What is a Rectangular Coordinate System

Answer:9x^4

Step-by-step explanation:

6x^4*3x^3 can be simplified to 18x^7 by separating out cand combining like terms  [6*3 = 18] and [x^4*x^3 = x^7]

This results in 18x^7 fr the top term

Do the same for the bottom term:  2x^2*x = 2x^3

We can now write:  (18x^7)/(2x^3)

The reduces to 9x^4

In geometry, transformation involves changing the position and/or size of a shape.

The transformation that will change the size of ABCD is dilation.

There are four transformations in geometry:

Of all types of transformation, dilation will change the size of the shape,

The new shape will either be enlarged or reduced

Either ways, the size of the shape will be altered.

When the size is altered, the perimeter will not remain the same.

Hence. dilation will change the perimeter of ABCD.

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Answer:

d

Step-by-step explanation:

edge2020

Option D is correct. The exponential function is increasing when time goes and the total return on investment.

An exponential function is of the form aˣ where 'a' is the base of the function and 'x' is the power of the function.

A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".

According to the question,

Let 'x' is the time in years and f(x) is the total return on investment. The below table shows the function over the interval.

                    x                                                    f(x)

 a decreasing quadratic function                 10,000

 an increasing quadratic function               12,201.90

a decreasing exponential function              14,888.64

an increasing  exponential function             22,167.15            

Quadratic function f(x) = ax² +b x +c  a > 0

Exponential function f(x) = a. bˣ +q                                    

Hence, the exponential function is increasing when time goes and the total return on investment.

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Given:

The equation is:

\(\dfrac{7}{3}+x=3\)

To find:

The value of x.

Solution:

We have,

\(\dfrac{7}{3}+x=3\)

Subtract both sides by \(\dfrac{7}{3}\).

\(\dfrac{7}{3}+x-\dfrac{7}{3}=3-\dfrac{7}{3}\)

\(x=\dfrac{9-7}{3}\)

\(x=\dfrac{2}{3}\)

Therefore, the value of x is \(\dfrac{2}{3}\) or it can be written as 0.667.

Answer:

The two triangles are sometimes congruent.

Step-by-step explanation:

I did it and got it correct

Answer:

please see detailed answers below

Step-by-step explanation:

to divide one fraction by another, just multiply the 2nd one upside down.

1) 2/7 ÷ 1/3  = 2/7 X 3/1 = 6/7

12) 1/2 ÷ 1/8 = 1/2 X 8/1 = 8/2 = 4

13) 3/8 ÷ 1/4 = 3/8 X 4/1 = 12/8 = 3/2

14) 2/5 ÷ 3/10 = 2/5 X 10/3 = 20/15 = 4/3

The value of x is 21.

From the attached diagram we can observe that the lines m and n are parallel to each other and these parallel lines are intersected by transversal t.

Let us assume that angle 'y' be a linear angle with (2x + 2)

(Both angles are below line n)

⇒ y + (2x + 2) = 180°          .............(1)

So that, angles (7x + 7) and angle y are alternate exterior angles.

We know that alternate exterior angles are equal.

⇒ (7x + 7) = y

From equation (1),

(7x + 7) + (2x + 2) = 180°    

9x + 9 = 180

9(x + 1) = 180

x + 1 = 20

x = 21

This is the required value.

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Find the complete question below.

Answer:

c. 2x.

Step-by-step explanation:

16x2 - 14x

Common factor of 16 and 14 =  2'

for x2 and x it is x,

Answer: 2x.

i. Range (A): The space spanned by the columns of matrix A. It represents all possible linear combinations of the columns of A.

ii. Null (A): The set of all vectors x such that Ax = 0. It represents the solutions to the homogeneous equation Ax = 0.

iii. Row (A): The space spanned by the rows of matrix A. It represents all possible linear combinations of the rows of A.

iv. Null (A): The set of all vectors y such that ATy = 0. It represents the solutions to the homogeneous equation ATy = 0.

The equation Ax = b has a solution only when b is in the Range (A). It has a unique solution only when the Null (A) contains only the zero vector.

The equation ATy = d has a solution only when d is in the Row (A). It has a unique solution only when the Null (A) contains only the zero vector.

Assuming the size of A is m × n:

When Ax = b has a unique solution, the space Null (A) must be equal to Rn. This means there are no non-zero vectors that satisfy Ax = 0, ensuring a unique solution.

When ATy = d has a unique solution, the space Null (AT) must be equal to Rm. This means there are no non-zero vectors that satisfy ATy = 0, ensuring a unique solution.

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Answer:

21.5sqft

Step-by-step explanation:

The area of the square is 10ft*10ft = 100sqft

The area of the circle is 5ft*5ft*pi = 25pi sqft

We're supposed to use 3.14 for pi, so the circle is around 25*3.14 sqft = 78.5sq ft

The area left over is 100sqft - 78.5sqft = 21.5sqft

Answer:

21.5 sq. feet

Step-by-step explanation:

Answer:

x = 62.5

Step-by-step explanation:

Express the ratios as equivalent fractions, that is

\(\frac{5}{8}\) = \(\frac{x}{100}\) ( cross- multiply )

8x = 500 ( divide both sides by 8 )

x = 62.5

The disjunction of -p or -q can be written as (-p) v (-q). So, we have to find the truth value of (-p) v (-q). So, the compound statement for the disjunction of -p or -q is (-p) v (-q), and its truth value is true.

using the following statements: p: There are 14 inches in 1 foot.

q: There are 3 feet in 1 yard.

Solution: We know that 1 foot = 12 inches, which means that there are 14 inches in 1 foot can be written as 14 < 12. But this statement is false because 14 is not less than 12. Therefore, the negation of this statement is true, which gives us (-p) as true.

Now, we know that 1 yard = 3 feet, which means that there are 3 feet in 1 yard can be written as 3 > 1. This statement is true because 3 is greater than 1. Therefore, the negation of this statement is false, which gives us (-q) as false.

Now, we can use the values of (-p) and (-q) to find the truth value of (-p) v (-q) using the disjunction rule. The truth value of (-p) v (-q) is true if either (-p) or (-q) is true or both (-p) and (-q) are true. Since (-p) is true and (-q) is false, the disjunction of (-p) v (-q) is true. Hence, the compound statement for the disjunction of -p or -q is (-p) v (-q), and its truth value is true.

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Answer:

The 50th term of the sequence that begins with - 6 is 288.

Step-by-step explanation:

An arithmetic progression, also known as an arithmetic sequence, is a set of numbers in which the difference between successive terms remains constant. The sequence 5, 7, 9, 11, 13, 15,... is, for example, an arithmetic progression with a common difference of 2.

Formula -\($a_{n}=a_{1}+(n-1) d$\)

It is in arithmetic progression as the common difference between all consecutive numbers is 6.

Let a1 be the first term and d be the common difference.

Therefore, a1 = - 6 and d = 6

For 50th term, a50 = a1 + (n - 1) d

= - 6 + (50 - 1) 6

= - 6 + 49 × 6

= - 6 + 294

= 288

Thus, the 50th term of the sequence is 288.

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Answer:

340 feet

Step-by-step explanation:

To get the number of feet, we simply make an addition of the number of feet dug on both days

The total will be 175 feet + 165 feet = 340 feet

Answer:

What is meant by "Explain your answer?"

   On tests & problem sets students are often asked to explain the reasoning behind their answers. They are often frustrated and/or confused by “explain.” What & why are they supposed to explain? Here is one answer:

   It isn't enough to get the right answer -- you have to be able to explain how you got it. To be sure you get enough practice at explaining yourself, it pays to discuss the questions with your fellow students and/or to write out explanations of your reasoning. You need to both

           (1) Include the right facts, principles, etc., AND

           (2) Explain the logic that you used to solve the problem. How did you get from the facts to the answer?

   It is not sufficient to pile up unselected facts (even if they are correct), OR just to state the facts (even if they are the right ones), without explaining how they relate to the problem at hand, OR to just explain the logical train of thought (even if it is correct), without any specifics.

   That's what you shouldn't do. What should you aim for??

   Try to explain as if you were talking to a fellow student in the class who is generally intelligent, prepared, etc., but can't figure out this particular question.  In other words, explain your reasoning step by step.  Don't just repeat all the related facts in the book or notes--try to pick out the important, relevant points, put them in logical order, and explain (or diagram) how one leads to the next. (In other words, pretend you are writing a simple* answer key.)

*Note: The keys provided after each exam or problem set are usually quite complex and go beyond what we expect from an individual student. The posted keys tend to be so long and involved because they include not only correct answers (& explanations) but also explanations of common student misconceptions.

How to Get the Most out of Explaining

   When you explain things to yourself, or to others, try not to use pronouns. Use nouns instead. This may sound silly, but it really helps you to be sure that you understand what you are saying. If you use pronouns or vague terms you can fool yourself into thinking you understand when you really don't. An example: Suppose you say "The gene is transcribed and it goes to the cytoplasm and is translated, which uses tRNA and mRNA." What do you mean by it and/or which?  Is it the gene or the mRNA? Does which refer to translation or transcription? Sometimes you know, and you are just using shorthand. But sometimes you don't know, and you don't even realize it until you are forced to pick the right terms to replace "it" and "which."  So try to be as specific as possible instead of as vague and as general as possible. Being specific has multiple advantages. It helps you to learn, it helps listeners understand what you are saying, and it helps graders on exams know that you really understand what you are talking about.

Answer:

-37.

Step-by-step explanation:

a2 = 2 a2-1 - 3

= 2 a1 - 3

= 2*-2 -3

= -7

a3 = 2 a3 - 3

= 2*-7 - 3

= -17

4th term a4

= 2*-17 - 3

= -37.

9514 1404 393

Answer:

  -374

Step-by-step explanation:

  f(8) = -8 +6 = -2

  g(8) = (3x -1)x +3 = (3·8 -1)8 +3 = 23·8 +3 = 187

Then the product is ...

  (g•f)(8) = g(8)•f(8) = 187·(-2)

  (g•f)(8) = -374

Answer:

-35

Step-by-step explanation:

-|35|

-35

Answer:

-35

Step-by-step explanation:

−|−5⋅(−7)|

Multiply inside the absolute values

−|35|

Take the non negative value inside the absolute value

- 35

A plasmid used in both yeast and bacteria requires two different selection markers because the same selection may not work for both hosts and bacteria and yeast recognize different promoters.

When using a plasmid in both yeast and bacteria, it is important to have two different selection markers for several reasons. First, the same selection, such as the presence of an antibiotic, may not be effective in both hosts. Different organisms have varying sensitivities to antibiotics, so a marker that works in bacteria may not work in yeast or vice versa. Therefore, two different selection markers are needed to ensure successful selection in both hosts.

Additionally, bacteria and yeast recognize different promoters, which are DNA sequences that control the initiation of gene expression. Promoters are specific to each organism and play a crucial role in regulating gene expression. By incorporating two different selection markers into the plasmid, each marker can be driven by a promoter recognized specifically by the corresponding host. This ensures that the selection marker is effectively expressed in the appropriate host organism, enabling accurate selection and maintenance of the plasmid.

In summary, using two different selection markers in a plasmid intended for both yeast and bacteria is necessary because the same selection may not be effective in both hosts, and different promoters are recognized by bacteria and yeast. This approach allows for successful selection and maintenance of the plasmid in both organisms.

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(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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Answer:

do math

Step-by-step explanation:

Answer:yes but that to is gonna get the same answer F(x) =1/2x+1/2

f-1(x) = [ ? ]x + [ ]

Step-by-step explanation:

Answer:

456,8

Step-by-step explanation:

325 / 185 / 10 * 8 * 325

The formula to use to write cos(17.6p) + cos(8.4p) as a product is: B. sum of cosines: \(2cos(\frac{x\;+\;y}{2} )cos(\frac{x\;-\;y}{2} )\).

The average of the original inputs is \(\frac{x\;+\;y}{2} =13p\)

Half the distance between the original inputs is \(\frac{x\;-\;y}{2} =4.6p\)

The sum as a product is: cos(17.6p) + cos(8.4p) = 2cos(13p)cos(4.6p).

In Mathematics and Geometry, the Bhaskaracharya sum and difference formulas that shows the relationship between sine and cosine values for trigonometric identities (two angles) can be modeled by the following mathematical equation;

cos(u + v) = cos(u)cos(v) - sin(u)sin(v)

cos(u - v) = cos(u)cos(v) + sin(u)sin(v)

cos(u + v) + cos(u - v) = 2cos(u)cos(v)

In this context, the formula to use in writing cos(17.6p) + cos(8.4p) as a product is given by:

sum of cosines: \(2cos(\frac{x\;+\;y}{2} )cos(\frac{x\;-\;y}{2} )\).

For the average of the original inputs, we have:

\(\frac{x\;+\;y}{2} =\frac{17.6\;+\;8.4}{2} \\\\\frac{x\;+\;y}{2} =13p\)

For half the distance between the original inputs, we have:

\(\frac{x\;-\;y}{2} =\frac{17.6\;-\;8.4}{2} \\\\\frac{x\;-\;y}{2} =4.6p\)

Therefore, the sum as a product can be written as follows:

cos(17.6p) + cos(8.4p) = 2cos(13p)cos(4.6p).

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Answer:

a = -4, b = 3, c = 6

Step-by-step explanation:

x² + 8x = 38

(x + 4)² - 16 = 38

(x + 4)² = 54

x + 4 = ± √54

x = -4 ± 3√6

The rate column will be:

A= 30

B= 20

C= x miles

D= x miles

It should be noted that rate simply means the measure, quantity, or frequency that one measure against another quantity or measure.

In this case, Jorden drives to the store at 30 miles per hour and on her way home she averages only 20 miles per hour.

Therefore, the rate column will be:

A= 30

B= 20

C= x miles

D= x miles

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Fill out the Rate column in the table below. Jorden drives to the store at 30 miles per hour. On her way home she averages only 20 miles per hour. If the total driving time takes half an hour, how far does she live from the store? Fill out the Rate column in the table below. a = b =

Answer:

\(\frac{5}{12}\)

Step-by-step explanation:

Make both fractions have a common denominator

\(\frac{5}{12}=\frac{50}{120}\)

\(\frac{6}{10}=\frac{72}{120}\)

Therefore, \(\frac{5}{12}<\frac{6}{10}\) since \(\frac{50}{120}<\frac{72}{120}\)

(a) The equation of the tangent plane of the graph of the function z = f(x,y) at the point (0,0,0) is given by z = f(0,0) + fx(0,0)(x-0) + fy(0,0)(y-0).

We have f(0,0) = ln(1 + 2(0) + 0) = ln(1) = 0, fx(x,y) = 2/(1+2x+y)² and fy(x,y) = 1/(1+2x+y)². Thus the equation of the tangent plane of the graph at (0,0,0) is z = 0 + 2(x-0) + 1(y-0) = 2x + y.

(b) The linear approximation of the function f(x,y) = ln(1 + 2x + y) at the point (0,0) is given by L(x,y) = f(0,0) + fx(0,0)(x-0) + fy(0,0)(y-0). We have f(0,0) = 0, fx(x,y) = 2/(1+2x+y)² and fy(x,y) = 1/(1+2x+y)².

Therefore, L(x,y) = 0 + 2x + y = 2x + y. We want to estimate the value of f(-0.3,0.1) using this linear approximation at (0,0). Therefore, x = -0.3 - 0 = -0.3 and y = 0.1 - 0 = 0.1. Then we have L(-0.3,0.1) = 2(-0.3) + 0.1 = -0.5. Thus, we can estimate that f(-0.3,0.1) ≈ -0.5.

The linear approximation is an important concept in Calculus. It is a way of approximating the value of a function at a point by using the values of the function and its derivatives at a nearby point. It is useful when we want to estimate the value of a function at a point that is close to a point where we know the value of the function and its derivatives.

The linear approximation is given by L(x, y) = f(a, b) + fx(a, b)(x-a) + fy(a, b)(y-b), where a and b are the coordinates of the point where we know the value of the function and its derivatives.

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A $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.  A $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

The formula to calculate the value of a CD after a specific duration at a specific interest rate compounded annually is given by:

A = P(1 + r/n)^(nt)

where P is the principal,

r is the annual interest rate,

n is the number of times compounded per year,

t is the number of years, and

A is the value of the CD at maturity.

Here, we need to calculate the value of a $1,000 initial investment in each bank's CD at maturity.

Let's calculate the value of a $1,000 investment in Bank ABC's CD.

P = $1,000

r = 5.0% compounded annually

t = 10 years

n = 1

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.05/1)^(1x10)A = $1,628.89

Therefore, a $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.

Let's calculate the value of a $1,000 investment in Bank XYZ's CD.

P = $1,000

r = 4.95% compounded daily

t = 10 years

n = 365

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.0495/365)^(365x10)A = $1,622.82

Therefore, a $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

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