find the product of (x+1) (x²+3x-4)​

Answer:

D

Step-by-step explanation:

for A if you subtract 3 from both sides and divide by 10 from both you get x = 0 so that has infinate solutions

for B you add 8 to both sides and divide by 16 getting the same thiong as A

For C you ditribut 4 to 2x and -3 getting 8x-12=8x-12 if you solve it you get the answer as A & B

For D if you subtract 12 from one side you get -6x = -6x -12 (-12)

causing you not to be able to solve it

The power series expansion of \(\(\frac{5}{{(6+x)^3}}\)\) using the binomial series is: \(\(\frac{5}{{(6+x)^3}} = \frac{5}{{6^3}} \left(1 - \frac{1}{2}\frac{x}{6} + \frac{1}{3}\left(\frac{x}{6}\right)^2 - \frac{1}{4}\left(\frac{x}{6}\right)^3 + \ldots\right)\)\)

The binomial series expansion can be used to expand the function \\((\frac{5}{{(6+x)^3}}\)\) as a power series. The binomial series is given by:\(\((1 + z)^\alpha = 1 + \alpha z + \frac{{\alpha(\alpha-1)}}{{2!}}z^2 + \frac{{\alpha(\alpha-1)(\alpha-2)}}{{3!}}z^3 + \frac{{\alpha(\alpha-1)(\alpha-2)(\alpha-3)}}{{4!}}z^4 + \ldots\)\)

To apply the binomial series to the given function, we can substitute\(\(z = \frac{x}{6}\) and \(\alpha = -3\)\). Then, we have:\(\(\frac{5}{{(6+x)^3}} = \frac{5}{{(6(1+\frac{x}{6}))^3}} = \frac{5}{{6^3(1+\frac{x}{6})^3}}\)\)

Now, we can rewrite the denominator as \(\((1+z)^{-3}\)\) and apply the binomial series expansion:\(\((1+z)^{-3} = 1 + (-3)z + \frac{{-3(-3-1)}}{{2!}}z^2 + \frac{{-3(-3-1)(-3-2)}}{{3!}}z^3 + \frac{{-3(-3-1)(-3-2)(-3-3)}}{{4!}}z^4 + \ldots\)\)

Substituting \(z = \frac{x}{6}\) back into the expansion, we obtain:\(\(\frac{5}{{(6+x)^3}} = \frac{5}{{6^3(1+\frac{x}{6})^3}} = \frac{5}{{6^3}} \left(1 - 3\left(\frac{x}{6}\right) + \frac{{-3(-3-1)}}{{2!}}\left(\frac{x}{6}\right)^2 + \frac{{-3(-3-1)(-3-2)}}{{3!}}\left(\frac{x}{6}\right)^3 + \ldots\right)\)\)

Simplifying and collecting like terms, we have:

\(\(\frac{5}{{(6+x)^3}} = \frac{5}{{6^3}} \left(1 - \frac{1}{2}\frac{x}{6} + \frac{1}{3}\left(\frac{x}{6}\right)^2 - \frac{1}{4}\left(\frac{x}{6}\right)^3 + \ldots\right)\)\)

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Answer:

It is NOT a function

Step-by-step explanation:

No it is NOT a function.....each value of x can only have one y value....

  this has two y values for   x = 2 :    y = 2 and 4    therefore not a function

Answer:

20.8333333333

Step-by-step explanation:

7 + 5 = 12. 250 divided by 12 equals 20.8333333333 or 20.833... You will have more than 20 and a half batches but you can just say about 21, however needed.

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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Answer: 4

Step-by-step explanation:

The x intercept is where the line intersects with the x axis

Counting from the origin (0,0), you can see that the x intercept is 4

Answer: 24. Is that one of your options?

Step-by-step explanation:

Answer:

84 kg

Step-by-step explanation:

its b so please mark me as a brainliest

We can explain the process of multiplying the number of mittens lost by 3 kittens and then multiplying the result by the voting age in the U.S.

To calculate the answer, we first need to know the number of mittens lost. Let's assume it is represented by "M." Next, we multiply M by 3 kittens, which results in 3M. Finally, we need the voting age in the U.S., denoted by "V." By multiplying 3M by V, we obtain the answer, which is 3M * V.

Without specific values for M (number of mittens lost), the number of kittens, and V (voting age in the U.S.), we cannot provide a numerical answer. However, the multiplication process is outlined above. To find the actual answer, you would need to substitute the appropriate values into the equation 3M * V.

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Answer:

x=6

Step-by-step explanation:

2x-5x+20=-7+5x-21

-3x-5x=-7-21-20

-8x=-48

x=6

Answer:

x=6

Step-by-step explanation:

2x-5x+20=5× -28

-3x+20=5x-28

-8x=-48

x=6

check:

2x-5(2)=-30-28

12-10=2

2=2

This is the answer hope you understand it

The trigonometric ratio for cos D is 24/25

To find the trigonometric ratio of cos D, we need to use the cosine function

cos D = adjacent / hypotenuse

In this case, the adjacent side is EF, which has a length of 72 units, and the hypotenuse is DF, which has a length of 75 units. Therefore, we have

cos D = EF / DF

Substitute the values in the equation

cos D = 72 / 75

To simplify this fraction, we can divide both the numerator and the denominator by the greatest common factor, which is 3

cos D = (72/3) / (75/3)

cos D = 24 / 25

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The given question is incomplete, the complete question is:

What is the trigonometric ratio for cosD ? Enter your answer, as a simplified fraction, in the boxes.

Answer:7/25

Step-by-step explanation:

i took the test

Tom will arrive in London at 4.10 pm, after travelling 140 miles at an average speed of 50 mph.

The formula to calculate the time taken is: Time = Distance/Speed

Using Tom's assumption that the coach is travelling at an average speed of 50 mph, the time taken for the journey from Newport to London can be calculated as follows:

Time = 140 miles/50 mph = 2.8 hours

Therefore, Tom will arrive in London at 1.30 pm + 2.8 hours = 4.10 pm.

To put this in context, it means that the coach will travel at an average speed of 70 km/h, covering a distance of 224 km in 2.8 hours. This is equivalent to covering 80 km in an hour.

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Answer:

Not valid

Step-by-step explanation:

Because 12 is minor than 15

The conjecture is not valid.

Mandy not gets a bonus.

Given that:

If a computer sales person sells at least 15 computers in a week, then she gets a bonus.

Maddy sells 12 computers in a week.

Conclusion: Maddy gets a bonus.

We have to check the conjecture is valid or not.

What is Conjecture?

A conjecture is a conclusion or proposition that is proffered on the tentative basis without the proof.

Now,

Here, if a person sells 15 or more computers in a week, she gets a bonus.

Maddy sells 12 computers in a week, which is less than 15.

So, Maddy did not get a bonus.

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Answer:

Below.

Step-by-step explanation:

Each kg is 100 grams so?

4x100=400 grams.

Answer:

4000 grams.

Step-by-step explanation:

There are 1000 grams to 1 kilogram. The prefix, kilo- , means one thousand.

Change 4 kg to grams:

4 kg x (1000 g/1 kg) = 4000 grams.

~

Answer:

Trick question I think because Dr.Price stopped to observe at location D. So 0, I'm not sure sorry. hope this helps :)

Step-by-step explanation:

Answer: (-1941.45)

Step - by - Step Explanaiton

In the given stem-and-leaf plot, we can conclude that there are at least 5 outliers

The number of outliers in the given stem-and-leaf plot can be determined by identifying values that are significantly higher or lower than the majority of the data.

To find the number of outliers in the stem-and-leaf plot, we need to analyze the data distribution and identify values that deviate significantly from the rest of the scores.

Looking at the stem-and-leaf plot, we observe that the majority of the scores are concentrated between 20 and 90. The numbers 2, 3, 4, 5, 6, 7, 8, 9, and 10 represent the tens digit of the scores, while the leaves represent the ones digit.

Upon examining the plot, we notice that there are a few values that stand out from the rest. These values are 00, 01677, 6899, 233569999, and 01268. Outliers are typically defined as values that fall outside the "typical" range of the data, and these values appear to deviate significantly from the majority of the scores.

To determine the exact number of outliers, we need to apply specific criteria. One common method is to use the 1.5 × IQR (interquartile range) rule. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of the data. Any values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR are considered outliers.

In this case, we don't have the exact raw data to calculate the quartiles and IQR. However, based on visual inspection of the stem-and-leaf plot, we can still identify the values mentioned earlier as outliers due to their significant deviation from the majority of the scores.

Therefore, in the given stem-and-leaf plot, we can conclude that there are at least 5 outliers

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1) n²+n is always an even integer

2. n² +n is always an even integer when n is even

3. n² +n is always an even integer when n is odd

Since, if n is an integer,

Then n = even or odd,

If n = even ⇒  = even

⇒ = even+ even = even  

Now, If n = odd ⇒  = odd   ( square of a odd number is always odd )

⇒  = odd + odd = even

Hence, however, n is odd or even,

is always an even number.

⇒ Options 1), 2) and 3) are correct.

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For Pearson correlation the most common purpose to examine is given by option a. The relationship between 2 variables.

The Pearson correlation is a statistical measure that indicates the extent to which two continuous variables are linearly related.

It measures the strength and direction of the relationship between two variables.

Ranging from -1 perfect negative correlation to 1 perfect positive correlation.

And with 0 indicating no correlation.

It is commonly used in research to examine the association between two variables.

Such as the relationship between height and weight, or between income and education level.

Therefore, the most common purpose of a Pearson correlation is to examine the relationship between 2 variables.

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The above question is incomplete, the complete question is:

The most common purpose for a Pearson correlation is to examine,

a. The relationship between 2 variables

b. Relationships among groups

c. Differences between variables

d. Differences between two or more groups

The best description of the geometric construction of the quotient z/w on the complex plane is; Option A; z is scaled by a factor of One-fifth and rotated 90 degrees clockwise

We are given;

z = 3(cos(15°) + i sin(15°))

w = 5(cos(90°) + i sin(90°))

Now, if we want to find the quotient z/w, it is clear that in geometric construction, the procedure will be to scale z by a factor of 1/5 and thereafter we will rotate by 90° clockwise.

Thus, option A is the correct answer.

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Answer:

The system y=-3x + 4 and 3y = -9x+ 12 would contain infinitely many solutions.

Step-by-step explanation:

Any system of equations that have the same equations would have infinitely many solutions.

In other words, if the two linear equations have the same slope and y-intercept, then the system of solutions would contain infinitely many solutions. So, their graphs would have exactly the same line

Also If the equation ends with a true statement, for instance, 3 = 3, then the system has infinitely many solutions or all real numbers.

Given the system of equations

\(y=-3x + 4\)

\(3y = -9x+ 12\)

Writing both equations in the slope-intercept form

\(y=mx+b\)

where m is the slope and b is the y-intercept

y=-3x + 4

Here,

m = -3

b = 4

3y = -9x+ 12

dividing both sides by 3

y = -3x + 4

Here,

m = -3

b = 4

As both equations have the same slope and y-intercept 'b'. Thus, the system of equations has infinitely many solutions.

Now checking:

\(\begin{bmatrix}y=-3x+4\\ 3y=-9x+12\end{bmatrix}\)

substitute y = -3x+4

\(\begin{bmatrix}3\left(-3x+4\right)=-9x+12\end{bmatrix}\)

for y = -3x+4

Expressing y in terms of x

\(y=-3x+4\)

Thus, the solution would contain

\(y=-3x+4,\:x=x\)

We know that If the equation ends with a true statement, for instance, x = x, then the system has infinitely many solutions or all real numbers.

Thus, the system y=-3x + 4 and 3y = -9x+ 12 would contain infinitely many solutions.

Answer:

40.6

35.9

i heop the answer is right

Answer:

Below

Step-by-step explanation:

See attached image below

Answer:

163/500

Step-by-step explanation:

we will not only clearly explain how to get the answer to 0.326 as a fraction, but also prove to you that our answer is correct.

First, note that 1000 multiplied by .326 will get rid of the decimal point. Therefore, make a fraction where the numerator is .326 times 1000 and denominator is 1000 like this:

.326 x 1000

1000

Next, multiply the numbers in the numerator together and keep the denominator as is. Now our fraction looks like this:

326

1000

The greatest common factor of 326 and 1000 is 2, which means you can divide the numerator and denominator by 2 and keep the same value:

326 ÷ 2

1000 ÷ 2

And when calculating the numerator and denominator in our fraction above, we get .326 as a fraction in the simplest form possible:

.326 =

163

500

Answer:

240 ft^2

Step-by-step explanation:

10*18=180

20*6=120

120/2 = 60

180+60=240

the surface area of the rectangular prism is 348 inches²

The surface area of a rectangular prism is given by: SA = 2 (lh +wh + lw ) Square units.

Given here: A rectangular prism with dimensions are 6 in.

We know the surface area of a prism is given by

2(wl+hl+hw)

where l is the length , w is width and h is the height.

Thus Surface area A=2(wl+hl+hw)

2·(8·6+9·6+9·8)=348

Thus the surface area of the rectangular prism is 348 inches²

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Answer:

All whole numbers are integers, so since 0 is a whole number, 0 is also an integer.

Answer:

yes

Step-by-step explanation:

integers are whole numbers and 0 is a whole number so yes

Answer:

10

Step-by-step explanation:

Because 5 + 5 is 10, so 1/2 of 10 + 1/2 of 10 = 10

Answer: D)14

Step-by-step explanation: The x-factors are both -3 but the y-factors are different so you count the distance between them

Answer:

No

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

   First of all, an irrational number is any number that can be changed into a fraction.

    As you can see here, 4/3 is a fraction but some fractions, such as 4/2 or 12/3, can be simplified into integers, like 2 and 4. 4/3 is 1.5, and decimals are not integers, the biggest subset inside the set of rational numbers.

Irrational numbers are pi, square roots, etc.

Hope this helps!