Answer:
x = 7, x = -2Step-by-step explanation:
Solving by completing square
-14 + x^2 = 5xx^2 - 5x - 14 = 0x^2 -2*2.5x + 6.25 - 20.25 = 0(x -2.5)^2 = 20.25(x - 2.5)^2 = 4.5^2x - 2.5 = 4.5 ⇒ x = 7x - 2.5 = -4.5 ⇒ x = -24. 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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–5(–2) = WILL GIVE 20 POINTS
Answer:
10Step-by-step explanation:
-5 (-2) = 10
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:
Please help I’ll give you brainiest!
Answer:
im pretty confident that its 15
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
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:
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
-4|6b-8|≤ 12
what is the answer?
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:
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
7 + 5v − 0 + 2v − 1 = ______
For each of the following statements, determine whether the statement is true or false (the latter including "not necessarily true"), and provide a brief explanation.
(a) A situation where everyone is playing a dominant strategy must be a Nash equilibrium.
(b) In a Nash equilibrium, everyone must be playing a dominant strategy.
(c) A two-person game in which each person has access to only two possible strategies will have at most one Nash equilibrium.
(d) In the following game, there exists only one pure-strategy equilibrium.
(e) In the following game of matching pennies, if player 2 plays (1/2∘H,1/2∘T) (i.e., plays both strategies with equal probability) then player 1 strictly prefers playing (1/2∘H,1/2∘ T ) to playing either H or T with probability 1.
(a) False. A situation where everyone is playing a dominant strategy does not necessarily guarantee a Nash equilibrium.
(b) False. In a Nash equilibrium, players may or may not be playing a dominant strategy.
(c) Not necessarily true. A two-person game with only two strategies for each player can have more than one Nash equilibrium.
(d) True. Without specific details about the game provided,
(e) False. In the game of matching pennies, if player 2 plays (1/2∘H,1/2∘T)
(a) False. A situation where everyone is playing a dominant strategy does not necessarily guarantee a Nash equilibrium. A Nash equilibrium occurs when no player can unilaterally change their strategy to improve their own payoff, regardless of what other players do. It is possible for a situation with dominant strategies for each player to result in a Nash equilibrium, but it is not a guarantee.
(b) False. In a Nash equilibrium, players may or may not be playing a dominant strategy. A Nash equilibrium simply represents a stable outcome where no player has an incentive to deviate from their chosen strategy given the strategies chosen by others. Players could be playing non-dominant strategies and still reach a Nash equilibrium.
(c) Not necessarily true. A two-person game with only two strategies for each player can have more than one Nash equilibrium. The number of Nash equilibria is not solely determined by the number of strategies available to each player but also depends on the payoffs and interactions between the strategies chosen by each player.
(d) True. Without specific details about the game provided, we cannot definitively determine if there exists only one pure-strategy equilibrium. However, if it is stated that there is only one pure-strategy equilibrium, then the statement would be true.
(e) False. In the game of matching pennies, if player 2 plays (1/2∘H,1/2∘T) with equal probability, player 1 does not strictly prefer playing (1/2∘H,1/2∘T) over playing either H or T with probability 1. Player 1's preferred strategy would depend on their own payoffs and the corresponding payoffs associated with the opponent's strategies. Without additional information about the payoffs in the game, we cannot make a definitive judgment on player 1's preferences.
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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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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:
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.
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:
The total land area on Earth is about 6 × 107 square miles. The land area of Australia is about 3 × 106 square miles. About how many times larger is the land area on Earth than the land area of Australia?
what is PEMDAS? and how do you use it?
Answer:
please excuse my dear aunt sallyStep-by-step explanation:
PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. For any expression, all exponents should be simplified first, followed by multiplication and division from left to right and, finally, addition and subtraction from left to right.
PEMDAS stands for Parentheses, Exponents, Multiply, Divide, Add, and Subtract.
How to use it?
Well, if you have a problem like:
19 + 4 x 3.
If someone didn't know the rule of PEMDAS, they would start from the beginning of the problem, but no.
If you follow the rule, MULTIPLYING comes before ADDING. So you need to solve whatever comes first in PEMDAS.
4 x 3 = 12, then plus 19 = 31
Did this help ? :)
HELP PLEASE 80 POINTS
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the equation. 4(px 1)=64 The value of x in terms of p is . The value of x when p is -5 is .
Answer:
x = 15/px = -3Step-by-step explanation:
Given4(px + 1)=64FindSolve for xFind x when p = -5Solution4(px + 1) = 644(px + 1)/4 = 64/4px + 1 = 16px = 15x = 15/pWhen p = -5, substitute p:
x = 15/px = 15/(-5) = -3Answer:
x = 15 px = -3Step-by-step explanation:
given equation: 4(px + 1) = 64
find
value of x in terms of p
let p = -5
4 (px + 1) = 64
4px + 4 = 64
x = 64 - 4
4p
x = 15
p
plugin the given value of p = -5
x = 15
-5
x = -3
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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Locate quadrilateral ABCD and quadrilateral EFGH on the coordinate plane. Use GeoGebra to identify the transformations that will map ABCD onto EFGH, and then describe them in the table. Enter the coordinates of the vertices of the images that you created. Paste a screen capture of the images below the table.
Answer:
See image attached
Step-by-step explanation:
The new coordinate of point E will be (1,1),
the new coordinate of point F will be (2,3),
the new coordinate of point G will be (-1,2),
the new coordinate of point H will be (0,1).
What is the transformation?A transformation is the shifting of the picture for changing the shape or position of a point or a geometric figure.
Transformation is a translation of the figure by which the orientation or size of a given figure is changed without any single effect on the shape.
What is the rotation?A rotation is one kind of translation in which the object rotates about a fixed point or axis. The direction of rotation may be either clockwise or anticlockwise.
As we know if we rotate a point of coordinate (x,y) 90° counter clockwise then the new coordinate of the point will be (-y,x).
Here the new coordinate of point A(1,-2) will be (2,1).
the new coordinate of point B(3,-1) will be (1,3).
the new coordinate of point C(2,-4) will be (4,2).
the new coordinate of point D(1,-3) will be (3,1).
As we know if we reflect the point of coordinate (x,y) about the y-axis then the new coordinate will be (-x,y).
Here the new coordinate of point A(2,1) will be (-2,1).
the new coordinate of point B(1,3) will be (-1,3).
the new coordinate of point C(4,2) will be (-4,2).
the new coordinate of point D(3,1) will be (-3,1).
As we know if we translate the point of coordinate (x,y) 3 units right then the new x coordination will be increased by 3. And the new coordinate will be (x+3,y).
Here the new coordinate of point A(-2,1) will be (1,1).
the new coordinate of point B(-1,3) will be (2,3).
the new coordinate of point C(-4,2) will be (-1,2).
the new coordinate of point D(-3,1) will be (0,1).
Therefore the final answer is attached below with a graph.
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Store A charges $1,200 for repairs with a 6 percent sales tax. Store B charges $1,350 with a 7 percent sales tax. Explain how you would determine the amount of money saved by using Store A instead of Store B?
Answer:
The total repair cost for each store is the cost of repairs added to the sales tax. The amount of money saved will be the difference between the two total costs.
Answer:
Gratuity of $180 I would multiply the actual repair cost without including tax to determine the gratuity. So just multiply $1200 by 0.15 getting $180. As an suggestion, calculating 15% in your head is actually quite simple. What you do is calculate 10%, divide that in half, then add together. So for the $1200 example, you have 1200/10 = 120 half of 120 is 60 120 + 60 = 180 So you have a top of $180.
Step-by-step explanation:
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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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
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
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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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:
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.
Part 1 out of 2 Select the word problem that can be modeled by the addition of two negative numbers. A Virginia sold her pottery for $5 and then sold a hat for $2. By how much did Virginia's account change after her transactions? B Amir bought a VCR for $8 and then resold it for $9. By how much did Amir's account change after his transactions? C Polly bought a cracker for $4 and then bought a parrot for $2. By how much did Polly's account change after her transactions? D Marcus sold a cat for $9 and then bought a plant for $4. By how much did Marcus's account changed after his transactions?
Answer: C Polly bought a cracker for $4 and then bought a parrot for $2
-$6
Step-by-step explanation:
Word problem which can be modeled by the addition of two negative numbers :
Option A:
Selling or making a sales will yield a positive value
OptionB:
Purchasing is negative, however, reselling is positive
OptionC:
Purchasing a cracker (c) for $4 = - 4
Purchasing a parrot (p) for $2 = - 2
Hence, both are negative
c + p
-4 + (-2)
= - $6
Option D:
Selling is positive ; purchasing is negative
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
