HELP HELP
Tommy rides in a motorboat against a river current for 25 km. Then he returns to his starting point by floating down river on a raft. Tommy travels 10 hours less on the motorboat than on the raft. Find the speed of the river current if the speed of the motorboat in still water is 12 km/h.
The speed of current is [tex]\rm 2 \:km/h[/tex].
What is the relation between distance,speed and time?The relationship between distance, time and speed can be presented as:
[tex]\begin{aligned} \rm Distance &= Speed \times Time\\\\Speed &= \dfrac{\rm Distance}{Time} \\\\\rm Time &= \dfrac{\rm Distance}{\rm Speed} \end[/tex]
Calculations:
Given:
[tex]\begin{aligned} \rm Distance\: traveled\: on\: motorboat &= 25\:km\\\rm Speed\:of\:motorboat\:in\:still\:water &= 12\:km/h \end[/tex]
Let the speed of the current be [tex]\rm x[/tex]
The speed of the boat traveling against the current is [tex]{(12 -\rm x) km/h}[/tex]
Time spent on motorboat is 10 hours less than time spent on raft.
Therefore:
[tex]\rm \dfrac{25km}{x\:km/h} - \dfrac{25km}{(12 - x)km/h} = 10[/tex]
The equation obtained will be:
[tex]\dfrac{25}{\rm x} - \dfrac{25}{(12-\rm x)} - = 10[/tex]
Multiplying both sides of the equation by [tex]\rm x(12 - x )[/tex]
[tex]\begin{aligned} \rm 25(12 - x) - 25x &= 10\times \rm x(12 - x)\\\\300 - 25x - 25x &= 120x - 10x^2\\\\300 - 50x &= 120x - 10x^2\\\\10x^2 - 120x - 50x + 300 &= 0\\\\10x^2 - 170x +300 &= 0\end[/tex]
Dividing the equation by 10
[tex]\rm x^2 - 17x + 30 = 0[/tex]
On factoring the equation,
[tex]\rm =x^2 - 2x -15x + 30 = 0\\\\=x(x - 2) -15(x - 2)\\\\=(x - 2)(x - 15)[/tex]
The values of x is 2 and 15.
Since speed of current i.e [tex](12 -\rm x)km/h[/tex] cannot be negative, [tex]\rm x = 2[/tex] is the only acceptable value.
Therefore the speed of current is 2 km/h.
Learn more about the topic here:
https://brainly.com/question/2292310
please help me solve this answer
Answer:it is a
Step-by-step explanation:
because it is only one under 3 miles
8 friends go to Subway and each get 1/2 of a sandwich. How many sandwiches did they get altogether?
find the product 6 * 1/3
Answer:
2
Step-by-step explanation:
Reduce the numbers with the greatest common factor which is 3
So.. 2
98.8% of 668.49km NEED ANSWERS QUICK
Answer:
the answer would be 660.46812 km
Step-by-step explanation:
The computation is shown below:
According to the question it is mentioned what is the 98.8% of 668.49 km
So, it would be
= 98.8% of $668.49 km
= 98.8% × 668.49 km
= 660.46812 km
Hence, the answer would be 660.46812 km
Please help when Kevin bought a new office phone, he borrowed $1,200 at a rate of 18% for 9 years
Answer:
where is the rest of the questions
The factors of a polynomial are (x + 3x - 2)(x+ 7) The polynomial has been graphed. How do the zeros relate to the factors?
A. The zero is the sum of the numbers inside the parenthesis
B. There is no relationship between the factors and the zeros.
C. The number inside each parenthesis are the zeros of the equation.
D. If you set each factor equal to 0 and solved you would get the zeros.
Answer:
its C I am pretty sure about it
Answer:
D: If you set each factor equal to 0 and solved you would get the zeros.
Step-by-step explanation:
Completed it on PL also because 0 should be base
1344 divided by 16
(Pls ans)
Answer:
84
Step-by-step explanation:
Answer:
84
Step-by-step explanation:
1344/16=84
the tax on a purchase of $20 is $2.80. How much tax will there be on a purchase of $45.50?
Answer:
$6.37
Step-by-step explanation:
You divide 2.80 by 20 to find the percentage of tax then you simply multiply your percentange by the cost. In this problem the tax was 14% or .14, so you multiply .14 by 45.50 to find the amount of tax on the purchase
Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large. Consider the following data, which represent the daytime household temperature the thermostat is set to when someone is home for a random sample of households. Determine the class midpoint, if necessary, for each class and approximate the mean and standard deviation temperature.
Temp Frequency Class Midpoint
61-64 34 63
65-67 68 66.5
68-69 196 69
70 191 70.5
71-72 122 72
73-76 81 75
77-80 52 79
The sample standard deviation is _____degrees°F.
Answer:
The sample standard deviation is 13.22°F
Step-by-step explanation:
Given - Often, frequency distributions are reported using unequal
class widths because the frequencies of some groups would
otherwise be small or very large. Consider the following data,
which represent the daytime household temperature the
thermostat is set to when someone is home for a random sample
of households. Determine the class midpoint, if necessary, for
each class and approximate the mean and standard deviation
temperature.
Temp Frequency Class Midpoint
61-64 34 63
65-67 68 66.5
68-69 196 69
70 191 70.5
71-72 122 72
73-76 81 75
77-80 52 79
To find - The sample standard deviation is _____degrees°F.
Proof -
Temp Frequency(f) Midpoint(m) m×f ( m - 70.73 )²×f
61-64 34 63 2142 2031.6
65-67 68 66.5 4522 1216.7
68-69 196 69 13524 586.6
70 191 70.5 13465.5 10.1
71-72 122 72 8784 196.8
73-76 81 75 6075 2224.4
77-80 52 79 4108 3556.4
∑f = 744 ∑m×f = 52620.5 ∑ = 9822.6
So, Mean = [tex]\frac{52620.5}{744}[/tex] = 70.73
Sample standard deviation = [tex]\frac{9822.6}{744 - 1} = \frac{9822.6}{743}[/tex] = 13.22
∴ we get
The sample standard deviation is 13.22°F
Use each number in the box once to complete the division
5÷6,206
Answer:
i believe it is 1,241.2
Step-by-step explanation:
well you use long division.
Using lengths a, b, and c in the right triangle shown, how are the trigonometric functions of defined?
Answer:
take a pic.of question
Step-by-step explanation:
gotta see the triangle
please help i will give brainliest
But least to greatest
Answer:
8.933,8.96,9.05,9.065,9.08,9.1
Step-by-step explanation:
Mr.moss has 4 gallons of paint. He painted 8 doors. How many benches can he paint with the paint that is left
Answer:
2
Step-by-step explanation:
I did 8 divided by 4 which is 2.
I hope this helps.
Please help me I’m desperateeee
Answer:
Step-by-step explanation:
First box: (0,1)
Second box: (0,-3)
Third box: (0,-4)
The Murphin Company has 2,342 employees and the Galdstock Company has 1,750 employees. How many fewer people work at the Galdstock Company than at the Murphin Company?
Answer:
592
Step-by-step explanation:
This is a subtraction problem.
2,342 - 1,750 = 592
(-1)15 =
................
What is 4^2 - (3.1 + 6.4) + 4.5 pls show ur work
also (area O O O O O O
Answer:
slide A= 6
slide B= 8
perimeter= 36
Area = 80
Step-by-step explanation:
Answer:
slide A= 6
slide B= 8
perimeter= 36
Area = 80
Step-by-step explanation:
Umm yea help me please:)
what is the square root of -20
Answer:
4.47213595
Simplify in the tenths place and get 4.47
Step-by-step explanation:
pls answer this-.....
AnswerS:
Let A be the surface area, b the base, h the height;
h₁=8.4 cm
h₂=7.8 cm
b= 9 cm
A= 3(1/2bh₁)+1/2 bh₂
A=3(1/2(9)(8.4))+1/2 (9)(7.8)
A= 148.5 cm³
Answer:
Step-by-step explanation:
The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.
Surface area of the square pyramid is given as:
Where,
B.A = Base Area of the pyramid = 9*9 = 81 in²
P = perimeter of the base = 4(9) = 36 in
L = slant height of pyramid = 9.2 in
Plug in the values into the given formula to find the surface are
Write an expression for the sequence of operations described below.
10 plus the quotient of 8 and u
Do not simplify any part of the expression.
Answer:
[tex]10 + \frac{8}{u}[/tex]
Step-by-step explanation:
Given
10 [tex]plus[/tex] the [tex]quotient[/tex]of 8 and u
Required
Represent as a mathematical expression
Square out the operators
10 [[tex]plus[/tex]] the [[tex]quotient[/tex]] of 8 and u
[tex]plus => +[/tex]
[tex]quotient => /[/tex]
Replace the operators with their signs
[tex]10 + \frac{8}{u}[/tex]
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answer:
No
Step-by-step explanation:
(2, 6) is not a solution to the given system of linear equations.
y = 5x - 4 = 5*2 - 4 = 10 - 4 = 6
y = - 1/2x + 8 = - 1/2 * 2 + 8 = - 1 + 8 = 7
Since, point (2, 6) does not satisfy to equation 2.
Therefore, (2, 6) is not a solution to the given system of linear equations.
Answer:
no
Step-by-step explanation:
What percent of $80 is $20
Answer: $20$20 is $25\%$25% of $80$80.
Step-by-step explanation:
25
Don operates a small craft store in which he sells other peoples crafts. He takes a 45% commission from the sales of all crafts. If he earns $958.00 Commission last week, how much did he sell?
Answer:
2,128
Step-by-step explanation:
958=45/100 x
958= 0.45* x
x=958/0.45
x=2,128 approximately
Hope that helps!
what shape can be formed from the following net?
Answer:
A Triangular Prism
Hope that helps!
Step-by-step explanation:
Answer: Triage
Step-by-step explanation:
which table shows ordered pairs that satisfy the function y=4x-2
A x -2, 0, 2
y -4, -2, 0
B x -2, 0, 2
y 10, 6, 2
C x -2, 0, 2
y -8, 0, 8
D x -2, 0, 2
y -10, -2, 6
==========================================================
Explanation:
If you plug in x = -2, then,
y = 4x-2
y = 4(-2)-2
y = -8-2
y = -10
This shows that the answer must be choice D, as this is the only answer that has x = -2 lead to y = -10. Note the first column of table D.
We could stop here if you wanted.
----------------------
If we kept going and plugged in x = 0, then,
y = 4x-2
y = 4(0)-2
y = 0-2
y = -2
We have x = 0 lead to y = -2. This matches with the second column of table D.
-----------------------
Lastly, if we plugged in x = 2, then we get,
y = 4x-2
y = 4(2)-2
y = 8-2
y = 6
So the third column of table D is also confirmed.
If 42,800 dollars is invested at an interest rate of 5 percent per year, find the value of the investment at the
end of 5 years for the following compounding methods.
What is the
Annual $
Semiannual $
Monthly $
Daily $
Continuously $
Answer:
Annual $54,624.85
Semiannual $54,787.62
Monthly $54,927.75
Daily $54,955.35
Continuously $54,955.35
Step-by-step explanation:
If 42,800 dollars are invested at an interest rate of 5 percent per year, to find the value of the investment at the end of 5 years for the following compounding methods, the following calculations must be performed:
Annual $54,624.85
42,800 (1 + 0.05 / 1)^5x1 = X = 54,624.85
Semiannual $54,787.62
42,800 (1 + 0.05 / 2)^5x2 = X = 54,787.62
Monthly $54,927.75
42,800 (1 + 0.05 / 12)^5x12 = X = 54,927.75
Daily $54,955.35
42,800 (1 + 0.05 / 365)^5x365 = X = 54,955.35
Continuously $54,955.35
42,800 (1 + 0.05 / 365)^5x365 = X = 54,955.35