Answer:
\(x=\frac{12}{7} \\y=\frac{12}{5} \\z=-12\)
Step-by-step explanation:
Let's re-write the equations in order to get the variables as separated in independent terms as possible \:
First equation:
\(\frac{xy}{x+y} =1\\xy=x+y\\1=\frac{x+y}{xy} \\1=\frac{1}{y} +\frac{1}{x}\)
Second equation:
\(\frac{xz}{x+z} =2\\xz=2\,(x+z)\\\frac{1}{2} =\frac{x+z}{xz} \\\frac{1}{2} =\frac{1}{z} +\frac{1}{x}\)
Third equation:
\(\frac{yz}{y+z} =3\\yz=3\,(y+z)\\\frac{1}{3} =\frac{y+z}{yz} \\\frac{1}{3}=\frac{1}{z} +\frac{1}{y}\)
Now let's subtract term by term the reduced equation 3 from the reduced equation 1 in order to eliminate the term that contains "y":
\(1=\frac{1}{y} +\frac{1}{x} \\-\\\frac{1}{3} =\frac{1}{z} +\frac{1}{y}\\\frac{2}{3} =\frac{1}{x} -\frac{1}{z}\)
Combine this last expression term by term with the reduced equation 2, and solve for "x" :
\(\frac{2}{3} =\frac{1}{x} -\frac{1}{z} \\+\\\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\ \\\frac{7}{6} =\frac{2}{x}\\ \\x=\frac{12}{7}\)
Now we use this value for "x" back in equation 1 to solve for "y":
\(1=\frac{1}{y} +\frac{1}{x} \\1=\frac{1}{y} +\frac{7}{12}\\1-\frac{7}{12}=\frac{1}{y} \\ \\\frac{1}{y} =\frac{5}{12} \\y=\frac{12}{5}\)
And finally we solve for the third unknown "z":
\(\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\\\\frac{1}{2} =\frac{1}{z} +\frac{7}{12} \\\\\frac{1}{z} =\frac{1}{2}-\frac{7}{12} \\\\\frac{1}{z} =-\frac{1}{12}\\z=-12\)
5.99 is greater less or equal 5.990
Answer:
They are different because they have different place values and the decmical is in a different place so 5.99 is less than 5.990
what is the answer to the following question choices: 1)9 2)0 3)2/3 4)3
I hope this helps you...
What is the equation of a line that is parallel to y=2/3x+4 and passes through the point (3,7)
Answer:
y=2/3x+5
Step-by-step explanation:
Parallel lines share the same slope so we already know the slope: 2/3.
Now we need to find the y-intercept for the equation. To do that, replace 4 with b. We have y=2/3x+b.
To find out what b is, we need to plug in the x and y values we are given into the current equation. We get 7=2/3(3)+b.
7=2+b
5=b
Now we can put all the information we have together.
y=2/3x+5
Engineering Mathematics
Form the differential equation of the family of curves, where A and B are arbitrary constants: 07. y = A e-5x + Beбx 08. y = A e7* + Be-8x
The differential equations for the given families of curves are 07. y' = -5\(Ae^(-5x)\)- \(Bxe^(-5x)\), and 08. y' = 7\(Ae^(7x)\) - 8\(Be^(-8x)\).
To form the differential equations for the given families of curves, we need to differentiate the given expressions with respect to x.
For the first family of curves, y = \(Ae^(-5x)\) + \(Be^(bx)\), differentiating both sides with respect to x gives:
y' = -5\(Ae^(-5x)\) - \(Bxe^(-5x)\)
Therefore, the differential equation for the first family of curves is y' = -5\(Ae^(-5x)\) - \(Bxe^(-5x)\).
For the second family of curves, y =\(Ae^(7x)\)+ \(Be^(-8x)\), differentiating both sides with respect to x gives:
y' = 7\(Ae^(7x)\) - 8\(Be^(-8x)\)
Therefore, the differential equation for the second family of curves is y' = 7\(Ae^(7x)\)- 8\(Be^(-8x)\).
These differential equations describe the relationship between the rate of change of y (y') and the variables x, A, and B for the respective families of curves.
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Elian and Alberto won tickets at a arcade. When they put their tickets together they had exactly 100. Alberto won 10 tickets less then Elian. Let A be the number of tickets Alberto won and e be the number of tickets Elian won.
Answer: See explanation
Step-by-step explanation:
Number of tickets Elian won = e
Number of tickets Alberto won = A = e - 10
Therefore, Elian + Alberto ticket = 100
e + (e - 10) = 100
2e - 10 = 100
2e = 100 + 10
2e = 110.
e = 110/2
e = 55
Elina has 55 tickets
Alberto has 55-10 = 45 tickets
Please help.
Which type of function best models the data in the table?
Hours After 6:00 a.m., x 0 2 4 6 8 10 12 14
Users Logged In, y 2,224 1,852 1,481 1,244 1,539 1,816 2,015 2,278
Select the correct answer.
a. linear function with negative slope
b. quadratic function with a negative value of a
c. quadratic function with a positive value of a
d. square root function
Answer:
c
Step-by-step explanation:
As you can see as x increases, y decreases until x = 8, then it increases. So this means that we have a minimum point for x = 8. So this is a quadratic function with a positive value of a. If a was negative then the function would have a maximum point and it's behaviour would be the opposite of this case (y would increase until x = 8 and then it decreases)
determine whether each of the following sets of quantum numbers for the hydrogen atom are valid. drag the appropriate items to their respective bins.
ml = 0 is valid so the sets of quantum numbers are validated or not validated as mentioned above.
Here are the given sets of quantum numbers for the hydrogen atom which need to be validated.
Set 1 (n=3, l=3, ml=0, ms=+1/2) - Valid or Not valid
Set 2 (n=2, l=1, ml=1, ms=-1/2) - Valid or Not valid
Set 3 (n=4, l=1, ml=0, ms=-1/2) - Valid or Not valid
The first step is to understand the set of quantum numbers. Each electron in an atom is assigned a set of four quantum numbers.
The four quantum numbers are: n, l, ml, and ms. The principal quantum number n, the angular momentum quantum number l, the magnetic quantum number ml, and the spin quantum number ms are the four quantum numbers that define the electron's state.
Set 1 (n=3, l=3, ml=0, ms=+1/2)
It is not valid because ml can be from -l to +l, and when l is 3, ml can be -3,-2,-1,0,1,2,3. So, the value of ml should be from -3 to +3.
Set 2 (n=2, l=1, ml=1, ms=-1/2)
It is valid because l = 1, so ml can be -1,0,1. Therefore, ml = 1 is valid.
Set 3 (n=4, l=1, ml=0, ms=-1/2)
It is valid because l = 1, so ml can be -1,0,1. Therefore, ml = 0 is valid.
Thus, the sets of quantum numbers are validated or not validated as mentioned above.
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What is the radius of a circle with an area of 78. 5 square inches? Use 3. 14 for pi. Enter your answer in the box.
Answer:
The radius is 5
Step-by-step explanation:
\(r^{2}\) = \(\frac{78.5}{3.14}\)
\(r^{2}\) = 25
r = \(\sqrt{25}\)
r = 5
hence the answer is 5
Can someone help? Will give brainly if correct!
Answer:
7.03, 6.75, 6.72, 6.08, 6.4
Step-by-step explanation:
What is the measure of the missing exterior angle?
Answer:
the missing angle is 148°
Step-by-step explanation:
the sum of all exterior angles of a triangle are 360°
so, 360-138-74 = 148°
is -14.76 rational or irrational
Answer:
rational
Step-by-step explanation:
cause it can be shown as a divition of real numbers
Is this a discrete or continuous function? Explain.
A graph with points (-5, -2), (1, 5), and (-5, 5) represents a discrete function.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is a discrete function?A discrete function can be defined as a type of function in which the ordered pair of values on the x-axis and y-axis are separate from each other and unconnected.
In conclusion, the function which this graph represents is a discrete function because both the domain (-5, 1) and range (-2, 5) have discrete set of values, rather than intervals.
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PLEASE HELP!! Solve for y.
Answer:
hypotenuse²=base²+height²
\( \sqrt{85 } {}^{2} = 6 {}^{2} + x {}^{2} \\ \)
85=36+x²85-36=x²49=x²49½=xx=7Katie is selling lemonade for $1.50 per cup. She decides to put them on sale for $0.90. What percent discount did she give on her lemonade? *
Answer:
40%
Step-by-step explanation:
1.50 - 0.90 = 0.60
0.60 cents are saved.
\(\frac{0.60}{1.50} = 0.4\)
0.4 = 40%
hope this helps :)
17 The top of a student's desk is in the shape
shown below; all distances are given in
inches. What is the area of this desktop in
square inches?
A. 170
B. 1500
C. 1700
D. 1850
E. 2000
the area of the student's desk is 1140 square inches. None of the options provided in the answer choices match the calculated area, so none of the given options are correct.
To find the area of the student's desk, we need to calculate the area of each individual shape and then add them together.
From the diagram, we can see that the desk is composed of two rectangles and a triangle.
Rectangle 1: The length is 20 inches and the width is 12 inches.
Area of Rectangle 1 = Length × Width = 20 in × 12 in = 240 square inches.
Rectangle 2: The length is 30 inches and the width is 10 inches.
Area of Rectangle 2 = Length × Width = 30 in × 10 in = 300 square inches.
Triangle: The base is 30 inches and the height is 20 inches.
Area of Triangle = (Base × Height) / 2 = (30 in × 20 in) / 2 = 600 square inches.
Now, we add the areas of the individual shapes together to find the total area of the desk:
Total Area = Area of Rectangle 1 + Area of Rectangle 2 + Area of Triangle
Total Area = 240 square inches + 300 square inches + 600 square inches
Total Area = 1140 square inches.
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you have a 10 mile one way distance to commute to work. the cost of your travel time is $60/hour. weather is not a factor. which mode should you use to commute?
Driving a personal car would be the most cost-effective mode of transportation for this commute, with a total daily cost of approximately $4.60 ($3.60 for gas + $1 for travel time).
Based on the given information, the most cost-effective mode of transportation for this commute would be to drive a personal car. Taking public transportation or carpooling may be more environmentally friendly options, but they may not save as much money as driving alone.
Assuming an average speed of 60 miles per hour on the highway, the commute would take approximately 20 minutes each way, or 40 minutes round-trip. This means the total cost of travel time for each workday would be $40 ($60/hour x 2/3 hour).
Using a cost calculator such as GasBuddy, we can estimate that the cost of driving 20 miles per day (round-trip) would be around $3.60 per day, assuming an average fuel efficiency of 25 miles per gallon and a gasoline price of $2.50 per gallon.
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For w(x)=4x-4 find w(-7) show your work
Answer:
-32
Step-by-step explanation:
To find w(-7) we have to substitute x with -7
w(x)=4x-4
w(x = -7) = 4(-7) -4
w(-7) = -28-4
w(-7) = -32
Find a particular solution Yp of the following equation using the Method of Undetermined Coefficients. Primes denote the derivatives with respect to x. y'' +17y=3 e 8x A particular solution is yp(x) =
The Method of Undetermined Coefficients is a technique used to find a particular solution to a homogeneous linear differential equation.
yp(x) = 3e 8x + c1e 4x + c2e 11x
We are attempting to find a particular solution, yp(x), to the given equation using the Method of Undetermined Coefficients. This method is used when we have a homogeneous linear differential equation with constant coefficients. The first step is to identify the complementary function, which is found by solving the homogeneous part of the equation (in this case, y'' + 17y = 0). The particular solution is then found by making an educated guess for the form of the solution and adjusting the constants of the solution until the equation is satisfied. In this example, we guessed that the particular solution is a linear combination of three exponentials: 3e 8x + c1e 4x + c2e 11x. We then adjusted the constants c1 and c2 until the equation was satisfied.
y'' + 17y = 3e 8x
y'' + 17y - 3e 8x = 0
Homogeneous equation: y'' + 17y = 0
Characteristic equation: r2 + 17 = 0
r = ± 4i
Complementary function: yc(x) = c1e 4x + c2e -4x
Particular solution: yp(x) = 3e 8x + c1e 4x + c2e 11x
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What color is a apple
Answer:
red or green
Step-by-step explanation:
Answer:
The color of an apple is Red or Green or Yellow
Step-by-step explanation:
please help 100 points if correct ! :)
please actually answer
Instructions
Part 1: Celebration!
Think of an activity that you enjoy or are interested in. Some examples are reading, swimming, or leveling up your gaming character. Use your activity to work through the following problems:
Create a scenario that leads to an inequality of the form ax + b > c. You can use any of the inequality symbols (>, ≥, <, ≤) in your inequality. For this step, just write the word problem.
Write the inequality and show all work to solve the inequality.
Graph the solution to your inequality on a number line.
Explain what your solution means in the context of the problem.
Well for the activity we can do a game.
In a game you start with 50 coins and everytime you kill a monster "x" you get 2 more coins.You need 100 coins to level up.
We can make the following inequality,
2x + 50 ≥ 100
So to find x we single it out,
2x + 50 ≥ 100
-50 to both sides
2x ≥ 50
Divide 2 by both sides
x ≥ 25
For the number line look at the image below ↓
The solution in the number line is the number of monsters killed in order to level up.
Hope this helps :)
a grocery store sells a bag of 5 lemons for $2.00 what is the unite cost of each lemon in the bag.
Answer:
.40 per lemon
Step-by-step explanation:
Take the total cost of the lemons and divide by the number of lemons
2.00 /5 = .40 per lemon
Order the numbers from least to greatest.
1
---10-
1
1
8
4
1
-4
Answer:
-4<1<4<8<10
Step-by-step explanation:
In Column III, describe (left, right, no change) how the added substance in Column II affects the equilibrium system in Column I. Column III Your explanation Column I Column II [Ni(H,0))*(aq) + 6NH, (aq) + HCl addition [Ni (NH).1** (aq) + 6H2O(1) [Cu(H,0) 1(aq) + 4Br(aq) + Add more [CuBr.]" (aq) + 4H,O(1) +65kJ heat (or increase temperature) SO (8) + 120(8) - SO, + Removal of heat heat (or decrease temperature) Ag,CO,(s) + 2Ag (aq) + CO, HCl addition (aq) CaCO, (s) - Ca' (aq) + CO, Rainwater (aq) addition CH,COOH (aq) → CH,COO (aq) + H(aq) Addition of CH,COONa
For the equilibrium system of Ni(H2O)6(aq) + 6NH3(aq) + HCl, adding more HCl will shift the equilibrium to the right, resulting in more Ni(NH3)2(aq) and H2O(l) being formed.
For the equilibrium system of Cu(H2O)4(aq) + 4Br-(aq) + heat, adding more heat (or increasing temperature) will shift the equilibrium to the left, resulting in less CuBr2(aq) and H2O(l) being formed.
For the equilibrium system of SO3(g) + 120(g) ↔ SO2(g) + O2(g), removing heat (or decreasing temperature) will shift the equilibrium to the right, resulting in more SO2(g) and O2(g) being formed.
For the equilibrium system of Ag2CO3(s) + 2Ag+(aq) + CO32-(aq), adding HCl(aq) will shift the equilibrium to the left, resulting in less Ag2CO3(s) and more Ag+(aq) and CO32-(aq) being formed.
For the equilibrium system of CaCO3(s) ↔ Ca2+(aq) + CO32-(aq), adding rainwater (which is typically slightly acidic) will shift the equilibrium to the left, resulting in less Ca2+(aq) and CO32-(aq) and more CaCO3(s) being formed.
For the equilibrium system of CH3COOH(aq) ↔ CH3COO-(aq) + H+(aq), adding CH3COONa(aq) will shift the equilibrium to the left, resulting in less CH3COO-(aq) and more CH3COOH(aq) being formed
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Determine an expression for the perimeter of the following shape. I need a step by step solution pleaseeeee:)
Answer:
The perimeter of the figure is: 8x + 34.
Step-by-step explanation:
The perimeter of a shape is the sum of the length of all its sides. In this case there is one side missing, we need to find its length. To do that we will have to use Pythagora's theorem, because we will create a right triangle as shown in the attached picture. Where a, b and c are the sides of the right triangle. We can determine the lengths of a and c. If we pay close attention to the figure we will realize that a is:
\(a = 2x + 5 - 2x = 5\)
While c is:
\(c = 2(x + 7) - (x + 5) - (x - 3)\\c = 2x + 14 -x - 5 -x + 3\\c = 2x - 2x + 12\\c = 12\)
We can now apply Pythagora's theorem:
\(b^2 = a^2 + c^2\\b^2 = 5^2 + 12^2\\b^2 = 25 + 144\\b = 13\)
With this we can sum all the sides and calculate the perimeter of the shape.
\(2x + 5 + x - 3 + 2x + x + 5 + 13 + 2(x + 7)\\2x + x + 2x + x + 2x + 5 - 3 + 5 + 13 + 14\\8x + 34\)
the stack can be compared to a line of people at a bank, where the first person in line is the first person served. group of answer choices true false
It is false to say that the stack may be compared to a bank line, where the first person in line gets served.
A linear data structure resembles a stack and a queue in that it follows a specific sequence for the actions required to store data. First In First Out is the sequence (FIFO). A line of individuals waiting to get something in a sequential order that begins at the front of the line is what one may see as a queue. It is an ordered list where deletions are made from the front and insertions are made from the rear end, which is known as the list's end.
Any line of customers waiting to use a resource where the person in line who arrived first is serviced first is an excellent illustration of a queue. Stacks and queues differ from one another in terms of removal. In a stack, the most recent item added is removed; in a queue, the most recent item added is removed.
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a 15-foot statue casts a 20-foot shadow. how tall is a person who casts a 4-foot-long shadow? question 19 options: a) 5 feet b) 0.33 feet c) 3.75 feet d) 3 feet
Answer:
d
Step-by-step explanation:
the ratio of height : shadow of statue is 15 : 20 = 3 : 4
the ratio of height : shadow of person will also be 3 : 4
jet height of person be h , then
\(\frac{h}{4}\) = \(\frac{3}{4}\) ( cross- multiply )
4h = 12 ( divide both sides by 4 )
h = 3
then the person is 3 feet tall
Answer:
d) 3 feet
Step-by-step explanation:
Events D and E are independent, with P(D)- 0.6 and P(D and E) - 0.18. Which of the following is true? A. P(E)- 0.12 B. P(E) = 0.4 C. P(D or E)-0.28 D. P(D or E) 0.72 E. P(D or E)-0.9
The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.
To determine the correct answer, let's analyze the given information.
We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.
Given:
P(D) = 0.6
P(D and E) = 0.18
Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:
P(D and E) = P(D) * P(E)
Substituting the given values:
0.18 = 0.6 * P(E)
To find the value of P(E), we can rearrange the equation:
P(E) = 0.18 / 0.6
P(E) = 0.3
Therefore, the correct answer is A. P(E) = 0.3.
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ASAP answer please it mathematics
Answer: D
Step-by-step explanation:
First, we see that each flower basket is the variable x. This is because that is what increases per situation. The constant fee no matter the amount of flower baskets for store A is $15, so for store A our equation is
Total spent=19.25x+15
And similarly, for store B it is
Total spent=17.50x+30
Now, to compare them we want to keep store A LESS THAN (<) store B ,
so we get that 19.25x+15<17.50+30, which is D
What is the absolute value of 23
Answer:
23
Step-by-step explanation:
Answer: 23
Step-by-step explanation:
When your finding the absolute value your just seeing how far away the number is from 0 on a number line...so if the number is negative it turns into a positive.
The speedometer on Leona's car
ws the speed in both miles per
and kilometers per hour. Using
the mile per hour rate that is
valent to 40 kilometers per hour.
Answer: 24.86miles/hr
Step-by-step explanation: Divide the speed by 1.609 to convert