The speed of the stream is 6 [tex]km/h[/tex]
Let the speed of the stream be x km/h.
Therefore, the speed of the boat upstream = (18 – x) km/h, and the speed of the boat
downstream = (18 + x) km/h.
The time is taken to go upstream = distance/speed
[tex]24/(18-x)[/tex] hours.
Similarly, the time is taken to go downstream =
[tex]24/(18+x)[/tex] hours.
According to the question,
[tex]24/(18-x) - 24/(18+x) = 1[/tex]
[tex]x^{2} +48x-324=0[/tex]
Using the quadratic formula, we get
[tex]x=\frac{-48+\sqrt{48^{2}+1296 } }{2}[/tex]
x = 6 or -54
Since x is the speed of the stream, it cannot be negative. So, we ignore the root x = – 54.
Hence the speed of the stream is 6 km/h.
Learn more about Boats and streams at
https://brainly.com/question/24166543?referrer=searchResults
Which statement cannot be assumed based on the diagram?
A) <GBE and <DBC are adjacent
B) <DBC is vertical to <FDE
C) <EDF and <EDC are adjacent
D) <ABG and <GBD are adjacent.
help please :)
The statement that cannot be assumed based on the diagram is ∠DBC is vertical to ∠FDE.
(A) ∠GBE and ∠DBC are adjacent angles. As we can see from the diagram, they have a common ray starting from the point B.(B) We cannot say that ∠DBC is vertical to ∠FDE from the diagram as we have no such direct relation between the angles.(C) ∠EDF and ∠EDC are adjacent angles. As we can see from the diagram, they have a common ray starting from the point D.(D) ∠ABG and ∠GBD are adjacent angles. As we can see from the diagram, they have a common ray starting from the point B.To learn more about angles, visit :
https://brainly.com/question/28451077
#SPJ1
There are 2 different maps of North Carolina. The scale on the first map is 1 cm to 2 km. The distance from Durham to Cary is 15 cm. The scale of the second map is 1 cm to 5 km. What is the distance from Durham to Cary on the second map
The distance from Durham to Cary on the second map is 75 km
The scale of the first map:
1 cm = 2 km
The scale of the second map:
1 cm = 5 km
Map scale: A distance on a map and its corresponding distance on the planet are related by a scale. The equivalent of a map scale can be expressed, typically using different units. or visually, using a bar scale.
Distance from Durham to Cary = 15 cm
Distance from Durham to Cary on the second map = Scale of the second map * Distance from Durham to Cary
= 5*15
= 75 km
Learn more about maps:
https://brainly.com/question/1670085
#SPJ1
QuestionQuestion 1Consider the function y=x - 5.What are the domain and range of this function?
According to the given function, which contains a square root, the domain must contain numbers that are greater than or equal to 5, otherwise, we would obtain the square root of a negative value, which is not real.
It means that the domain is
[tex]x\ge5[/tex]The range contains numbers greater than 0, this is because the minimum value of the domain is 5, when we evaluate the function at this value, the result is 0, which means that the range is:
[tex]x\ge0[/tex]The answer is the first option.
Help im litteraly failing
The solution to the given system of linear equations is x = 3, y = -3. That is, (3, -3)
The graph of the system of equations is shown below
Solving system of linear of linear equationsFrom the question, we are to determine the apparent solution to the given system of linear equations
The given system of equations is
y = -2x + 3
y = 1/3x - 4
Set the two equations equal
That is,
-2x + 3 = 1/3x - 4
Multiply through by 3
-6x + 9 = x - 12
Add 6x to both sides of the equation
-6x + 6x + 9 = x + 6x - 12
9 = 7x - 12
Add 12 to both sides of the equation
9 + 12 = 7x - 12 + 12
21 = 7x
x = 21/7
x = 3
Substitute the value of x into the first equation
y = -2x + 3
y = -2(3) + 3
y = - 6 + 3
y = - 3
The solution is (3, -3)
The graph is shown below
Learn more on Solving system of linear equations here:
#SPJ1
Find the surface area of the figure
A scientist needs 1.8 liters of a 22% alcohol solution. She has available a 33% and a
17% solution. How many liters of the 23% and how many liters of the 17%
solutions should she mix to make the 22% solution?
Step-by-step explanation:
the approach of the other answer is basically correct, but we need to use the correct numbers.
so, I assume that the 33% of the first solution is correct, and not the 23% mentioned later.
x = liters of the 33% solution.
y = liters of the 17% solution.
we know that
x + y = 1.8
and therefore
x = 1.8 - y
and then we want to enforce the desired result (ab% are simply 0.ab)
0.33x + 0.17y = 0.22×1.8
we use the identity from above in this equation :
0.33(1.8 - y) + 0.17y = 0.396
0.594 - 0.33y + 0.17y = 0.396
0.198 - 0.16y = 0
0.198 = 0.16y
y = 1.2375 liters
x = 1.8 - y = 1.8 - 1.2375 = 0.5625 liters
if the first solution is truly only 23%, then we only need to change the number :
0.23(1.8 - y) + 0.17y = 0.396
0.414 - 0.23y + 0.17y = 0.396
0.018 - 0.06y = 0
0.018 = 0.06y
y = 0.3 liters
x = 1.8 - y = 1.8 - 0.3 = 1.5 liters
There are 15 squares and 6 triangles. What is the simplest ratio of triangles to total shapes?
Answer: 2:7
Step-by-step explanation:
[tex]\displaystyle\\\frac{6}{15+6} =\\\\\frac{6}{21} =\\\\\frac{2(3)}{7(3)} =\\\\\frac{2}{7} =\\\\2:7[/tex]
The ratio of triangles to total shapes in simplest form is 2 : 7.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, There are 15 squares and 6 triangles.
Therefore, The total number of shapes is (15 + 6) = 21.
So, The ratio of triangles to total shapes is,
triangle/total shapes = 5/15 + 6.
triangles/total shapes = 6/21.
triangles : total shapes = 6 : 21 = 2 : 7
learn more about proportion here :
https://brainly.com/question/7096655
#SPJ2
how many whole numbers are there between 121and176
TO KNOW HOW MANY WHOLE NUMBERS THERE ARE BETWEEN 121 AMD 176 WE CAN SIMPLY GET THEIR DIFFERENCE.
THE DIFFERENCE IS THE NUMBER OF WHOLE NUMBERS INBETWEEN 121 AND 176.
[tex] = 176 - 121 \\ = 55[/tex]
THERE ARE 55 WHOLE NUMBERS BETWEEN 121 AND 176.
Answer:
54
Step-by-step explanation:
Whole numbers are 0,1,2,3,... Following that pattern forever.
Take a simpler example. How many whole numbers between 2 and 5? It would be just 3 numbers; 3 and 4.
We could subtract 5-2 to get 3 and then subtract 1 more to get the answer of 3
What if I wanted to know the number of whole numbers between 3 and 7?
The numbers would be 4,5,6.
7-3 = 4 and then subtract 1 more to get the answer that there are 3 whole numbers between 3 and 7.
176 - 121 = 55 take one more away to get 54
is 120% reduction or enlargement
120% is considered an enlargement since the scale factor is greater than one.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
It is considered a reduction of the scale factor is less than one, and an enlargement if the scale factor is greater than one.
120% = 1.2 > 1, hence an enlargement.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
HELP ASAP, ITS DUE TODAY AT MIDNIGHT!!!!! 92 POINTS!!!!!!!!!!!
The relationship is that number sense can be used to solve area models or partial products.
What is number sense?Number sense refers to a set of important numerical skills. It includes the capacity to comprehend numbers and concepts such as more and less. Some people have a better sense of numbers than others.
Number sense is a set of abilities that enable humans to work with numbers. These abilities are essential for performing math as well as many other jobs.
In this case, partial products model of multiplication. This is a model which breaks numbers down into their factors. or place values in order to make multiplication easier. This depicts number sense.
Learn more about number sense on:
https://brainly.com/question/3503411
#SPJ1
Simplify (2√5)²
Please help fast!
Answer:
20
Step-by-step explanation:
Simplify the following:
(2 sqrt(5))^2
Multiply each exponent in 2 sqrt(5) by 2:
2^2×5^(2/2)
2/2 = 1:
2^2×5
2^2 = 4:
4×5
4×5 = 20:
Answer: 20
To enroll in lessons to learn about pottery wheel throwing, you must pay an rollment of $20 for each lesson. The pottery studio also charges you $2.99 pe pound for the amount of clay used.To enroll in lessons to learn about pottery wheel throwing, you must pay an enrollment of $20 for each lesson. The pottery studio also charges you $2.99 per pound for the amount of clay used. Write an expression for the total cost of a person using c pounds of clay during a lesson. Use the expression to calculate the cost of a lesson where Sam uses 3.5 pounds of clay.
Answer:
cost per day = 2.99(c)+20
sam's lessons cost $30.47 per day
Step-by-step explanation:
2.99 (price of clay used per pound) * c (pounds of clay used) + 20 (cost of lesson)
2.99(c)+20
since sam uses 3.5 pounds of clay per lesson that's 2.99(3.5)+20, which is equal to 30.47
Find the ordered pair (x,y) 6x-y=6
Answer:
Step-by-step explanation:
(1,0),(2,6). Explanation: express the equation, giving y in terms of x. ⇒y=6x−6. now choose any value for x , substitute into the equation
What are the similarities and differences between these problems
Using an exponential function, it is found that:
The pool has 1106 gallons after 50 minutes.The poll will have less than 1000 gallons after 66.6 minutes.What is an exponential function?An exponential function is modeled according to the following rule:
[tex]y = ab^{\frac{x}{n}}[/tex]
In which:
a is the initial value.b is the rate of change.n is the period of the change of change.Considering that the pool has 1500 gallons, and drains 3% every 5 minutes, the parameters of the function are given as follows:
a = 1500, b = 1 - 0.03 = 0.97, n = 5.
Hence the amount of water in the poll after x minutes is given by:
[tex]y = 1500(0.97)^{\frac{x}{5}}[/tex]
After 50 minutes, the amount of water in the pool is:
[tex]y = 1500(0.97)^{\frac{50}{5}} = 1500(0.97)^{10} = 1106[/tex]
1106 gallons.
The poll will have less than 1000 gallons when:
y = 1000 (we can use it because the function decreases continuously).
Hence:
[tex]1500(0.97)^{\frac{x}{5}} = 1000[/tex]
[tex](0.97)^{\frac{x}{5}} = \frac{1000}{1500}[/tex]
[tex](0.97)^{\frac{x}{5}} = \frac{2}{3}[/tex]
[tex]\log{(0.97)^{\frac{x}{5}}} = \log{\left(\frac{2}{3}\right)}[/tex]
[tex]\frac{x}{5}\log{0.97} = \log{\left(\frac{2}{3}\right)}[/tex]
[tex]x = 5\frac{\log{\left(\frac{2}{3}\right)}}{\log{(0.97)}}[/tex]
x = 66.6 minutes.
What is the missing information?The capacity of the pool is missing, and it is of 1500 gallons.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
a=96.5 rounded to 1 DP
b= 6.48 rounded to 2 DP
Find the maximum of a - b
how do you find B and M in y = 9 - 5x ?
For the linear function y = 9 - 5x, it is found that:
The coefficient M is the slope of M = -5.The coefficient B is the intercept of B = 9.How to identify coefficients m and b in a linear function?A linear function, in slope-intercept format, is modeled according to the following rule below:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).In the context of this problem, the linear function is modeled as follows:
y = 9 - 5x.
In standard format, with the slope in front, we have that:
y = -5x + 9.
Meaning that the coefficients are given as follows:
m = -5, which is the slope of the function.b = 9, which is the intercept of the function.More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Rewrite 7x + 49 using a common factor.
Here are some options it gave me.
(A) . 7(x + 7)
(B). 7(x + 49)
(C). 7x(x + 7)
(D). 7x(x + 49)
7x + 49 rewritten using common factor is 7(x + 7)
How to find common factors?A common factor is a whole number which is a factor of two or more numbers.
In other words, common factors of two or more numbers are a number which divides each of the given numbers exactly.
For example the common factor of 24 and 36 are 1, 2, 3, 4, 6 and 12.
Therefore,
rewriting 7x + 49 using common factors is as follows:
7x + 49 = 7(x + 7 )
learn more on common factor here: https://brainly.com/question/13275492
#SPJ1
PLEASE HELP! this is probably easy, THANK YOU! please let me know if you can’t see properly it is a little hard to see thank you
Use the given information to find mZKJR.
m/RJI=12x-3, m/KJR = 6x - 5,
and m/KJI = 172°. Find m/KJR.
The measure of ∡KJR is 69°.
What is the sum of two supplementary angles?
Two angles are referred to as supplementary angles if their combined value is 180°. A straight angle is created when supplementary angles are combined (180°).
In other words, ∡A and ∡B are supplementary if ∡A plus ∡B equals 180°. Angles A and B are described as "supplements" of one another in this context.
In math, A° + B° = 180°.
Given, m∡RJI = 12x - 3, m∡KJR = 6x - 5, m∡KJI = 172°
As seen from diagram, m∡RJI + m∡KJR = m∡KJI
⇒ (12x-3)+(6x-50) = 172° ⇒ 18x - 53 = 172° ⇒ x = ([172 + 53]/18)° = 12.5°
Therefore, the value of x = 12.5°
Thus, m∡KJR = 6x - 5 = (6*12.5) - 5 = 69°
To learn more about this, tap on the link below:
https://brainly.com/question/22262639
#SPJ9
HELP ASAP NEEDS TO BE DONE BEFORE TONIGHT
The equation of the straight line is 3y + 2x = 15
The generic form of a straight line, Ax + By = C, is also the typical form for two-variable linear equations.
Standard form is used, for instance, in the linear equation 4x+7y= 1. This method makes it easy to find the two intercepts (x and y) of an equation.
Y = mx + c is the cartesian equation for a straight line, where m denotes the gradient or slope of the line and c denotes the location of its y-axis intersection.
Two geometrical objects are perpendicular if they cross at a right angle.
We are aware that the product of the slopes of two lines when they are perpendicular equals -1.
The given straight line is of the form y =3/2 x - 1 .
Slope of the straight line = 3/2
Slope of the perpendicular(90°) line (m) = -2/3
The equation of a line is formulated by :
y -y₁ = m (x - x₁ )
The straight line passes through (-3 , 7)
∴y - 7 = -(2/3) (x + 3 )
or, -2x - 6 = 3y - 21
or, 3y + 2x = 15
Therefore the equation of the straight line is 3y + 2x = 15 .
To learn more about straight lines visit:
brainly.com/question/21627259
#SPJ1
write the fraction for the following
Answer:
A- 2/4
simplified-1/2
B- 3/5
C- 4/9
D-3/3 which=1
so basically D is 1
hope this helped
please mark as brainliest and have a good day!
Step-by-step explanation:
Design a pseudocode and the corresponding flow chart for calculating; the area of a circle,the perimeter of a rectangle, the perimeter of a square
See below for the pseudocode and the flowchart is added as an attachment
What is a pseudocode and a flowchart?Flowcharts and pseudocodes are used as prototypes of actual programs.
Flowcharts are in graphical form, while pseudocodes are in the form of texts.The flowchart and pseudocode do not conform to programming syntaxHow to design the pseudocode and the flowchart?Area of circle
The pseudocode is as follows:
StartInput radius, rCalculate Area, A = pi * r^2Display AreaStopPerimeter of rectangle
The pseudocode is as follows:
StartInput dimensions, l and bCalculate Perimeter, P = 2 * (l + b)Display PerimeterStopPerimeter of square
The pseudocode is as follows:
StartInput dimensions, lCalculate Perimeter, P = 4 * lDisplay PerimeterStopSee attachment for the flowcharts
Read more about flowchart and pseudocode at
https://brainly.com/question/14311123
#SPJ1
what property does 5(a) = a(5) belong to?
Associative Property
Commutative Property
Inverse Property
Identity Property
Answer:
Commutative Property for Multiplication
Answer:
Commutative Property for Multiplication
Step-by-step explanation:
Can someone please help me with this problem?
Answer:
Symmetric property of congruence
I need help with my work
Answer:
1. acute angle (less than <90)
2. right angle (approximately <90)
3. obtuse angle (more than <90)
4. acute angle (less than <90)
The festival of Midnight Sun Theatre has 7875 seats arranged in 75 equal rows. How many seats are in each row?
Answer:
105 cause you will divide to get the total
What Property’s are used in each step?
Step 1 5x+9+5x+12=(5x+9)+(5x+12)
Step 2 = 5x+(9 +5x)+12
Step 3 = 5x+(5x+9)+12
Step 4 =(5x+5x)+(9+12)
Step 5 = (5 + 5)x+ (9 + 12)
Step 6 = 10x + 21
The property used is Distributive property
What is Distributive property ?
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
Given, equation
5x+9+5x+12
Step 1 =(5x+9)+(5x+12)
Step 2 = 5x+(9 +5x)+12
Step 3 = 5x+(5x+9)+12
Step 4 =(5x+5x)+(9+12)
Step 5 = (5 + 5)x+ (9 + 12)
Step 6 = 10x + 21
The property used in this equation is called Distributive property
Hence, the property use in here Distributive property
To learn more about Distributive property click on the link
https://brainly.com/question/2807928
#SPJ9
Which one doesnt belong
Answer:
267 times 6
Step-by-step explanation:
Determine whether the graph is linear or non linear and explain
The given graph represents a non-linear function.
What are linear and non-linear functions?When a function is plotted on a graph, a linear function produces a straight line, whereas a nonlinear function does not (it is curved in some way). While the slope of a nonlinear function is continuously changing, the slope of a linear function is constant.Take two points in the graph and calculate the slope:
Slope of (-2,1) and (0,2) = (2-1)/(0-(-2) = 1/2
Slope of (2,1) and (0,2) = (2-1)/(0-2) = 1/(-2)
As the slope of the given graph is variable, it is a non-linear function.
To know more about linear and non-linear functions visit:
https://brainly.com/question/21107621
#SPJ9
Please help can’t figure out running out of time
The Inverse Function Line Test
A given graph represents a function only if for every value of x there is only one corresponding value of y.
This can be checked by using a vertical line and moving it through the x-axis. If that line intersects the graph more than once, then the graph does not correspond to a function.
The image shows a graph and if we move our imaginary vertical line from x=-2 to x=7 that line would intersect the graph only once. This means that the graph corresponds to a function in the domain [-2,7].
For the inverse function to exist, the horizontal line test must be passed.
Imagine a horizontal line moving through the y-axis. It would intersect the graph only once from y=0 to y=6.
We can conclude this graph corresponds to a function and it has an inverse function because it passed the horizontal line test.
Answer: D.