac{5}{8} = 2.625\\-2\frac{3}{5} = 2.6\\\\2.625 *-2.6 = -6.825\\\\-6.825 = -6\frac{33}{40}[/tex]
Solve for x.
3x + 2
2x + 6
x = [?]
Answer:
4
Step-by-step explanation:
Im assuming you mean the first and second equation equal each other:
3x+2=2x+6
x=4
3x^2+5x^2+3x+1=(3x-1)(x^2+A)+B
Answer: If the question is to solve for A: A= [tex]\frac{15x+1-B}{3x-1}[/tex]
If the question is to solve for B: B= 15x+1-3xA+A
Step-by-step explanation:
A: Move terms to the left.
B: Simplify both sides.
Answer:
a=8x^2+3x+1-b/3x-1 -x^2; xdoes not equal 1/3
Step-by-step explanation:
hope this helps
1.4 (x + 5) + 1.6x = 52
Simplify <3
Can you please factor the problems below and explain/show all your steps. I will be attaching a photo with the problems as well in case they are more understandable on there. Also if you can please explain how you used the key concepts from the photo in your work if you used them.
Factor: 2a^3 + 4a^2 + 8a
Factor: 6y^4 - 294y^2
Factor: 5x^2 + 50x +125
---------------------------------------
To factor each expression, we apply the given concepts, that is, greatest common factor, difference of squares and perfect squares.
---------------------------------------
Expression 1:
The expression is:
[tex]2a^3 + 4a^2 + 8a[/tex]
First, we find the gcf of the numbers 2, 4 and 8, which is 2.
Of the exponents, the gcf between 3, 2 and 1 is 1, so:
[tex]2a^3 + 4a^2 + 8a = 2a(\frac{2a^3}{2a} + \frac{4a^2}{2a} + \frac{8a}{2a}) = 2a(a^2 + 2a + 4)[/tex]
---------------------------------------
Expression 2:
The expression is:
[tex]6y^4 - 294y^2[/tex]
The gcf of 6 and 294 is 6.
The gcf of the exponents 2 and 4 is 4.
Thus:
[tex]6y^4 - 294y^2 = 6y^2(\frac{6y^4}{6y^2} - \frac{294y^2}{6y^2}) = 6y^2(y^2 - 49)[/tex]
Then, applying the difference of squares:
[tex]y^2 - 49 = (y - 7)(y + 7)[/tex]
Thus, the factored expression is:
[tex]6y^2(y^2 - 49) = 6y^2(y - 7)(y + 7)[/tex]
---------------------------------------
Expression 3:
The expression is:
[tex]5x^2 + 50x + 125[/tex]
The gcf of the coefficients, 5, 50 and 125 is 5, so:
[tex]5(\frac{5x^2}{5} + \frac{50x}{5} + \frac{125}{5}) = 5(x^2 + 10x + 25)[/tex]
Applying the perfect square, we get that:
[tex]x^2 + 10x + 25 = (x + 5)^2[/tex]
Tus, the factored expression is:
[tex]5(x^2 + 10x + 25) = 5(x+5)^2[/tex]
A similar question is given at https://brainly.com/question/11930822
Your classmate is unsure about how to use side lengths to determine the type of triangle. How would you explain this to your classmate?
Answer:
To determine the type of triangle using side lengths, you could use the converse of the Phythagorean theorem, acute triangle inequality theorem, and the obtuse inequality theorem. For example, if the square of the longest side of a triangle is greater than the sum of the squares of the other two sides, than its obtuse. And if the square of the longest side is less than the sum of the squares of the other two sides, then it would be acute. And if the square of the longest side is equal to the sum of the squares of the two other sides, then it would be a right triangle.
Step-by-step explanation:
it marks it correct on edge and it is not a sample answer.
have a jolly day!
142°
3xº + 220
X =
degrees.
Step-by-step explanation:
hope it will help you market is brilliant
If you open an already created budget Excel spreadsheet, what is one feature it has when calculating amounts?
A) There isn't an already created budget Excel spreadsheet.
B) Formulas are already included that will calculate the totals for you.
C) You need to create formulas by yourself to calculate the totals.
D) You can use a calculator to add the numbers.
Formulas are already included that will calculate the totals for you.
Someone please help with this
Answer:
g(-3) = 1
Step-by-step explanation:
We use the top piece of the function since x = -3
g(-3) = x+4 and x = -3
g(-3) = -3 +4 = 1
An isosceles triangle has one angle of 30 degrees. Calculate the possible sizes of the other 2 angles
Answer:
75 and 75
Step-by-step explanation:
Answer:
Hello,
Step-by-step explanation:
2 solutions:
30° is angle of the base: other angle of the base is 30° and the main angle is 180°-30°-30°=120°30° is the main angle, angles of the base are (180°-30°)/2=75° and 75°.Nike is offering a 30% discount on shirts. A shirt at the store has an original cost of $25. What is the cost of the shirt, in dollars, after the discount
Answer:
$17.5
Step-by-step explanation:
original price of shirt=$25
discount on shirt=30%
discount on shirt in $=$25*30%
discount on shirt=$7.5
cost of shirt after discount=origanl price-discount
=$25-$7.5
=$17.5
-3 find the value. -3 ( 2 ) ² x (4)
pls tell the answer step by step pls
(-2/3)^(-2) × x × (3/4)-3
(-3/2)^2 × x ×(4/3)^3
-3/2×-3/2×4/3×4/3×4/3×x
= 16/3 × x
= 16x/3
Must click thanks and mark brainliest
pls help asap .........................
Answer:
40
Step-by-step explanation:
We can split this figure into two figures, a square and a trapezoid. The square, as shown has a side length of 4. That means that the area of the square is 16. The trapezoid, has base lengths of 2 and 4, and a height of 8. We can plug that into the area of a trapezoid formula:
[tex]\frac{2+4}{2}(8)[/tex]
Two plus 4 is 6, and 6 divided by 2 is 3. Three times 8 is 24.
24 plus 16 (the area of the square) is equal to 40, which is the area of the shape.
answer
answer
asap
pls
Answer:
true
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
An integer can be written as a fraction by giving it a denominator of one
