let s = speed in still water
let c = rate of the current
then
(s-c) = effective speed up-stream
and
(s+c) = effective speed down-stream
Write a distance equation for each way; dist = time * speed
5/6*(s-c) = 5
1/2 *(s+c) = 5
Now we get rid of the fractions
5(s-c)=30
s + c = 10
5s - 5c = 30
s + c = 10
siplifying:
s - c = 6 (1)
s + c = 10 (2)
adding:
2s = 16, then s = 8
8 mph is the boat speed in still water
According with (2):
8 + c = 10, then c = 2
2 mph is the speed of the current
Line segment EF has endpoints at (2,-4) and (5,-9)
If ST is congruent to EF and has one endpoint at (4,9), which of the following points could be the second endpoint?
A.(-4,-3)
B.(-1,12)
C.(22,-3)
D.(-4,11)
Please show work so I can understand how to do it.
The second endpoint of ST is B(-1,12).
It is given in the question that:-
Endpoints of line segment EF are (2,-4) and (5,-9).
One of the endpoint of ST is (4,9).
We have to find the second endpoint of ST.
As both of the line segments are congruent hence, the length of each line segment will be same.
We can find the length of the line segment EF using the distance formula.
Length of the line segment EF :-
[tex]\sqrt{(-9-(-4)^2+(5-2)^2}=\sqrt{(-9+4)^2+3^2}=\sqrt{25+9}=\sqrt{34} units[/tex]
Hence, length of the line segment ST should also be the same.
We can check that from the options and get B(-1,12) as the answer.
To learn more about distance formula, here:-
https://brainly.com/question/28956738
#SPJ1
Use the ALEk calculator to write 3/32 as a percentage
Answer:
9.4%
Step-by-step explanation:
To convert any given imporper fraction into a percentage, we multiply it by 100. This way, we can convert the fraction given as following:
[tex]\frac{3}{32}\times100\rightarrow9.4\%[/tex]The storage area in an art room has 24 separate bins. Each bin can hold 8 packs of markers, crayons, or colored pencils. Each pack holds 8 items. The art teacher has 240 markers, 320 crayons, and 336 colored pencils. How many empty bins will the art teacher have once all of the markers, crayons, and pencils are put away?
In order to find the number of empty bins, let's calculate how many packs will be made with the given material.
240 markers can be organized in 240/8 = 30 packs
320 crayons can be organized in 320/8 = 40 packs
336 colored pencils can be organized in 336/8 = 42 packs
In total we have 30 + 40 + 42 = 112 packs
Each bin can hold 8 packs, to in order to hold 112 packs, we need 112/8 = 14 bins.
We have 24 bins. Since 14 will be used, we will have 24 - 14 = 10 empty bins.
Hello!! I need help with this Vector problem below. Can anyone please explain the problem step by step please? I really need to understand it!
Find the magnitude and
direction angle of v = 6i+ 4j.
Round direction angle to nearest degree.
The magnitude of the vector is v = [tex]\sqrt{52}[/tex]
and the angle of the vector θ = 10 degrees
What are vectors?An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
Given ; Vector = v = 6i+ 4j
The given points are ( 6 , 4 )
x = 6 units and y = 4 units
The magnitude of the given vector can be calculated by :
v = [tex]\sqrt{6^2 + 4^2}[/tex]
v = [tex]\sqrt{36 + 16}[/tex]
v = [tex]\sqrt{52}[/tex]
the magnitude of the vector = v = [tex]\sqrt{52[/tex]
The angle of the vector :
tan θ = [tex]\frac{y}{x}[/tex]
tan θ = [tex]\frac{4}{6}[/tex]
tan θ = 2/3
thus θ = tan-1 2/3
θ = 10.3°
To know more about vectors you may visit the link which is mentioned below:
https://brainly.com/question/14033610
#SPJ1
What is the slope of the line that passes through the points (-2, 6)(−2,6) and (-12, 2)(−12,2)? Write your answer in simplest form.
Answer:Given points are (6, -2) and (12, -2). Find the slope of the line using the formula m = (y2 - y1)/(x2 - x1) Here, y1 = -2, y2 = -2, x1 = 6 and x2 = 12
⇒ m = (-2 - -2)/(12 - 6) = 0/6 = 0
Step-by-step explanation: i hoped i helped a little :)
A cube has a side length of 3x^6 units. A smaller cube has a side length of x^2 units. How many smaller cubes will fit in the larger cube?
please simplify it because i am a grade 8 student
The number of smaller cube that will fit in the larger cube is 27x¹³ considering their volumes.
Volume of a cubeThe volume of a cube with length l is l × l × l = l³
From the question, we have that the length of the bigger cube is 3x^6 and that of the smaller cube is x² hence;
volume of the larger cube = (3x^6)³
volume of the larger cube = 27x^18
and,
volume of the smaller cube = (x²)³
volume of the smaller cube = x^5
We need to divide the volume of the larger cube by volume of the smaller cube to know what amount of the smaller cube that can fit in to the bigger cube.
So (27x^18)/(x^5) = 27x¹³
Therefore the number of the smaller cube to fit in to the bigger cube is derived as 27x¹³ for any real values of x.
Learn more about volume of a cube here: https://brainly.com/question/1972490
#SPJ1
Convert the polar equ what is the angle between the ropes? Round to the nearest degree.ation r = 16 sin θ to a rectangular equation.
The angle between the ropes is 53°.
We are given that a barge is being towed by two tugboats using ropes. The force vectors of the two tugboats are represented by F1 and F2. A vector is an entity that has both a magnitude and a direction. The vectors are F1 = 11000i + 5000j and F2 = 14500i + -8000j. We need to find the angle between the ropes. The best method is to find the dot product. Let the angle between the ropes be θ. We can say that cos(θ) = F1.F2/(|F1|*|F2|) = (11000*14500 + 5000*-8000)/[√[(11000)² + (5000)²] * √[(14500)² + (-8000)²]] = (11*14.5 + 5*-8)/[√[(11)² + (5)²] * √[(14.5)² + (-8)²]] = 119.5/[√146*√274.25] = 119.5/200.1 = 0.597. So, the value of θ is 53°.
To learn more about angles, visit :
https://brainly.com/question/28451077
#SPJ9
i need help like instantly
The proof for the congruence of angles 3 and 4 is given by the image presented at the end of the answer.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, that is, having the same angle measure.
The vertical angles in this problem are listed as follows:
1 and 3.2 and 4.What is the transitive property of congruence?The transitive property of congruence defines that:
If two angles are congruent to a third angle, then the two angles are also congruent between themselves.
Hence the angles that are congruent based on the transitive property of congruence are given as follows:
2 and 3, as both 2 and 3 are congruent to 1.3 and 4, as both 3 and 4 are congruent to 2.More can be learned about vertical angles at brainly.com/question/1673457
#SPJ1
each book in a certain library is classified in one of three categories: fiction, nonfiction, or biography. the ratio of the number of fiction books to the number of nonfiction books is 4 to 3, and the ratio of the number of nonfiction books to the number of biographies is 3 to 2. if there are at least 10,000 books in the library, what is the least number of books that could be in the library?
The number of fiction books in the library is equal to 16
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given the ratio of fiction to nonfiction books in a classroom, the library is 2 to 3, and then the total ratio of both books will be 2+3 = 5. If there are 24 books non-fiction books in the library, to get the number of fiction books that are there we will follow the following steps.
First, we will calculate the total number of books in the shelf;
3/5 x Total number of books = total non fiction books
3/5 * Total number of books = 24
3*Total number of books = 5*24
3*Total number of books = 120
Total number of books = 120/3
Total number of books = 40
Therefore there are 40 total books on the shelf.
Total number of fiction books = 2/5 * 40
Total number of fiction books = 2* 8
Total number of fiction books = 16 books
Hence there are 16 fiction books on the shelf.
To know more about an expression follow
https://brainly.com/question/23122462
#SPJ1
Luke is making a gelatin dessert to bring to a picnic. He combines strawberry gelatin and lemon gelatin in a large tray. Then, he decides to make a smaller tray to keep at home. In the small tray, he combines half the amount of strawberry gelatin and half the amount of lemon gelatin. Which tray of gelatin will taste more like lemon?
Thanks
The tray of gelatin that would taste more like lemon would be = the both trays.
What is a dessert?A dessert is defined as the part of a course meal that is usually taken at the end of a three course meal.
In the making of a gelatin dessert by Luke he made the following combinations;
strawberry gelatin and lemon gelatin = Large tray
½ strawberry gelatin and ½ lemon gelatin = Small tray
The tray that will taste more of lemon would be the both trays because the same measurement of lemon gelatin was used for both the large and small tray.
Learn more about dessert meals here:
https://brainly.com/question/28550641
#SPJ1
Answer:
neither
Step-by-step explanation: its just neither
40 PIONTS FOR ANSWERING 2 Q'S, I WILL PICK BRIANLISET
6. For the Raleigh company, create a table to represent the cost of the cab ride given the number of miles provided for miles 5, 10, 15 and 20. List the cost for the cab ride for 15 miles.
My answer (tell me if it is right or wrong)
for 15 miles your cost would be $42.45 inclueding the fee of $1.95
7. For the Raleigh company write an equation in slope-intercept form to represent the amount charged, C, for m number of miles.
Answer:
$3.86
tell me if im wrong
Answer:
6: your answer is correct
7: C=2.7m+1.95
Step-by-step explanation:
6:
5 15.25
10. 28.95
15. 42.45
20. 55.95
question 7
slope intercept form is y=mx+b
m is slope and b is y intercept
Slope is 2.70 since that is how much we go up for a mile
And 1.95 is y intercept since it is where we start no matter what and we have to add that constant fee every time
y=2.70x+1.95
We change the y to c and the x to m to fit the problem
C=2.70m+1.95
Hopes this helps please mark brainliest
I don't know how to get AAS or ASA moveover how to explain it
Answer:
Step-by-step explanation:
The bisector forms peripendicular (90) angles VZW and WZY. It also divides the side in half so you have VZ=ZY. It seems like you wrote everything else for the question
-2(-3.4)what is the answer
6.8
1) Let's calculate this product by distributing the factor -2 multiplying the number within the parentheses.
-2(-3.4) Equal signs yield positive and remove the parentheses
6.8
2) So 6.8 is the answer for that product.
hurry!!!!! pls!!!!!! how do I solve this?
The value of x in the above diagram is 9
what is a triangle?A triangle is a polygon with 3 sides and 3 angles.
Triangles are of different types: isosceles, equilateral, scalene and right-angle triangles.
from the diagram, the triangle is and isosceles triangle and for isosceles triangle the base angles are equal.
so that,
5x+36 = 9x
by collecting like terms,
9x - 5x = 36
4x = 36
x = 36/4
x = 9
In conclusion the solution to the given problem is x = 9
Learn more about triangles: https://brainly.com/question/24382052
#SPJ1
Write down the value of 3²
Answer:9
Step-by-step explanation:
it is the same as 3x3
Tell whether the line for each pair of equations is parallel, perpendicular, or neither y = 1/4 x + 10
-2x + 8y = 6
I need help on a problem
Here, from the figure we see that,
Line EI is parallel to HG.
And EH and GI act as the transversal lines for the given parallel pair.
So, we get
[tex]\begin{gathered} \angle G=\angle I\text{ (alternate angles)} \\ \angle E=\angle H\text{ (alternate angles)} \\ \angle EFI=\angle GFH(vertically\text{ opposite angles)} \end{gathered}[/tex][tex]\text{Also in }\Delta EIF\text{ side }FI\text{ is given equal to side }FG\text{ in }\Delta FGH[/tex]Therefore, we have two angles and one side equal in two triangles.
Henceproved that , they are congruent with the ASA (Angle Side Angle)rule.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Jonas is planning out his route for an upcoming race. He uses negative numbers to represent points before
the finish line and positive numbers to represent points after the finish line.
On Jonas's map, there is a bridge at -91 meters, and a restaurant is at 14 meters.
What does 0 meters represent?
Choose 1 answer:
B
The restaurant
The bridge
The finish line
Using logical reasoning, we can say that the 0 meter represents the (C) finish line.
What is logical reasoning?In addition to formal deduction, two more categories of logical thinking are frequently distinguished: induction and abduction. The following can be explained if one has a precondition or premise, a conclusion or logical consequence, and a rule or material conditional that indicates the conclusion given the precondition.Example: "Everything outside gets wet when it rains. Since the grass is outside, it gets wet when it rains." This kind of logic is frequently compared to mathematical logic and philosophical logic.So, we know that:
There are negative numbers before the final line.There are positive numbers after the finish line.So, it is obvious that 0 meters will represent the finish line itself.Therefore, using logical reasoning, we can say that the 0 meter represents the (C) finish line.
Know more about logical reasoning here:
https://brainly.com/question/28418750
#SPJ1
Correct question:
Jonas is planning out his route for an upcoming race. He uses negative numbers to represent points before
the finish line and positive numbers to represent points after the finish line.
On Jonas's map, there is a bridge at -91 meters, and a restaurant is at 14 meters.
What do 0 meters represent?
Choose 1 answer:
(A) The restaurant
(B) The bridge
(C) The finish line
Two neighbors bought plants from the same store to improved their yards. James spend $77 on 7 daylilies and 8 shrubs. Liz spent $140 on 14 daylilies and 14 shrubs. what is the cost of one Daylily and one shrub?
Step 1. First, let's define the variable we are going to use:
[tex]\begin{gathered} d\longrightarrow\text{ price of a daylily} \\ s\longrightarrow\text{price of a shrub} \end{gathered}[/tex]Step 2. Find the first equation from the information about James.
James spends $77 on 7 daylilies and 8 shrubs, this is described in the following equation:
[tex]7d+8s=77[/tex]Step 3. To find the second equation we use the information about Liz.
Liz spends $140 on 14 daylilies and 14 shrubs. The equation describing this is:
[tex]14d+14s=140[/tex]Since all of the numbers involved in this equation are multiples of 14, we can divide the whole equation by 14 to simplify it:
[tex]\begin{gathered} \frac{14d+14s=140}{14} \\ \\ d+s=10 \end{gathered}[/tex]Step 4. Define the system of equations.
From step 2 and step 3 we have our two equations:
[tex]\begin{gathered} 7d+8s=77 \\ d+s=10 \end{gathered}[/tex]Step 5. The method we will use to solve this system of equations is the substitution method. To use this method, we solve one of the equations for 1 variable. In our case, we solve the second equation for d:
[tex]\begin{gathered} d+s=10 \\ d=10-s \end{gathered}[/tex]And the second step of the substitution method is to substitute that value into the first equation:
[tex]\begin{gathered} 7d+8s=77 \\ \text{Substituting d=10-s} \\ 7(10-s)+8s=77 \end{gathered}[/tex]Step 6. Solve the previous equation for s.
[tex]7(10-s)+8s=77[/tex]using the distributive property to multiply 7 by 10 and 7 by -s:
[tex]70-7s+8s=77[/tex]Combining like terms:
[tex]70+s=77[/tex]Subtracting 70 to both sides of the equation:
[tex]\begin{gathered} s=77-70 \\ s=7 \end{gathered}[/tex]The cost of one shrub is $7.
Step 7. Now that we know the value of s, we can find the value of d using the equation we had previously solved for d in step 5:
[tex]d=10-s[/tex]Substituting s=7:
[tex]\begin{gathered} d=10-7 \\ d=3 \end{gathered}[/tex]The cost of one daylily is $3.
Answer:
The cost of one shrub is $7 and the cost of one daylily is $3.
In this question, assume that the car uses the same amount of petrol for each mile it travels.
A car uses 55 litres of petrol to travel 495 miles.
How much petrol would the car use on a trip of 160 miles?
Give your answer to the nearest litre.
The quantity of petrol used to travel 160 mile is 17.78 liters
The quantity of petrol used to travel 495 miles = 55 liters
Here we have to use the unitary method
The unitary method is defined as the method that uses to find the unit rate
The quantity of petrol used to travel 1 mile = The quantity of petrol used to travel 495 miles / 495
Substitute the values in the equation
The quantity of petrol used to travel 1 mile = 55 / 495
= 1 /9 liters
The quantity of petrol used to travel 160 mile = The quantity of petrol used to travel 1 mile × 160
Substitute the value in the equation
The quantity of petrol used to travel 160 mile = (1 / 9) × 160
= 17.78 liters
Hence, the quantity of petrol used to travel 160 mile is 17.78 liters
Learn more about unitary method here
brainly.com/question/22056199
#SPJ1
What is the value of Arc cosine (negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)?
StartFraction pi Over 6 EndFraction
StartFRaction pi Over 4 EndFraction
StartFraction 3 pi Over 4 EndFraction
StartFraction 5 pi Over 6 EndFraction
The value of arccos(-√3/2) is 5π/6.
In the given question,
We have to find the value of [tex]arccos(-\frac{\sqrt{3}}{2})[/tex].
The given term is [tex]arccos(-\frac{\sqrt{3}}{2})[/tex].
We using the quadrant rule.
The value is in negative so we check in which quadrant the value of cos negative.
As we now that in second quadrant only the value of sine and cosine is positive and all value are negative.
The second quadrant of 180 degree or we can also write 180 degree as π.
From the trigonometry table we know that at 30 degree or (π/6) the value of cos is √3/2.
So the value of cos at which -√3/2 is
-√3/2 = cos(π - π/6)
-√3/2 = cos(π×6/6 - π/6)
-√3/2 = cos(6π/6 - π/6)
-√3/2 = cos{(6π- π)/6}
-√3/2 = cos 5π/6
So we can write it as
arccos(-√3/2)=arccos(cos 5π/6)
Since there is a arccos and cos both so only left 5π/6.
arccos(-√3/2)=5π/6
Hence, the value of arccos(-√3/2) is 5π/6.
To learn more about trigonometry quadrant link is here
https://brainly.com/question/7196312
#SPJ1
Answer:
d
Step-by-step explanation:
Warm-up:
Determine the Cost of Goods Sold for one Holiday Basket:
1 basket $24.00 per dozen
2 lbs. Cheddar cheese $1.50 per pound
1 canned ham $60.00 per dozen
3 jars of jelly $1.00 each
6 oranges $2.00 per dozen
1 box crackers 2.00 per box
cellophane wrap $.50 each
Note: Each basket has only one of each item in it.
Cost of Goods Sold: $
Suggested selling price: $
The cost of Goods Sold will be $93.5
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
The Cost of Goods Sold for one Holiday Basket:
1 basket = $24.00 per dozen
2 lbs. Cheddar cheese = $1.50 per pound
1 canned ham = $60.00 per dozen
3 jars of jelly = $1.00 each
6 oranges = $2.00 per dozen
1 box crackers = 2.00 per box
Cellophane wrap = $.50 each
Now,
Since, Each basket has only one of each item in it.
So, The total cost = $24 + $1.50 x 2 + $60 + $1 x 3 + $1 + $2 + $0.50
= $93.5
Thus, The cost of Goods Sold will be $93.5
Learn more about the Addition visit:
https://brainly.com/question/4721701
#SPJ1
5. A shipping company is sending a fragile package with these dimensions: 6 in. x 7 in. * 2 in. If the boxthey use to send it is 9 in. x 9 in. x 3 In., how many cubic Inches of packing peanuts can they fit into thebox?
First, we need to calculate the volume of the package and the volume of the box
Package
[tex]V_P=6\times7\times2=84in^2[/tex]Box
[tex]V_B=9\times9\times3=243in^3[/tex]we need to subtract the volume of the package from the volume of the box
[tex]V=V_B-V_P=243-84=159in^3[/tex]159 in^3 of packing peanuts will fill into the box
UU UN INSUL OUUU Convert a fration: m=- 4444 21 x= -2 3 2 91 40 = IU m=-5 2 and 3 32°+x- Which two integers does V5 go between? 1 and 2 49 x=100 x=180 7 and 8 4 and
I'll get the slope of the arrow on the graph
P1 = (-1, 1)
P2 = (-4, 3)
slope = m = (3 - 1) / (-4 + 1)
m = 2/-3
slope = m = -2/3
Will mark Brainliest for right answer
Answer:
Toni had the highest score.
Step-by-step explanation:
Terri - 45/50 = 90%
Toni - 92%
Tina - 8/9 = 89%
Can someone please help me?
Part A) The definition of speed can be used to establish the equation of the line that depicts the relationship between distance and time, which is (y = 62x).
Part B) Option c
What is a speed, exactly?
Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path.
Given:
In 3 hours and 186 miles, Car X goes.
To find the equation of the line that represents the relationship between distance and time, perform the following steps:
Step 1: Assume that car X traveled a total distance of y miles and traveled that amount in x minutes.
Step 2: The speed is determined by the distance to time ratio.
speed = distance / time
Step 3: Add the distance and time values to the equation above.
Speed = y/x —— (1) (1)
Step 4 - Based on the provided information, the speed is determined by:
speed = 186/3 = 62
Step 5: Adding the speed value to the equation (1).
y/x = 62
y = 62x
(Y = 62x) is the equation of the line that depicts the relationship between space and time.
Refer to the following link for more details about speed
https://brainly.com/question/3004254
#SPJ1
describe a dataset where defining a confidence interval would be important for testing validity of data
The sample's data values ought to be unrelated to one another. The sample data need to be consistent. Data from the quantitative ordered pair sample should be gathered at random or in a way that is representative of the overall population. The sample's data values ought to be unrelated to one another.
A confidence interval is a much better tool to use if we wish to communicate the level of uncertainty surrounding our point estimate (CI). A confidence interval (CI) is a symmetrical range of values where the results of repeated, related experiments are likely to fall. The middle of this range corresponds to our point estimate.
Confidence intervals, which describe how closely study results match reality or how dependable they are based on statistical theory, are regularly mentioned in scientific publications.
Learn more about to confidence interval visit here:
https://brainly.com/question/24131141
#SPJ4
If a triangle has 2 sides measuring 10 and 64 then the 3rd side must be less than what value
Answer:
It must be less than 180º.
Step-by-step explanation:
A triangle always adds up to 180º which then means that since two angles have already been stated that means the total of those two angles is 74º which you subtract from 180º to get 106º which is the measure of the third angle.
Using the figure below, tell if the triangles are congruent, and if so by what theorem?
help me please is urgent .