Answer:
The equations 3·x - 6·y = 9 and x - 2·y = 3 are the same
The possible solution are the points (infinite) on the line of the graph representing the equation 3·x - 6·y = 9 or x - 2·y = 3 which is the same line
Step-by-step explanation:
The given linear equations are;
3·x - 6·y = 9...(1)
x - 2·y = 3...(2)
The solution of a system of two linear equations with two unknowns can be found graphically by plotting the two equations and finding the coordinates of the point of intersection of the line graphs
Making 'y' the subject of both equations gives;
For equation (1);
3·x - 6·y = 9
3·x - 9 = 6·y
y = x/2 - 3/2
For equation (2);
x - 2·y = 3
x - 3 = 2·y
y = x/2 - 3/2
We observe that the two equations are the same and will have an infinite number of solutions
Answer pls…………………………..
Answer:
Option 3
Step-by-step explanation:
Brainliest please~
Pythagorean Theorem a=11 b=60 c=?
Answer:
61
Step-by-step explanation:
The Pythagorean Theorem is a fundamental in geometry that involves looking at two sides of a right triangle and finding out the length of it. Let's use the formula with the corresponding numbers.
The formula for this question would be \(c=\sqrt{a^2 + b^2}\)
Since we know that a = 11 and b = 60, we can do the following and substitute :
\(c = \sqrt{11^2 + 60^2}\)
11 squared is 121
60 squared is 3600
Now we need to add the two number together :
121 + 3600
3721
Since this number is under the square root, we have to square root it. :
\(\sqrt{3721}\)
61
Therefore c is equal to 61.
which expression is equivalent to the equation in the picture
Answer: C) \(3x^3+ 6x^2 + 5x +10\)
Step-by-step explanation:
Using the FOIL method since we're multiplying two binomials. We get...
F: Firsts
\(3x^2(x)\)=\(3x^3\)
O: Outside
\(3x^2(2) = 6x^2\)
I: Insides
\(5(x) = 5x\)
L: Lasts
\(5(2) = 10\)
Put them together and we have \(3x^3+ 6x^2 + 5x +10\)! These two are both equivalent since the form given in the question was factored form and this form is just the same thing expanded!
Answer:
C
Step-by-step explanation:
Cost, revenue, and profit are in dollars and x is the number of units. If the marginal cost for a product is MC = 2x + 5 and the production of 10 units results in a total cost of $540, find the total cost function. C(x) =
The all out cost capability is C(x) = 2x + 110. The dollar amounts for the cost, revenue, and profit, as well as the number of units, are x.
The given minor expense (MC) for an item is MC = 2x + 5. Let's locate the function of total costs. Cost (C) = Total Cost (TC) / Number of Units (x)The total cost of 10 units is estimated to be $540, as we know from previous experience. We should substitute this worth in the above equation. C(10) = 540/10C(10) = 54Now, we should see as the proper expense. When there are no units produced, the fixed cost is presented as the cost.
That is when x = 0. Let's seek it out. When x is zero, C(x) equals Fixed Cost. From the given equation, MC equals 2x + 5, and when x is zero, MC equals 2(0) + 5 = 5. Let the fixed cost be a. Then,C(x) = 2x + 5aThe complete expense capability is given by C(x) = 2x + 5a. We really want to track down a with the end goal that when x = 10, the all out cost capability is 540.C(10) = 2(10) + 5a = 54On tackling, we get,a = 22The complete expense capability is given by,C(x) = 2x + 5a = 2x + 5(22) = 2x + 110Therefore, the all out cost capability is C(x) = 2x + 110. The dollar amounts for the cost, revenue, and profit, as well as the number of units, are x.
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You may need to use the appropriate appendix table or technology to answer this question. The following results are for independent random samples taken from two populations. Sample 1 Sample 2 n1 = 20 n2 = 30 x1 = 22.8 x2 = 20.1 s1 = 2.2 s2 = 4.6 (a) What is the point estimate of the difference between the two population means? (Use x1 − x2. ) 2.7 (b) What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.) (c) At 95% confidence, what is the margin of error? (Round your answer to one decimal place.) (d) What is the 95% confidence interval for the difference between the two population means? (Use x1 − x2. Round your answers to one decimal place.)
a). The difference between the two population means is estimated at a location to be 2.7.
b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.
c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).
d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.
What is standard deviations?The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.
Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample
\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).
With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.
We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).
The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the
average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).
Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).
The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).
As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.
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The lines represented by the equations 20y−24x=−20 and 5y−6x=−5 are...
a)perpendicular
b)the same line
c)neither parallel nor perpendicular
d)parallel
Answer:
parallel i think
Step-by-step explanation:
parallel because it's a unknown error
Answer:
Choice B
Step-by-step explanation:
The best way to compare two lines is to solve for y.
The first equation:
For \(20y-24x=-20\) the first thing we should do is add the 24x on both sides which will cancel out itself on the left side \(20y=24x-20\). Now all we have to do is divide the 20 on both sides to leave us with \(y=\frac{6}{5}-1\).
The second equation:
For \(5y-6x=-5\) the first thing we should do is add the 6x on both side which will cancel itself on the left side \(5y=6x-5\). Now all we have to do is divide the 5 on both sides to leave us with \(y=\frac{6}{5}x-1\).
Now for the comparison:
They are the same exact line. If you were to graph them they would overlap each other.
helpppppp ill mark u brainlest
Answer:
an=a+(n-1)d
part B is 1
Step-by-step explanation:
please mark me as brainlest
Answer:
See below ~
Step-by-step explanation:
Part (A) :
⇒ aₙ = aₙ₋₁ + 1/2
⇒ Each consecutive term follows this recursive rule
Part (B) :
With each term number increase of 1, the term value increases by 1/2.
What is the correlation?
A.Positive Trend
B.Negative Trend
C.No Trend
If it has one, what would be the equation for line of best fit?
A. y=3x
B.y=3/4x+1
C.y=10
D.y=1/4x
The correlation here in the provided graph is a positive trend and the equation for line of best fit will be as follows:
y = 1/4x
Define correlation?Correlation is a statistical method for determining the association or relationship between two variables. To put it another way, the correlation coefficient formula facilitates the calculation of the correlation coefficient, which assesses the degree to which one variable depends on another.
The correlation coefficient is a numerical indicator of correlation. Between -1 and 1, the correlation coefficient is found. An inverse association between two variables is shown by a negative correlation coefficient. A high correlation coefficient means that the two variables directly affect one other's values. There is no association between the two variables, according to a zero-correlation coefficient.
Here in the question,
The graph shows a positive trend as its increasing upwards. The equation for the line of best fit will be y =1/4x.
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if f(x) = 3x - 4 and g(x) = x^2, find the value of f(3) - g(2)
Answer:
\(\huge\boxed{\sf 1}\)
Step-by-step explanation:
Given functions:f(x) = 3x - 4
Put x = 3
f(3) = 3(3) - 4
f(3) = 9 - 4
f(3) = 5 ------------------(1)Also,
g(x) = x²
Put x = 2
g(2) = (2)²
g(2) = 4 --------------(2)Subtract Eq. (2) from Eq. (1)
f(3) - g(2):= 5 - 4
= 1\(\rule[225]{225}{2}\)
Answer:
F(3) -g(2) = 1
Step-by-step explanation:
F(3)= 3(3) -4= 5
g(2)= \(2^{2}\) = 4
f(3) -g(2)= 5-4 =1
PLD HELP ME I WILL FAIL PLS
Answer:
C
Step-by-step explanation:
uh.....
3 1/8 hope this helps you pass
Solve the following inequality algebraically.
x^2+2x-24< 0
Answer:
-6<x<4
Step-by-step explanation:
x^2+2x-24=0
(x-4)(x+6)=0
x-4=0
x+6=0
x=-6,4
x<-6 false
-6<x<4 true
x>4 false
so -6<x<4
Given mn, find the value of x.
(7x-30)
(6x-10)
Considering that lines m and n are parallel, we have that angles (7x - 30)º and (6x - 10)º are congruent angles, hence the value of x is of x = 20º.
What does the problem show?The problem is incomplete, but researching it on the internet, we have that:
There are two parallel lines, and the angle of (6x - 10)º is alternate interior with the opposite angle by the same vertex of (7x - 30)º, hence they are congruent.
What are congruent angles?Congruent angles are angles that have the same measure, hence, the value of x can be found as follows:
7x - 30 = 6x - 10
7x - 6x = 30 - 10
x = 20.
The value of x is of x = 20º.
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4. Consider the ground state of the Harmonic Oscillator with the potential in the k standard form V = x² so the potential well is centered at x = 0. 2 (a) Evaluate the values of (x²) and σ₂ = √
(a) To evaluate (x^2) for the ground state of the Harmonic Oscillator, we need to integrate x^2 multiplied by the square of the absolute value of the wavefunction ψ0(x).
(b) The expectation value of p^2 for the ground state of the Harmonic Oscillator is simply the eigenvalue corresponding to the momentum operator squared.
(c) By calculating the uncertainties in position (Δx) and momentum (Δp) for the ground state, we can verify that their product satisfies Heisenberg's uncertainty principle, Δx · Δp ≥ ħ/2.
(a) In the ground state of the Harmonic Oscillator, the wavefunction is given by \(\psi_0(x) = \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{2\sigma^2}}\), where \(\sigma\) is the standard deviation.
To evaluate \((x^2)\), we need to find the expectation value of \(x^2\) with respect to the wavefunction \(\psi_0(x)\). Using the formula for the expectation value, we have:
\((x^2) = \int_{-\infty}^{\infty} x^2 \left|\psi_0(x)\right|^2 dx\)
Substituting the given wavefunction, we have:
\((x^2) = \int_{-\infty}^{\infty} x^2 \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{\sigma^2}} dx\)
Evaluating this integral gives us the value of \((x^2)\) for the ground state of the Harmonic Oscillator.
To evaluate \(\sigma_2\), we can simply take the square root of \((x^2)\) and subtract the expectation value of \(x\) squared, \((x)^2\).
(b) To evaluate \((p^2)\), we need to find the expectation value of \(p^2\) with respect to the wavefunction \(\psi_0(x)\). However, in this case, it is clear that the ground state of the Harmonic Oscillator is an eigenstate of the momentum operator, \(p\). Therefore, the expectation value of \(p^2\) for this state will simply be the eigenvalue corresponding to the momentum operator squared.
(c) The Heisenberg's uncertainty principle states that the product of the uncertainties in position and momentum (\(\Delta x\) and \(\Delta p\)) is bounded by a minimum value: \(\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\).
To show that the uncertainty product satisfies the uncertainty principle, we need to calculate \(\Delta x\) and \(\Delta p\) for the ground state of the Harmonic Oscillator and verify that their product is greater than or equal to \(\frac{\hbar}{2}\).
If the ground state wavefunction \(\psi_0(x)\) is a Gaussian function, then the uncertainties \(\Delta x\) and \(\Delta p\) can be related to the standard deviation \(\sigma\) as follows:
\(\Delta x = \sigma\)
\(\Delta p = \frac{\hbar}{2\sigma}\)
By substituting these values into the uncertainty product inequality, we can verify that it satisfies the Heisenberg's uncertainty principle.
Regarding the statement \((x) = 0\) and \((p) = 0\) for this problem, it seems incorrect. The ground state of the Harmonic Oscillator does not have zero uncertainties in position or momentum. Both \(\Delta x\) and \(\Delta p\) will have non-zero values.
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i need help I dont get this can someone explain?
Answer:
428
160
12.7
Step-by-step explanation:
So I'm pretty sure all it's asking you do is divide the product (number on the right) by the number on the left!
So 42.8/\(\frac{1}{10}\)=428
1600/10=160
1.27/\(\frac{1}{10}\)=127
PLEASE HELP ME ITS ALGEBRA 1 ANYONE PLEASE !!!
Answer:
answer of this question is r=0.94
Answer: oh god
Step-by-step explanation:
Find the value of p in the inequality.
three fourths times p plus 8 is greater than or equal to 3
The value of p that we get by solving the inequality given in the question is \(p\geq \frac{-20}{3}\)
The given inequality is
\(\frac{3}{4}p+8\geq 3\)
⇒\(\frac{3}{4}p\geq 3-8\) (subtracting 8 on both sides)
⇒\(3p\geq -5*4\) (multiplying both sides by 4)
⇒\(p\geq \frac{-20}{3}\) (dividing both sides by 3)
⇒\(p\geq -6.667\)
Therefore the value of p must be greater than or equal to -20/3 or -6.667
That is, \(p\geq -6.667\)
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Kaitlan sold 60% of her hockey card collection at the fall market sale. If she sold 240 cards, how many cards were in her collection?
Answer:
400
Step-by-step explanation:
Ok so if 60% of the total is 240 than create an expression:
60% of x=240
Now divide both sides by 3:
20% of x=80
Multiply both sides by 5 ( because 5 times 30 is 100):
100% of x=400
Thats the answer hope this helped! :)
400 cards were in her collection.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Total hockey cards sold= 240
So, Kaitlan sold 60% of her hockey card
let the total number of Hockey cards be x.
So, 60% of x= 240
60 x /100 = 240
x= 24000/ 60
x= 400
Hence, 400 cards were in her collection.
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What is rate of change for 3=2x-21
Answer:
Step-by-step explanation:
I believe I need 2 variables to properly work this out but x=12
3=2x-21
24=2x
12=x
For each equation, find y when x = -6. Then find x when y = 20.
A y = 6x +8
B. y = x
C. y = -x + 5
D.y = 6.5x+7
Answer:
A) x = 2
y = -28
B) x = 30
y = -4
C) x = -15
y = 11
D) x = 2
y = 46
Step-by-step explanation:
Hope this helps :D I'm in class so I can't explain rn I hope you understand the concept.
have a nice day
Peter had $50 to spend at a fair. He spent $15.20 on rides. He wants to buy some fudge
that costs $8 a pound to take home. Which inequality shows the maximum number of
pounds of fudge, p, that Peter can buy with the money he has left?
A. p < 4.35
B. p > 4.35
C. p < 8.15
D. p > 8.15
Answer: A, p<4.35
Step-by-step explanation:
8p<50-15.20 (Set up and subtract)
8p<34.80 (Divide)
p<4.35
Question
A square based pyramid has a height of 6 feet and the edge length of the base is 2 feet. A second square based pyramid is 2 feet taller and the edge length of the base is 0.5 feet greater than the first pyramid. How much greater is the volume of the second pyramid than the volume of the first pyramid? Round your answer to the nearest hundredth.
please help
A pyramid is a solid shape with a specified shaped base. The required answer is 8.67 cubic feet.
A pyramid is a solid shape with a specified shaped base. While a square based pyramid is a type of pyramid which has its base to be a square.
Volume of a square based pyramid = \(\frac{1}{3}\) x base area x height
Also, are of a square = length x length
So that,
i. For the first pyramid;
volume = \(\frac{1}{3}\) x (2 x 2) x 6
= 8 cubic feet
The volume of the first pyramid is 8 cubic feet.
ii. For the second pyramid, we have;
height = 8 feet
base side = 2.5 feet
So that.
Volume = \(\frac{1}{3}\) x (2.5 x 2.5) x 8
= 16.6667
Volume = 16.67 cubic meters
The volume of the second pyramid is 16.67 cubic meters.
Therefore, the volume of the second pyramid is greater than the volume of the first pyramid by;
volume of the second pyramid - volume of the first pyramid = 16.67 - 8.0
= 8.67 cubic feet
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Write an expression to represent:
Eight more than the product of two and a number
x
xx.
Answer:
2x+8
Step-by-step explanation:
The mathematical expression will be;
⇒ 2x + 8
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
⇒ '' Eight more than the product of two and a number x''.
Now,
Since, The algebraic expression is,
⇒ '' Eight more than the product of two and a number x''.
Hence, We get the mathematical expression as;
⇒ Product of 2 and number x = 2x
And, 8 more than 2x = 2x + 8
Thus, We get the mathematical expression as;
⇒ 2x + 8
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HELPP PLEASE ILL MAKE YOU THE BRAINIEST Find the area of the rhombus
Answer:
D1×D2/2sq
445×5= 225
225/2
=112.5
What sequence of transformation takes A to its image, B?
A, Reflection over the x-axis and translation 2 units down
B, reflection over the y-axis and translation 2 units down
C, translation 2 units down and 90* rotation about the origin
D, translation 12 units right and 90* rotation about the origin
Answer:
C
Step-by-step explanation:
What is the value of -5 ?
Answer:
-1 because if you look you have multiple it
Step-by-step explanation:
hope this help
the top of a 13 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. how fast is the bottom of the ladder sliding along the ground away from the wall when the bottom of the ladder is 12 feet away from the base of the wall?
we know that
speed = distance/time
speed = dx/dt
Let x = the distance from the base of the ladder to the base of the wall
y = the distance from the tip of the ladder to the base of the wall, we have:
x^2+y^2 = 13^2
y^2=13^2-12^2 = 169 - 144 = 25 => y = 5 ft
2x dx/dt + 2y dy/dt = 0
2*5* dx/dt + 2*5*(-4) = 0
10 dx/dt = 40
dx/dt = (40/10) ft/sec
dx/dt = 4 ft/sec
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those causes of variation which are large in magnitude and are not part of the normal variation are:
The causes of variation which are large in magnitude and are not part of the normal variation are known as Outliers.
What is an Outlier? An outlier is a value that is far greater or less than the majority of other values in a given dataset. These may be due to a variety of factors, including statistical errors or data entry mistakes, but they may also represent actual phenomena that have an impact on the overall results. These causes are not typically part of the normal variation of the process. Thus, outliers are not considered a part of the normal variation.
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fastest will get brainly
A playground has a length of
x + 3 feet and a width of x - 1 feet
1. Write a polynomial to express the area of the playground.
Answer:
Area=(x+3)(x-1)
Ara=(x^2)-x+3x-3
Area=(X^2)+2X-3
URGENT HELP PLEASE
The work of a student to solve the equation 2(3x - 4) = 8 + 2x + 4 is shown below:
Step 1: 2(3x - 4) = 8 + 2x + 4
Step 2: 5x - 6 = 12 + 2x
Step 3: 5x – 2x = 12 + 6
Step 4: 3x = 18
Step 5: x = 6
In which step did the student first make an error and what is the correct step? (5
points)
Answer:
In second step
6x-8 = 12+2x
5x = 20
x = 4
Step-by-step explanation:
Hope it helps you!
When a new cellphone is put on the market, the demand each month can be described by the function C of t is equal to negative square root of the quantity t squared plus 4 times t minus 12 end quantity plus 3 where C (t) represents the demand of the cellphone (measured in millions of people) and the time, t, is measured in months. Which of the following solution(s) are valid for a positive demand? (7, 0) and (3, 0) (–6, 3) and (2, 3) (6, 3) (2, 3)
Answer:
(2, 3)
Step-by-step explanation:
Answer:
It is (2,3)
Step-by-step explanation: