Question 2
What are the rational roots of P(x) = x³ + 2x - 1?

O x = 1, x = -1
O x = 1, x = 0
O x = 1, x = 2
O This polynomial has no rational roots.

Step 1

Given; What is the precise definition of a limit in calculus?

The required definition is;

Answer;

Let f be a function defined on some open interval containing a (except possibly at a).

Then the limit as x approaches a of f is L written as;

if and only if

Answer:   Take the help of the Percentage Difference From X to Y Calculator to evaluate the increase/decrease from 105 to 125 is 19.0476% on dividing the absolute value with the average value and multiplied by 100.

Step-by-step explanation:

Hope Fully this helps you

X+1 depicts horizontal linear equation as x = -1 and slope = 0.

Given that the slope is 0, it shows a horizontal linear equation.

Every point on a horizontal line has the same y-coordinate.

If two points have the same y coordinate, b, then the line's equation is y=b.

The y-intercept of the horizontal line y=b is the point (0,b). The line y=0 is the only x-intercept for horizontal lines.

Horizontal lines have zero slope.

As a result, in the slope-intercept equation y = mx + b, m = 0. The equation is Y = b, where b is the y-coordinate of the y-intercept.

A line that is perpendicular to the x-axis is referred to as a horizontal line.

The graph of a relation of the form x = 5 is a line parallel to the origin since the value of x never changes.

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Based on the given task and the percentage of quarters in the coins, the total number of coins is 80 coins.

To calculate the total coins;

Let

Then, you will

Percentage of quarters = Number of quarters

15% of x = 12

15/100 × x = 12

0.15 × x = 12

0.15x = 12

x = 12 / 0.15

x = 80 coins

In conclusion, the total number of coins is 80 coins.

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The means are the same and the standard deviations are different.

There are two lists given for which the means and the standard deviations need to be compared. So we first find the mean and standard deviation of each list one-by-one using the formulas,

Mean = (1/n)∑x

Variance = [(1/n)∑x²]- mean²

Standard deviation = √variance

List A  

x:  1      2     3      4     5      6

x²: 1      4     9    16    25     36

n = 6

Mean = (1/6)[1+2+3+4+5+6] = 21/6 = 3.5

Variance = 1/6[1+4+9+16+25+36] - 3.5² = 15.167-12.25 = 2.917

Standard deviation = √2.917 = 1.71

List B

x:  2    3    3     4     4    5

x²: 4    9    9    16   16   25

Mean = 1/6(2+3+3+4+4+5) = 21/6 = 3.5

Variance = 1/6(4+9+9+16+16+25)-3.5² = 13.167 - 12.25 = 0.917

Standard deviation = √0.917 = 0.9576

Hence the means are the same and the standard deviations are different.

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Answer:

angle A: 75 degrees

Step-by-step explanation:

because m and n are both 180 degree angles so when you do 180-105 you get 75

a,d,e,h=105 degrees

b,c,f,g= 75

because 105+75=180

When the function f is transformed to g, the equation is -45.5x

The equation of function f is given as

f(x) = 6.5x

The transformation is given as

The above transformation rule can be represented as

(x, y) = (-x, 7y)

When the above rule is applied, we have the following equation

g(x) = -7f(-x)

So, we have

g(x) = -7 * 6.5x

Evaluate

g(x) = -45.5x

The above equation is a linear function

So, the domain and the range are the set of all real values and the y-intercept is 0

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The z-scores that are the cutoffs are given as follows:

a. z = 1.645.

b. z = -1.96.

c. z = -0.51.

d. z = 0.

e. z = 0.

The z-score of a measure X of a variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, we have that:

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The non real roots of the polynomial x³ – 7x² + 15x – 25 = 0 are; 1 + 2i, 1 – 2i

Non real roots are simply imaginary roots.

We are told that the real roots of the equation  x³ – 7x² + 15x – 25 = 0 is 5.

Now, it means that (x - 5) is a factor of the given polynomial. Thus, we can factorize the polynomial as;

(x - 5)(x² - 2x + 5) = 0

Now, to find the non - real roots, we will use quadratic formula on (x² - 2x + 5) to get;

x = [-(-2) ± √((-2)² - (4 * 1 * 5))]/2(1)

x = (2 ± √(-16))/2

x = 1 ± 2i

x = 1 + 2i, 1 – 2i

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Answer:

c

Step-by-step explanation:

Answer

2

Step-by-step explanation:

1 + 1 =2

In Mrs. Brown’s 75% percent of the class likes to dance .

What are mathematics operations?

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Given:

number of students in Mrs. Brown’s class = 24

number of students likes to dance = 18

Then to find the percent of the class likes to dance we divide 18 by 24 and multiply with 100:

percent of the class likes to dance = (18/24) x 100

percent of the class likes to dance = 75%

Therefore,  in Mrs. Brown’s 75% percent of the class likes to dance .

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Answer:75%

Step-by-step explanation:

number of students in Mrs. Brown’s class = 24

number of students likes to dance = 18

Then to find the percent of the class likes to dance we divide 18 by 24 and multiply with 100:

percent of the class likes to dance = (18/24) x 100

percent of the class likes to dance = 75%

Therefore,  in Mrs. Brown’s 75% percent of the class likes to dance.

Answer:

Yes.

Step-by-step explanation:

Divide 430/17 and you get around 25, signifying the correct answer is right in the middle of Hailey's estimation.

The ratio is 1:8 and 1:64

Since each tile is one sixth of an inch in width and one fourth of an inch in length.

That is L1= 1/4  in addition to W1= 1/6 inches.

The real tiles are one sixth of a foot long and one tenth of a foot wide.

Since 1 foot equals 12 inches, that is in inches and inches. that is L2=2 and W2= 4/3

So, the length of the tile divided by its real length is equal to L1/L2

=(1/4)/2= 1/8

In addition, the relationship between the area of the tile in the model and the real area is given by:

(1/4 x 1/6)/ 2 x 4/3

= 1/64

Second method

Since there is a 1/8 ratio between the width of the model's tiles and their real width

As a result, there is dilatation with a scale factor of 1/8.

By virtue of dilatation, their area ratio = (1/8)^2 =1/64.

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Answer:

Step-by-step explanation:

c lol

A list of fixed fees for services recorded on the encounter form is called the Superbills.

The purpose of encounter forms, often referred to as super bills, is to "document services performed by recording the diagnostic and procedure codes, which serve as the foundation for billing and receipt of payment for services." Every time a patient or customer receives a service, the provider records that service, often into medical claims software that may automate much of the subsequent procedure.

This technique entails coding (procedure codes and, if necessary, diagnostic codes), billing/invoicing, and/or transmission to the patient's or client's insurance provider. For the client's health and treatment plans as well as for proper billing, it is crucial to make sure that the appropriate information is documented. This is why encounter forms are such a crucial component of healthcare.

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Answer:

18.23

Hope this is right! (don't worry I did the math)

While traveling to his grandmothers for Christmas, George had been asleep for 50% of the entire journey and this distance is found by reviewing the information given to us.

The length of the entire journey taken to get from one point to another is the distance travelled. Travel distance is not a vector. It has no orientation.

In this question,

Let us take that George had been asleep for x distance.

Then according to question, we can form the equation

3/4 = 1/2x + x

3/4 = 3x/2

x = 1/2

so, the total distance travelled is 50% of the entire journey.

Displacement is the straight path between the initial and final points, whereas distance travelled is the actual length the body covers.

The International System of Units defines a meter as the distance unit.

How can velocity be used to calculate distance travelled?

Finding the area under the velocity, in particular when velocity is positive on an interval, allows us to determine the total distance travelled.

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Answer:EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Step-by-step explanation:

The mode for the number of customers counted by Lowes entering the store for the week is 1100.

The mode of a data is that with the highest frequency.

According to Lowe's counts, we have the following data:

There are three 1100 in the seven data counted by Lowes

we will notice after careful observation that we have more of the data 1100 with the highest frequency of 3 out 7 data counted.

Thus, we can conclude from our understanding that the mode of the data which is that with the highest frequency is 1100.

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To find the final cost of the sales tax you need to:calculate the tax

As the sales tax is 9.75% you calculate the 9.75% of $200.00

The equation of the line perpendicular to 12y = 2x + 10 and passing though the point (-2,-1) is  y = -6x -7.

Writing the equation  12y = 2x + 10 in slope intercept form, we get,

y = (1/6)x + 5/6

The slope of the line is 1/6.

We know that,

Product of slope of two lines perpendicular to each other = -1.

Let the slope of the line perpendicular to the given line be m.

Hence, we can write,

m*(1/6) = -1

m = -6

Let the line perpendicular to the given line be y = mx + c.

It is given that the line perpendicular to the given line goes through (-2,-1).

Hence, we can write,

-1 = -6.(-1) + c

-1 = 6 + c

c = -7

Hence, the slope-intercept form of the line perpendicular to the given line is y = -6x -7.

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Answer: a

Step-by-step explanation:

because 140 squared = 200x=48/4

The first and second graphs represent even function.

If f of x is equal to f of −x for all the values of x, then it is called Function. This implies that function is same for the positive x-axis and the negative x-axis. Trigonometric even function, and secant function are some of the examples of even function.

Following are the properties of an even function:

As the graph of first and second is symmetric about the y axis, therefore both represent even functions.

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Given the equation that

The expression

is equivalent to

then the answer is option D

Since the root and the exponent commute, this also can be written as

then the answer is option B

And by the same reason, this can be written as

then the answer is option E

Answer:

40

Step-by-step explanation:

2400 divided by 60 is 40

I hope this helps!

the equation of the line will be:

then

and we obtain

and making the subtraction, we have

which is the same as

Answer: see answers below

Step-by-step explanation:

F(x) is bascially the y

the absolute value means any numbers that you use for x when substituted into x-2 will always be a positive number even if x-2 is negative as with any number 3 or greater, or any number -3 or less.  

for the values that are 0, 1, 2, 3, 4 or 0, -1, -2  the answer for f(x) will be a negative number.  All other numbers positive or negative for x will result in a positive answer.  

So you need to graph your line with an arrow on each end to show it goes to infinity.  in your chart you choose a number for x, and the f(x) number (which is equivalent to the y number for purposes of graphing.

I cannot draw on her a graph for you because I don't have that ability without an app for that.  

here are some sample points for your chart.  THe first number in each parenthesis is x and the second is f(x)

(-1, -2),  (-2, -1), (0, -3), (-3, 0), (1, -4), (2, -5), (3-4), (4,-3), (5-2), (6, -1)  All other numbers positive or negative for x will result in f(x) being positive.

You only need two sets of points to put on the graph to draw the line through.  

So negative values for f(x) can only be -1, -2, -3, -4, -5.   x can include all negative numbers through infinity.

Positive will include all positive numbers through infinity for x  and f(x).

F(x) cannot decrease beyond -5.   x can decrease all numbers  through infinity.

Equation of the line passing through the point of (-20, 4) and perpendicular to the line [(2x + 5y) = 10] will be [2y = (5x + 108)].

As per the question statement, a line passes through the point of (-20, 4) and is perpendicular to the line [(2x + 5y) = 10].

We are required to determine the equation of the above-mentioned line.

To solve this question, we need to know about the formula to express the point-slope form of a line, which goes as, [(y - y₁) = m(x - x₁)],

where (x₁, y₁) is a point through which the line passes, and "m" is the slope of the line.

Also, we need to know about the mathematical fact that, the product of the slopes of two perpendicular lines equate to (-1), i.e., if (m₁ and m₂) are the slopes of two perpendicular lines, then [(m₁ * m₂) = (-1)].

Converting [(2x + 5y) = 10] into the point-slope form of line, we get,

(2x + 5y) = 10

or, [5y = {(-2x) + 10}]

or, [y = {(-2/5)x + 2}]

Therefore, Slope of the line [(2x + 5y) = 10] is (-2/5).

Hence, slope of the line perpendicular to [(2x + 5y) = 10] is [-1/(-2/5)], i.e.,

Slope of the line perpendicular to [(2x + 5y) = 10] is (5/2).

Now, using [m = (5/2)] and (x₁, y₁) as (-20, 4), equation of the line will be

[(y - 4) = (5/2){x - (-20)}]

or, [(y - 4) = (5/2)(x + 20)]

or, [(y - 4) = (5/2x) + 50]

or, [2(y - 4) = 5x + 100]

or, [(2y - 8) = (5x + 100)]

or, [2y = (5x + 108)]

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