There are three unknown variables in the given problem, which are X, Y1, and Y2. There are also three equations, which are X=a+bY1, X=c−dY2, and Y1=Y2.
Each equation relates to one unknown variable, and there is one additional equation that equates Y1 and Y2.
Having as many equations as unknown variables is important to determine a unique solution. In this case, since we have three equations and three unknown variables, a unique solution exists.
The first equation, X=a+bY1, relates X to Y1. It states that X is equal to the sum of a and b times Y1. This equation represents the relationship between X and Y1.
The second equation, X=c−dY2, relates X to Y2. It states that X is equal to the difference between c and d times Y2. This equation represents the relationship between X and Y2.
The third equation, Y1=Y2, equates Y1 and Y2, meaning they are equal to each other. This equation ensures that Y1 and Y2 have the same value.
By simultaneously solving these three equations, we can find values for X, Y1, and Y2 that satisfy all the equations and maintain the equality between Y1 and Y2. The solution will provide a unique combination of values for the variables that satisfy the given relationships.
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Box of cereal contains 23.4 ounces. Cost $5.49. What’s the cost per ounce?
Answer:
it 4.262295082
Step-by-step explanation:
you have to divid the ounces by the cost
What is the term for the changes that resulted from Europeans settling in the new world?
Answer:
The Columbian Exchange. Hopefully this is right :)
Step-by-step explanation:
Consider the following statement: If 4x = 8, then x = 2. What is the inverse of the statement? If 4x ≠ 8, then x ≠ 2. If x = 2, then 4x = 8. If 4x = 8, then x = 2. If x ≠ 2, then 4x ≠ 8.
Answer:
If x = 2, then 4x = 8
Step-by-step explanation:
In mathematics, an inverse function or statement can be described as a function or statement which reverses another function or statement.
In the question, we are given:
If 4x = 8, then x = 2
That is, x = 2 is obtained by solving fo x from 4x = 8 as follows:
4x = 8
x = 8 / 4
x = 2
From the options given, on the statement "if x = 2, then 4x = 8" reverses the statement "if 4x = 8, then x = 2". This is because x = 2 now comes first before 4x = 8 as against what obtained initially where 4x = 8 comes first before x = 2.
Therefore, the correct option is "If x = 2, then 4x = 8".
Answer:
So if x would equil 2, then (4x) = 8
Step-by-step explanation:
Because
Catherine saved some money and plans to add the same amount each week to her savings account. The table represents the number of weeks that she will save, x, and the total amount of money that she will have in her account, y.
Weeks, x
Dollars in account, y
4
74
6
86
9
104
11
116
Which linear equation represents Catherine’s situation?
y = one-sixth x + 70
y = 6 x + 50
y = StartFraction 1 Over 9 EndFraction x + 104
y = 11 x + 116
Answer:
b y=6x+50
Step-by-step explanation:
i got it right hope this helps
Answer:
B-y = 6 x + 50
Step-by-step explanation:
Nicole tutors English. For each hour that she tutors, she earns 50 dollars,
Let E be her earnings (in dollars) after tutoring for H hours,
Write an equation relating E to H. Then use this equation to find Nicole's earnings after tutoring for 15 hours,
Equation: 10
Nicole's earnings for 15 hours: [] dollars
Answer:
750 dollars
Step-by-step explanation:
If you multiply 15 by 50, you get 750. E × H = 750
Complete the input-output table for the linear function y = 3x.
y
-2
a
-3
0
0
1
3
2
b
3
с
2 units down
2) reflection across the x-axis
1).
)
A) J\(-2,-4), K (2, -1), L (2,-5)
B) K(5,0), L(5, 4), J'(1,3)
C) K (5,-2), L'(5,2), J'(1, 1)
D) J'(-1,3), K (-5,0), L'(-5, 4)
D
Answer:
A
Step-by-step explanation:
HELP I HAVE NO TIME! BRAINLIEST AND 10 POINTS! Here is the equation and the answer. Please show the steps you would do to get this answer!
Answer:
n = 86
Step-by-step explanation:
Step 1: Write equation
41 + n = 127
Step 2: Subtract 41 on both sides
n = 86
Step 3: Check
Plug in x to verify it's a solution.
41 + 86 = 127
127 = 127
I need help with this geometry
Answer:
Step-by-step explanation:
Imagine foling the graph diagonly and the orange shape would directly line up with the black shape
Use set theoretic or vector notation or both to describe the points that lie in the given configurations
v = (1,−1, 2)+t(2, 3, 1) satisfies the equation 5x −3y −z −6 = 0.
To describe the points that satisfy the given equation and configuration, we can use set-theoretic and vector notation.
Set-theoretic notation:
Let A be the set of points that satisfy the equation 5x - 3y - z - 6 = 0 and lie on the line defined by the vector v = (1, -1, 2) + t(2, 3, 1), where t is a real number.
A = {(x, y, z) | 5x - 3y - z - 6 = 0, and there exists t ∈ ℝ such that (x, y, z) = (1, -1, 2) + t(2, 3, 1)}
Vector notation:
Let v0 = (1, -1, 2) be the initial point on the line, and let d = (2, 3, 1) be the direction vector of the line.
The set of points that satisfy the equation and lie on the line can be represented as:
A = {v0 + t * d | 5(v0 + t * d) - 3y - z - 6 = 0, t ∈ ℝ}
In this notation, v0 represents the initial point on the line, t is a scalar parameter, and d represents the direction vector of the line.
Both notations describe the same set of points that satisfy the equation and lie on the given configuration.
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–5(–2) = WILL GIVE 20 POINTS
Answer:
10Step-by-step explanation:
-5 (-2) = 10
4√5+5√5 is equal to ?
A)9√5
B)9√10
C) 5√10
D) 7√5
Answer:
B is the correct answer.
help plsss asappp it’s on khan
Answer:
I guess the answer is
[tex] \frac{19}{20} [/tex]
-4|6b-8|≤ 12
what is the answer?
figure is shown what is the measure of
Answer:
121.1-108.2 try that.
Step-by-step explanation:
Answer:
58.9
step-by-step explanation:
180-121.1= 58.9
Write a delta-epsilon proof that shows that the function f(x) = px , pER is continuous on its
domain.
The function f(x) = px, where p is a real number, is continuous on its domain by the definition of continuity, as for any ε > 0, there exists a δ > 0 such that |f(x) - f(a)| < ε whenever |x - a| < δ.
To prove that the function f(x) = px, where p is a real number, is continuous on its domain, we need to show that for any ε > 0, there exists a δ > 0 such that |f(x) - f(a)| < ε whenever |x - a| < δ.
Let's proceed with the delta-epsilon proof:
Given a value of ε > 0, we need to find a corresponding δ > 0. Let's choose δ = ε/|p|. Note that δ will be positive as ε and |p| are both positive.
Now, consider any two points x and a such that |x - a| < δ. We want to show that |f(x) - f(a)| < ε.
Using the definition of f(x) = px, we can calculate:
|f(x) - f(a)| = |px - pa| = |p(x - a)|
Since |x - a| < δ, we know that |x - a| < ε/|p|. Multiplying both sides by |p| gives:
|p(x - a)| < |p| * (ε/|p|)
The |p| terms cancel out:
|p(x - a)| < ε
Since ε > 0, |p(x - a)| < ε implies that |f(x) - f(a)| < ε.
Therefore, for any ε > 0, we have found a δ = ε/|p| such that |f(x) - f(a)| < ε whenever |x - a| < δ. This satisfies the definition of continuity.
Hence, we have proven that the function f(x) = px, where p is a real number, is continuous on its domain.
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Which intervals show f(x) decreasing ? Check all that apply
Answer:
(-∞,-1.25]∪[1,2.5]
Step-by-step explanation:
i'm assuming there are no answer choices, so the intervals at which there is a negative slope for this function are:
(-∞,-1.25]∪[1,2.5]
the brackets indicate that the point is included, and the parentheses indicate that it is not included. comment under my response if you need further clarification:)
A farmer plans to enclose two adjacent rectangular pens against a barn wall (see figure).
The farmer has 270 feet of fencing available and wants to create the largest possible area.
Create a function for the enclosed area A in terms of x.
Find the dimensions that give the maximum area.
Answer: Let's assume that the pig pens need to be fenced in the way shown in the diagram above.
Then, the perimeter is given by
4
x
+
3
y
=
160
.
4
x
=
160
−
3
y
x
=
40
−
3
4
y
The area of a rectangle is given by
A
=
L
×
W
, however here we have two rectangles put together, so the total area will be given by
A
=
2
×
L
×
W
.
A
=
2
(
40
−
3
4
y
)
y
A
=
80
y
−
3
2
y
2
Now, let's differentiate this function, with respect to y, to find any critical points on the graph.
A
'
(
y
)
=
80
−
3
y
Setting to 0:
0
=
80
−
3
y
−
80
=
−
3
y
80
3
=
y
x
=
40
−
3
4
×
80
3
x
=
40
−
20
x
=
20
Hence, the dimensions that will give the maximum area are
20
by
26
2
3
feet.
A graphical check of the initial function shows that the vertex is at
(
26
2
3
,
1066
2
3
)
, which represents one of the dimensions that will give the maximum area and the maximum area, respectively.
Hopefully this helps!
Step-by-step explanation: hope this helps
Which diagram shows lines that must be parallel lines cut by a transversal?
Answer:
2nd diagram
Step-by-step explanation:
2nd diagram shows lines that must be parallel lines cut by a transversal.
In the second diagram, line m is transversal of lines r and s, which is making corresponding angles of 91°.
So, line r || line s.
The diagram that represent the lines where it must be parallel lines cut by a transversal should be considered 2nd diagram.
What is transversal?In terms of geometry, a transversal refer to the line that passes via two lines in the similar plane at two different points. Transversals play a vital role in creating whether two or more other lines should be considered in the Euclidean plane are parallel.
Hence, The diagram that represent the lines where it must be parallel lines cut by a transversal should be considered 2nd diagram.
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The Ladybugs are coming to town for a concert. There is such excitement that the concert hall has set up six lines at the box office. Interestingly, the first line is very very long, but the second line has one person more than the first line, and the third line has one more person than the second line and so on, Each of the other line has one more person than the one before it. Altogether, there are 327 people in all six lines. How many people are in each of the six lines?
Answer:34
Step-by-step explanation:
A dumpster in the shape of a rectangular prism has a volume of 240 cubic feet. The length of the dumpster is 4 feet less than twice the width w, and the height is 1 foot less than the width.
Find the equation, in terms of w, that could be used to find the dimensions of the dumpster in feet. Your answer should be in the form of a polynomial equals a constant.
Answer:
Step-by-step explanation:
v=240
l= 2(w)-4
h=(w-1)
v= l*w*h
240=(2w-4)(w-1)w
we then foil
(2w^2 - 6w + 4) w
lastly multiply the w in
ANSWER: 2w^3 - 6w^2 + 4w = 240
Please help I’ll give you brainiest!
Answer:
im pretty confident that its 15
Step-by-step explanation:
An exponential function, f (x), is graphed on the coordinate plane. What is the equation for the function?
A. f(x)=2(3)^x
B. f(x)=4(2)^x
C. f(x)=3(2)^x
D. f(x)=3(4)^x
Answer:
C. f(x)=3(2)^x
Step-by-step explanation:
Answer: f(x)=3(2)^x
Step-by-step explanation:
Hellllppppppeee pleaseeee!!!!!!
Answer:
Scale Factor = 2
Step-by-step explanation:
ABC is your original triangle and A'B'C' is the dilation. You know these are similar triangles so only one side has to be used to find the scale factor. AB has a length of 3 and A'B' has a length of 6 so you know the side lengths of A'B'C' are going to be 2 times the size of triangle ABC side lengths. This gives you a scale factor of 2.
Use the method of your choice to determine the probability below. Being dealt three threes off the top of a standard deck of well-shuffled cards. The probability is____
The probability of being dealt three threes off the top of a standard deck of well-shuffled cards can be calculated using the following method:
Method 1: The probability of drawing the first three from a deck of 52 cards is 4/52 or 1/13, since there are four threes in a deck of 52 cards.
The probability of drawing the second three is now 3/51, as there are only three threes left in the deck of 51 cards.The probability of drawing the third three is now 2/50, since there are only two threes left in the deck of 50 cards.
So, the probability of being dealt three threes off the top of a standard deck of well-shuffled cards is:
Probability = (1/13) × (3/51) × (2/50) = 6/132600 = 1/22100
Therefore, the probability of being dealt three threes off the top of a standard deck of well-shuffled cards is 1/22100.
Method 2: Another method to calculate the probability of being dealt three threes off the top of a standard deck of well-shuffled cards is using combinations. There are a total of 52C3 ways to draw three cards from a deck of 52 cards without replacement.
Out of these, there is only one combination that has three threes. Therefore, the probability of being dealt three threes off the top of a standard deck of well-shuffled cards is:
Probability = 1/52C3 = 1/22100
Hence, the probability of being dealt three threes off the top of a standard deck of well-shuffled cards is 1/22100.
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4. y = (x+2)²-4
Axis of symmetry
Vertex
y-intercept
maximum or minimum
x-intercept(s)
Domain
Range
For the given quadratic we have:
Axis of symmetry: x = -2Vertex: (-2, -4)Y-intercept: y = 0Minimum: y = -4x-intercepts: x = -2 ± 2 Domain --> (-∞, ∞)Rrange --> [-4, ∞)How to describe the quadratic equation?We have a quadratic equation in vertex form, it is:
y = (x+2)²-4
We can see that the vertex is at (-2, -4)
Then tha axis of symmetry must be at the same x-value than the vertex, so it is at:
x = -2
Now, our quadratic equation has a positive leading coefficient, then in opens upwards, thus, we have a minimum at the vertex, and it is:
minimum: y = -4
y-intercept:
Here just evaluate in x = 0.
y = (0+2)²-4 = 0
The x-intercepts, we need to solve:
0 = (x + 2)² - 4
4 = (x + 2)²
±2 = x + 2
-2 ± 2 = x
These are the x-intercepts.
Finally, the domain is the set of all real numbers and the range is the set of all real numbers larger than the minimum, so:
D --> (-∞, ∞)
R --> [-4, ∞)
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how do you figure out if functions are inverses or not
Answer:
For instance, if the point (1, 3) is on the graph of the function, then the point (3, 1) is on the graph of the inverse. That is, if you start with x = 1, you will go to y = 3; then you plug this into the inverse, and you'll go right back to x = 1, where you started from.
Step-by-step explanation:
Answer:
Well, we learned before that we can look at the graphs. Remember, if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.
Step-by-step explanation:
5.
Five students each write an equation.
Student 1
y=-3x + x?
Student 2
7x
10
Student 3
y = 4(2 - x)
Student 4
y =
(x - 1)
Student 5
y =
Which two students write an equation of a nonlinear function?
A Student 1
B
Student 2
C Student 3
D
Student 4
E
Student 5
Write the coordinates of the vertices after a reflection over the line y=3?
The coordinates of the vertices after a reflection as follows:A → (2, 2)B → (5, 2)C → (4, 5).
Given that we are to reflect the coordinates of vertices over the line y = 3, we can conclude that the reflection will be on the x-axis.
Therefore, for a reflection in the line y = 3, the coordinates of the vertices after reflection are obtained by replacing y with 6 − y.
We are given the following triangle, therefore:
vertices coordinates for ABC: A(2, 4), B(5, 4) and C(4, 1)
For vertex A, its new coordinates after reflection will be (2, 2)
For vertex B, its new coordinates after reflection will be (5, 2)
For vertex C, its new coordinates after reflection will be (4, 5)
Hence, the coordinates of the vertices after a reflection over the line y = 3 are as follows:A → (2, 2)B → (5, 2)C → (4, 5).
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Can somebody please help me on this question?
14. Solve the following equations. Give your answers in the
interval 0º < x < 360°.
d) 1 + 3 sin x=0
Answer:
x ≈ 199.5°, x ≈ 340.5°
Step-by-step explanation:
Given
1 + 3sinx = 0 ( subtract 1 from both sides )
3sinx = - 1 ( divide both sides by 3 )
sinx = - [tex]\frac{1}{3}[/tex]
Since sinx < 0 then x is in the third/ fourth quadrants, thus
x = [tex]sin^{-1}[/tex] ([tex]\frac{1}{3}[/tex] ) ≈ 19.5° ← related acute angle, then
x = 180° + 19.5° = 199.5°
x = 360° - 19.5° = 340.5°
Solution is x = 199.5°, x = 340.5° for 0° < x < 360°
