A riverboat travels 54 km downstream in 2 hours. It travels 57 km upstream in 3 hours. Find the speed of the boat and the speed of the stream
Here we must write and solve a system of equations to find the speed of the boat and the speed of the stream. We will find that the boat's speed is 23km/h and the river's speed is 4km/h.
First, remember the relation:
Distance = Speed*Time.
Now let's define the variables we will be using:
B = boat's speedR = river's speed.When the boat travels downstream, the total speed of the boat is the speed of the boat plus the speed of the river, and we know that in that case it travels 54km in 2 hours, then:
54km = (B + R)*2h
When the boat travels upstream, we must subtract the speed of the river. In that case, we know that the boat travels 57km in 3 hours, then we have:
57km = (B - R)*3h
Then our system of equations is:
54km = (B + R)*2h
57km = (B - R)*3h
To solve this, first, we need to isolate one of the variables in one of the equations, let's isolate B in the second one:
57km = (B - R)*3h
57km/3h + R = B
19 km/h + R = B
Now we can replace that in the other equation:
54km = (B + R)*2h
54km/2h = B + R
27 km/h = B + R = (19 km/h + R) + R
Now we can solve this for R:
27 km/h = 19km/h + 2*R
27 km/h - 19km/h = 2*R
8 km/h = 2*R
(8km/h)/2 = 4km/h = R
Now that we know the value of R, we can use:
B = 19 km/h + R = 19 km/h + 4km/h = 23 km/h
So the boat's speed is 23km/h and the river's speed is 4km/h.
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If you have a book to read that is 20 pages, and you have read 15% of the book, how many pages as you read?
Answer:
3
Step-by-step explanation:
20*.15=3
which coasts the most per disk a 10 pack for 5.99 , a 25 pack for 12.50 or 50 pack for 18.75
Answer:
25 disc for 12.50 is the most.
Step-by-step explanation:
You would have see how much each cost for one.
1. 10 for 5.99.
5.99 ÷ 10 is 0.599. So basically .60 cents.
2. 25 for 12.50.
12.50 ÷ 25 is 2. So basically 2 dollars per disc.
3. 50 for 18.75
18.75 ÷ 50 is 0.375. So basically .38 cent.
Now compare them.
1. 0.60
2. 2
3. 0.38
25 disc for 12.50 is the most.
someone help me with my assignments
Answer: Choice A
Step-by-step explanation: You are given the inequality g is less than or equal to. Greater/less than and equal to, you use solid circle. Greater/less than, you use open circle. From there, you just look at the inequality in which direction is it going at and from there, you should be able to select your choice which happens to be the first one.
I hope this explanation helps.
Best to you!
how many times as large is the 4 in the tenthousands place as the 4 in the ones place
Consider the equation of a circle x^{2} -2x + y^{2} - 4y - 4 = 0 if the line 2x - y + a = 0 is its diameter. then find the value of a?
Answer:
Step-by-step explanation:
Find the centre first by reoriganisation it into the form (x - cx)^2 + (y -cy)^2 = r^2
x^2 + y^2 + 6x -6y +5 = 0
(x + 3)^2 - 9 + (y - 3)^2 - 9 + 5 = 0
(x + 3)^2 + (y - 3)^2 = 13
The radius does not matter the centre is ( -3, +3)
The diameter must pass through the center so substituting into the equation for the line
2x-y+a = 0
-6 -3 + a = 0 so a = 9
The value of 'a' is 0 and this can be determined by using the standard form of the equation of a circle.
Given :
Equation of a Circle -- [tex]x^2-2x+y^2-4y-4=0[/tex]
Equation of a Line -- 2x - y + a = 0
The following steps can be used in order to determine the value of 'a':
Step 1 - First make the equation of a circle in standard form.
[tex]x^2-2x+y^2-4y-4=0[/tex]
[tex](x-1)^2-1+(y-2)^2-4-4=0[/tex]
[tex](x-1)^2+(y-2)^2 = 3^2[/tex]
Step 2 - From the above step, it can be concluded that the center of the circle is (1,2).
Step 3 - If (1,2) is the center of the circle then it also satisfies the equation of diameter (2x - y + a = 0).
2x - y + a = 0
2(1) - 2 + a = 0
a = 0
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juan saves 12 the first week of the year. he increase the amount each week by 4, write a function that represent the sequence
Answer:
12,16,20,24,28,32,36,40 (continue to add 4)
Step-by-step explanation:
A function that represents the given sequence is f(n) = 4(2+n).
What is an arithmetic sequence?A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.
Given that, Juan saves 12 in the first week of the year, and increases the amount each week by 4, therefore, the difference between the amount of any two consecutive weeks is 4.
Hence, it represents an arithmetic sequence with the first term a₁ = 12 and the common difference d = 4.
The nth term of an arithmetic sequence is given by:
aₙ = a₁ + (n-1)d
Substitute a₁ = 12 sand d = 4 into the above equation:
aₙ = 12 + (n-1)4
= 12 +4n -4
= 8 + 4n
= 4(2+n)
Hence, a function that represents the given sequence is f(n) = 4(2+n).
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A group of friends is sharing 25 pounds of berries. Type the answer to each question in the boxes below. If each friend received of a pound of berries, how many friends are shar berries? 2 friends If 5 friends are sharing the berries, how many pounds of berries does each receive? pound(s)
simplify (6)/(\sqrt(3))
Find the volume in cubic yards of a rectangular solid with length 3.8 yards, width 2.2 yards, and height 2.3 yards
Answer:
19.228 cubic yards
Step-by-step explanation:
volume = l×w×h
[tex]v = (3.8)(2.2)(2.3) \\ = 19.228 \: {yards}^{3} [/tex]
The area of a circle is 2
square meters. Determine
the radius.
[tex]\text{Area of circle} = \pi r^2\\\\\implies 2 = \pi r^2\\\\\implies r^2 = \dfrac 2{\pi}\\\\\\\implies r = \sqrt{ \dfrac 2{\pi}} = 0.798~ \text{m.}[/tex]
Answer:
r≈.8m
Step-by-step explanation:
Formula used
A=πr2
r=√a/π =√2/π ≈.79788
rounded it is .8m
Does anyone know how to solve this?
The answer is B but can anyone explain it please
Answer: sorry no
Step-by-step explanation: sorry i dont want to explain it.
7 1/2 divided by 2 5/8 in simplest form
Answer:
[tex]2\frac{6}{7}[/tex]
Step-by-step explanation:
First you have to convert the mixed numbers to an improper fraction which first let's do the top so that would be: [tex]\frac{\frac{15}{2}}{2\frac{5}{8}}[/tex]
Next, lets do the bottom of that so that would become: [tex]\frac{\frac{15}{2}}{\frac{21}{8}}[/tex]
After that you have to apply the fraction rule [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex] so that would be: [tex]\frac{15\cdot \:8}{2\cdot \:21}[/tex]
Towards the end, you have to cancel out that equation so then it becomes: [tex]\frac{20}{7}[/tex]
Finally, you convert the improper fractions to mixed numbers so that is now: [tex]2\frac{6}{7}[/tex]
Have a great day!
After divide, the value in simplest form is, 20/7.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
⇒ 7 1/2 divided by 2 5/8
Now, Divide the numbers as;
⇒ 7 1/2 divided by 2 5/8
⇒ 15/2 ÷ 21/8
⇒ 15/2 × 8 / 21
⇒ 15×8 / 2×21
⇒ 5×4/7
⇒ 20 / 7
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if the stated rate on each of these loans was 5%, would they all have equal, effective annual rates? explain.
Answer:
im the Akash Shukla and Aap I will get them back to
A provisional license holder under 18 may not drive without special permission _____________________ .
A between 8:00 a.m. and 9:00 pm
B between 12:00 am and 5:00 am
C between 5:01 am and 11:59 pm
D between 6:00 a.m. and 6:00 pm
Answer:
C
Step-by-step explanation:
A provisional license holder under 18 may not drive without special permission between 5:01 am and 11:59 pm.
Gary weighed 187 pounds after graduating
high school. 5 years later he weighs 228
pounds. By what percentage has his weight
changed?
Plz helppppppp
eat chili snacks and spicy to burn fat
Which of the following trinomials can be factored using the square of the difference?
NO LINKS!!
Answer:
d) 16x² -56x +49
Step-by-step explanation:
The square of a binomial difference will have the form ...
(ax -b)² = a²x² -2abx +b²
__
The sign of the linear term will be negative, which eliminates choices A and C.
The linear term will be double the product of the roots of the other two terms.
In choice B, the linear term has a factor of 5 that appears nowhere else, so that cannot be a perfect square.
Choice D factors as ...
16x² -56x +49 = (4x -7)² . . . . the square of a difference
the permiter of one face of cube is 60 cm then its volume :
Step-by-step explanation:
a cube has 6faces.
side = 60/6 = 10cm
volume = 1000cm³.
hope this helps you.
Graph the line that passes through the points (2,−3) and (4, "-3)and" determine the equation of the line.
Answer:
y=-3x+3
Step-by-step explanation:
what is the answer to the following?
9+(60x8)-120?
80(50-24)+20?
Answer:9+(60x8)-120= 369
80(50-24)+20= 126
Step-by-step explanation:
Which is the solution to the inequality?
Y+ 15 < 3
A. y <-12
B. y >-12
C. y <18
D. y> 18
Answer: A
Step-by-step explanation:
Subtract 12 from both sides:
y + 15 - 15 < 3 - 15
Simplify:
y < -12
What is the ratio of 1/2 to 6?
(A) 12
(B) 3
(C)1/3
(D)1/6
(E) 1/12
Answer:
e, 1/12
Step-by-step explanation:
1) turn the first fraction into a whole number, the closest whole number being 1.
what did you multiply 1/2 by to get 1? the answer would be 2.
whatever you do to oneside, do to the other. when you multiply 6 by 2, you get twelve.
therefore, the answer is 1/12
Write the ratio 1 1/3 to 3 1/9 as a simplified fraction
Answer:
First ratio:4/3
Second:28/9
The coordinates of the point that is a reflection of Y(-4,-2) across the x-axis are what. The coordinates of the point that is reflection of y across the y-axis are what?
Answer:
Step-by-step explanation:
across x axis:(-4,2)
across y-axis:(4,-2)
What are all the fractions that are between 1/2 and 1.
Answer:
2/4, 3/5,3/4, 2/3,13/25, 27/50 11/20, 14/25, 29/50,31/50, 63/100,16/25,33/50,17/25,7/10,18/25,37/50,19/25,77/100,39/50,4/541/50, 83/100, 21/25 , 17/20, 43/50 , 87/100,22/25,9/10, 91/100, 23/25, 93/100, 47/50, 19/20 , 24/25 97/100, 49/50,99/100(note that I did not state all the fractions between 1/2 and 1)
Step-by-step explanation:
Firstly one half(1/2) represents 0.50 as a decimal and 1 would be 1.00
This is like saying finding Fractions that give you percentages between 50% and 100%
for example:
you could simplify 52/100 and get 31/50
31/50 as a decimal would be 0.52 and 0.52 falls between(0.50 and 1.00) 1/2 and 1
example 2: 89/100= 0.9 (same as0.90) and [90/100] is same as 9/10 = 0.9
0.90 or 0.9 (zero point nine) is not the same as 0.09(zero point zero nine
If you are using a casio calculator, you can simplify the fraction by putting in your numerator then pressing |a b/c| button then enter the denominator, then the calculator should simplify the fraction, if the fraction remains the same, this means that it cant be further simplified.if your calculator has
| a b/c| then you can also use it.
or use an online calculator or simplify if you wish
To find the decimal of that fraction you can simply divide the numerator by the denominator, Example; 82/100 is same as 0.82 and 41/50 is same as 0.82.
The 11th term of the AP -3, -1/2, 2 . .... is
Given AP is -3 ,-1/2,2,..
First term = -3
Common difference = (-1/2)-(-3)
⇛d = (-1/2)+3
⇛d = (-1+6)/2
⇛ d = 5/2
We know that nth term = an = a+(n-1)d
11th term = (-3)+(11-1)(5/2)
⇛a 11 = -3+(10)(5/2)
⇛a 11 = -3+(5×5)
⇛a 11 = -3+25
⇛ a 11 = 22
11th term of the AP = 22.
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The 4th term of ap is 10 and the 11th term of it exceeds 4th term by 1 find the sum of 20 terms ....
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Answer:
2
Step-by-step explanation:
initial term = -3
common difference = .5
-3 + .5 for 11 times from 3 = positive 2
72 is 45% of what number?
Answer:
160
Step-by-step explanation:
we have, 45%×x = 72
or, 45÷100×x = 72
multiplying both side by 100 and diving both side by 45,
we have x= 72×100÷45
x= 160 ANSWER(b) A sum of money was to be shared among three friends Keisha, Tracey, and Kerry-Ann, in the
ratio 7:9:11 respectively. If Kerry-Ann received $3,300.00, find the sum of money that was
between the three friends.
The sum of money that was shared between the three friends is $8100
The ratio at which the money was shared = 7 : 9 : 11
Total ratio = 7 + 9 + 11
Total ratio = 27
Amount received by Kerry-Ann = $3300
Let the total amount shared by the three friends be T
Amount received by Kerry-Ann = (11/27) x T
3300 = 11T / 27
11T = 27(3300)
11T = 89100
T = 89100/11
T = 8100
The sum of money that was shared between the three friends is $8100
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If x = (1/2)(16 - 8y), then x =
Answer:
x = 8 - 4y
Step-by-step explanation:
16/2 = 8
8y/2 = 4y
The value of x of the expression is x = 8 - 4y.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
x = (1/2)(16 - 8y)
Removing the parenthesis.
x = 16/2 - 8y/2
x = 8 - 4y
Thus,
The value of x is 8 - 4y.
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Kendall tracked the amount of water his windowsill plant needed each week over ten weeks. Her data is shown below.
Which of the following is true?
A.
There is a negative association between the number of weeks and the ounces of water the plant needed.
B.
There is a positive association between the number of weeks and the ounces of water the plant needed.
C.
There is no association between the number of weeks and the ounces of water the plant needed.
D.
There is both a positive and negative association between the number of weeks and the ounces of water the plant needed.
Answer:
Perfort the indicated operation Show your solution in
the gevin below