What are the three types of solutions to a system of linear equations in two variables?

The required answers are:

a. The linear approximating polynomial at a = 1: P₁(x) = x - 2

b. The quadratic approximating polynomial at a = 1: P₂(x) = -3 + 3x - x²

c. Appromating the given quantity -1/1.06 for P₁(x) and P₂(x): -3.06 and -7.30 respectively.

Using Taylor polynomial series, the required approximating polynomials are calculated.

The Taylor polynomial series is

Pₙ(x) = ∑ [tex]\frac{f^n(a)}{n!}[/tex](x - a)ⁿ; limits from 0 to n

Where fⁿ(a) is the nth derivation of f(x) at a

The first order(linear) Taylor polynomial series is

P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹

The second order(quadratic) Taylor polynomial series is

P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) +  [tex]\frac{f''(a)}{2!}[/tex](x - a)²

The given function is f(x) = -1/x at a = 1

f(a) = f(1) = -1

f'(x) = -(-1/x²) = 1/x²; f'(a) = f'(1) = 1

f''(x) = -2/x³; f''(a) = f''(1) = -2

a. Linear approximating polynomial:

From the Taylor series, we have

P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹

On substituting,

P₁(x) = -1 + (1/1!)(x - 1)¹

       = -1 + (x - 1)

       = x - 2

b. Quadratic approximating polynomial:

From the Taylor series, we have

P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) +  [tex]\frac{f''(a)}{2!}[/tex](x - a)²

On substituting,

P₂(x) = f(1) + (1/1!)(x - 1) +  (-2/2!)(x - 1)²

        = -1 + (x - 1) - (x - 1)²

        = -1 + x - 1 - (x² - 2x + 1)

        = x - 2 - x² + 2x - 1

        = -3 + 3x - x²

c. Approximating the given quantity -1/1.06:

Substituting x = -1.06 in P₁(x) and P₂(x),

P₁(x) = x - 2

⇒ P₁(-1.06) = (-1.06) - 2 = -3.06

P₂(x) = -3 + 3x - x²

⇒ P₂(-1.06) = -3 + 3(-1.06) - (-1.06)² = -7.30

Therefore, the approximating polynomials are calculated by using Taylor polynomial series.

Disclaimer: The given question is incomplete. Here is the complete question.

Question:

a. Find the linear approximating polynomial for the following function centered at the given point a.

b. Find the quadratic approximating polynomial for the following function centered at the given point a.

c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.

f(x) = -1/x , a = 1; approximate -1/1.06

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19 books can fit into a bookshelf that has a width of 19/4 feet

An equation is an expression that shows the relationship between two or more number and variables.

The bookshelf is 4 3/4 feet wide = 19/4 feet

1 ft = 12 in, hence:

19/4 feet = 19/4 feet * 12 in per feet = 57 inches

Number of books = 57 inches / 3 in = 19

19 books can fit into a bookshelf that has a width of 19/4 feet

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When sampling with replacement is used, an element that has already been chosen is put back into the sample frame and given the chance to be chosen again.

In the case of sampling without replacement, an element is eliminated from the sample frame after it has been chosen.

In this question, we are supposed to state the differences between sampling with replacement and sampling without replacement.

Generally speaking, sampling without replacement is more effective than producing representative samples using replacement sampling. It prevents the inclusion of the same population element in the sample several times.

By "drawing from a hat" or by using a computer program that simulates the same process, you select the sample at random using the lottery method.

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The equation of the unique function exists g(x) = -4(x-3)².

The polynomial of degree two exists named a quadratic polynomial and the equation corresponding to a quadratic polynomial P(x) exists named a quadratic equation.

Given: F(x) = x²

The vertical stretch by a factor of 4 exists can be satisfied by (b)

if we use a vertical stretch, it transforms the y-values which causes it to seem skinnier when graphed.

Multiply 4 by f(x) which provides 4x².

As the reflection over the x-axis, so multiply it by -1 to f(x), which results in -4x².

Shift the graph right 3 which exists by moving it right, so by adjusting the x values indicating use f(x-3), to obtain this subtract the value from x when you move right, and add the value to x when you move left.

Hence, the unique graph would be g(x) = -4(x-3)²

Therefore, the correct answer is option B. g(x) = -4(x-3)².

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Considering the definition of the absolute value function, the expression is written as -7m + 56.

The absolute value function is defined as follows:

That is, where the expression is negative, it is multiplied by -1, while where it is not negative the expression is kept.

In this problem, the expression is:

|7m - 56|

For m < 8, we have that one example is m = 0:

7(0) - 56 = -56.

The expression is negative, hence the signal is changed, that is:

|7m - 56| = -(7m - 56) = -7m + 56.

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Using translation concepts, the equation of F(x) is:

A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The parent function is:

[tex]G(x) = x^4[/tex]

For function F(x), we have that:

Then the equation is:

A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]

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The transformation of the coordinate (-8, -3)  R 270° and T-2,-1 is (-5, -9)

Transformation is the change of the coordinates of a shape either by rotation, reflection or translation.

Analysis:

When coordinates (x, y) rotate 270° the resulting coordinates become (-y, x)

so coordinates (-8, -3) after 270° rotation becomes ( 3, -8)

When it is translated 2 units to the left and 1 unit down, that is -3 + -2 = -5 and -8 + -1 = -9

Therefore the transformed coordinate becomes (-5, -9)

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Answer: D

Step-by-step explanation:

sorry if its wrong

From the conversation it can be inferred that Paul's approach to getting on the horse is methodical (option c).

A methodical attitude or behavior refers to the preference of people to use an organized method and sequences to perform an activity correctly.

According to the above, it can be inferred that Paul behaves in a methodical manner because he prefers to relate to the horse slowly and in a controlled manner before proceeding to mount it.

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A factor of the polynomial function is (d) x + 4

The solution of the cubic function f(x) are given as:

−4, 5/3, and 1.

This means that:

x = -4, x = 5/3 and x = 1

Set the above equations to 0

x + 4 = 0, x - 5/3 = 0 and x - 1 = 0

From the list of options, we have

(d) x + 4

Hence, a factor of the polynomial function is (d) x + 4

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Answer:

11.2 square meters

Step-by-step explanation:

This is a very simple question. Basically, it's the area of a rectangle with the area of a circle subtracted. The area of a circle is calculated with the following formula:

[tex]\pi \times r^{2} [/tex]

Where r is the radius. We know the diameter is 1m, so we can simply halve this value to find the radius of 0.5m. Substituting in this value, we find the area of the circle to be:

[tex]\pi \times {0.5}^{2} \approx0.78539816339744830961566[/tex]

Now let's calculate the area of the rectangle, which is simply 3x4=12. Subtracting our earlier value from 12, we are left with an answer of 11.2 (to 1 d.p)

Answer: 0=-4.9t²+19.6t+24.5

Step-by-step explanation:

[tex]s(t)=gt^2+v_0t+s_0\\v_0=19,6\ \frac{m}{s} \ \ \ \ s_0=24,5\ m\ \ \ \ g=-4,9\ \frac{m}{s^2} \ \ \ \ S(t)=0\ (the\ object \ hitts\ the \ ground)\ \Rightarrow\\0=-4,9t^2+19,6t+24,5.[/tex]

You have fifteen blankets that each take up 557 cubic inches of space. In a 14-inch moving box, we can pack approximately 5 blankets.

The Volume that can take up by single blanket is 557 cubic inches.

The dimension of the moving box = 14 × 14 × 14

Hence, the volume of the moving box = 2744 cubic inches

The total number of blankets that can be packed in the given moving box = 2744/557 = 4.92 ≅ 5

Therefore, in a 14-inch moving box, there can be 15 blankets with 557 cubic inches of space of each can be packed.

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Answer:G

Step-by-step explanation:

4/9 times 2/8= 1/9

Answer:

G 1/9

Step-by-step explanation:

add all of the cards together that will get you 9 then you take the hearts overing it by total then times it by 2 overing by 8 or

4/9x2/8

A)f(x)=3/5 and -1.

B)f(x)=(3/5, 0) and (-1, 0).

C)f(x)=(-0.2, -3.2)

D)f(x)= = -0.2.

Function: f(x) = 5x² + 2x-3.

a) Completely factor f(x)

  f(x) = 5x² + 2x-3.

        = 5x² + 5x-3x − 3

         = 5x(x+1)-3(x+1)

         =(5x-3)(x+1)

f(x)=3/5 and -1.

b)The x-intercepts of the graph of f(x):

    f(x) = 5x² + 2x-3.

At f(x) = 0, the x-intercepts are present.

Therefore, x-intercepts are (3/5, 0) and (-1, 0).

c) The end behavior of the graph of f(x):

      f(x) = 5x² + 2x-3.

The middle of the zeros is the vertex's x-coordinate.

           =-0.2

Find the y-coordinate of the vertex, and substitute the found value of x into the given equation:

   f(-0.2)= 5(-0.2)² + 2(-0.2) − 3

           =-3.2

d)The steps you would use to graph f(x):

The axis of symmetry is the x value of the vertex.

Therefore, the graph is symmetrical at about x = -0.2.

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The required probability is 0.171.

What is probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We can find required Probability as shown:

From 10 coins we choose 7 he guessed correct with probability of each 1/2. For three remaining coins he failed to predict the outcomes of the flip with the probability of 1/2 for each. Similarly for 8,9 or 10 successive trials. Let X denote number of successive trials

[tex]P(X\geq 7)= \tbinom{10}{7}.\frac{1}{2^{10}}+\tbinom{10}{8}.\frac{1}{2^{10}} +\tbinom{10}{9}.\frac{1}{2^{10}}+\tbinom{10}{10}.\frac{1}{2^{10}}[/tex]

[tex]=120.\frac{1}{2^{10}} +45.\frac{1}{2^{10}} +10.\frac{1}{2^{10}} +.\frac{1}{2^{10}}[/tex]

[tex]=\frac{120+45+10+1}{2^{10}}[/tex]

[tex]=\frac{176}{1024}[/tex]

=0.171

Hence, the required probability is 0.171.

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Given question is incomplete. This is complete question:

A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?

The linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:

C(m) = 0.08316m + 31.36331

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (x,y) are given as follows:

(225, 50.3), (1100, 111), (1375, 143), (1675, 187), (1950, 214), (2250, 196).

Hence, inserting these points in the calculator, the linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:

C(m) = 0.08316m + 31.36331

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$6.12

A percentage is some portion of a whole number. Multiple methods can be used to find percentages.

Multiplication to Find Percentages

One of the easiest ways to find percentages is to multiply the original number by a decimal. To do this, one first needs to turn the percentage into a decimal.

For example,

To convert a percentage to a decimal, just move the decimal point 2 places to the left.

Then, multiply this decimal by the whole number, and the answer, in this case, will be the tip.

19% of $32.20

Now, to solve we can just multiply.

The exact answer is 6.118. However, since we are using money, we are going to round to the nearest hundredth place. This gives the final answer of $6.12.

The least and greatest amounts that the two friends could spend on food are 100 and 140 respectively

Functions and values

Functions are expressions written in terms of letters known as variables. Given the equation that represents the food budget of two friends as shown;

1/2(x-120)=10

where x is the amount spent on food.

In order to determine the least and greatest amounts that the two friends could spend on food,

For the least amount

-(x-120) = 20

-x+120 = 20

x = 100

For the greatest amount

(x-120) = 20

x = 140

Hence the least and greatest amounts that the two friends could spend on food are 100 and 140 respectively

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The statements that are  true about this study are

This is further explained below.

Generally, a scientific technique is used to create a discovery, test a theory or show an established truth.

In conclusion, The following are accurate claims concerning this study:

Random sampling is used in this investigation. In this investigation, a control group is used. Repeated measurements are employed in this investigation.

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The number that is represented by the question mark in the sequence is 2

Sequence are set of numbers that follow a predefined and predetermined patterns guided by a rule

The sequence of numbers is given as:

111= 0, 3213=0,

7756= 1,  7662= 2,

6855= 3,   8096= 5,

6666=4  8193= 3,

9313= 1,   8639= 4,

1234=0,   2581 = 2,

7186= 3,  2(6)7(9)=

From the complete question, the values of the sequence are determined by the count of numbers that are circled or in brackets

In the 2(6)7(9), two numbers are circled.

The numbers are 6 and 9

This means that the value of 2679 is 2

i.e. 2(6)7(9)= 2

Hence, the number that is represented by the question mark in the sequence is 2

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Total slack is calculated by the late finish minus early finish and the late start minus the early start

Total slack is simply the amount of time taken for a task to be delayed before the project finish date is delayed. It can be positive or negative.

It is calculated as the calculated as the value of the Late Finish minus the Early Finish field, and the Late Start minus the Early Start field.

Total slack = Late finish - early finish + late start - early start

Thus, the total slack is calculated by the late finish minus early finish and the late start minus the early start.

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The correct option is a) -0.15.

The weakest correlation relationship between two variables is given by -0.15.

With the aid of correlation, the strength of the relationship between two variables can be determined. We can tell from this study whether there is no correlation, weak correlation, or a strong correlation between the two variables.

Two different types of correlation exist:

The correlation value (r) always lies between -1 and 1.

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The complete question is -

Which of the following is the weakest correlation relationship between two variables?

a) -0.15

b) 0.27

c) -0.70

d) 0.55

The measure of segment AD in the similar triangle is 45.07 mm

Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. Also, their corresponding angles are congruent.

Triangle FEA and triangle ABC are similar triangles by the angle angle similarity postulate, therefore:

13/AD = 15 / (15 + 37)

AD = 45.07 mm

The measure of segment AD in the similar triangle is 45.07 mm

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Based on the calculations, the maximum price per share that Schultz should pay for Arras is approximately equal to $53.00.

First of all, we would determine the cash flows for the company until the growth rate changes at a constant perpetual rate:

Year 1: $8,000,000(1 + 0.09) = $8,720,000.

Year 2: $8,720,000(1 + 0.09) = $9,504,800.

Year 3: $9,504,800(1 + 0.09) = $10,360,232.

Year 4: $10,360,232(1 + 0.09) = $11,292,652.88.

Year 5: $11,292,652.88(1 + 0.09) = $12,308,991.6392.

Year 6: $12,308,991.6392(1 + 0.06) = $13,047,5311.137552.

Next, we would calculate the terminal value in Year 5:

TV₅ = CF₆/(RWACC - g)

TV₅ = CF₆/(0.11 - 0.06)

TV₅ = $12,308,991.6392/0.05

TV₅ = $246,179,832.784.

By using Arras' cost of capital, we would determine its present value:

V₀ = $8,720,000/(1 + 0.11) + $9,504,800/(1 + 0.11)² + $10,360,232/(1 + 0.11)³+ $11,292,652.88/(1 + 0.11)⁴+ ($12,308,991.6392 + $246,179,832.784)/(1 + 0.11)⁵.

V₀ = $8,720,000/(1.11) + $9,504,800/(1.11)² + $10,360,232/(1.11)³+ $11,292,652.88/(1.11)⁴+ ($12,308,991.6392 + $246,179,832.784)/(1.11)⁵.

V₀ = 7,855,855.8559 + 7,714,308.9035 + 7,575,312.3467 + 7,438,820.2323 + 153,400,536.1422.

V₀ = $183,984,855.4806.

For the market value of the equity, we have:

S = 183,984,855.4806 - 25,000,000

S = $158,984,855.4806.

Now, we can find the maximum price per share:

Maximum price per share = 158,984,855.4806/3,000,000

Maximum price per share = $52.9949 ≈ $53.00.

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Hence, the age of his brother when brain is [tex]11[/tex] is [tex]19.[/tex]

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

Brian is [tex]8[/tex] and his brother is twice his age.

As age of brain is [tex]8[/tex].

His brother is twices than his age is [tex]8(2)=16[/tex]

When the age of brain is [tex]11[/tex] then [tex]3[/tex] added to his present age.

Then the age of his brother is [tex]16+3=19[/tex]

Hence, the age of his brother when brain is [tex]11[/tex] is [tex]19.[/tex]

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The percent of the time Nicholas earned is the percent of the time 25%

The 5 values of the given box plot are;

The minimum fee = 20

In the first quartile, the 25th percentile point, Q₁ = 25

In the median or second quartile, the fiftieth percentile factor, Q₂ = 30

The 1/3 quartile, the 75th percentile point, Q₃ = 40

The maximum value = 55

The range = The most value - The minimal fee

The range = 55 - 20 = 35

We are aware that Nicholas earned $25 or less from the minimum value up to the first quartile, Q₁, which is the 25th percentile point, in which we've got 25 percent of the statistics points.

Consequently, the percentage of the time Nicholas earned $25 or much less is 25 percent of the time.

In mathematics, a percentage is a variety of ratios that can be expressed as a fraction of 100. If we have to calculate the percent of various, divide the wide variety by way of the whole and multiply by way of a hundred. For this reason, the shared approach is a component in line with a hundred. The phrase according to cent means in keeping with one hundred.

A relative cost indicates the hundredth component of any amount. One percent (symbolized 1%) is the hundredth part; for this reason, a hundred percent represents the whole lot and two hundred percent specifies two times the given amount.

Multiply the entire number amount through the decimal equal to the proportion. The end result is the share portion quantity. (consequently, this answers the question “How a whole lot is 24 percentage of 500,” you examine that 24 percent of 500 is a hundred and twenty).

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Answer:

Your answer should be 52!!

Step-by-step explanation:

Work included on the picture below.

Answer:

B.

Step-by-step explanation:

If the measures of angles 3 and 4 add to 90, then lines r and p meet at right angles making them perpendicular.

Answer: B.

Answer:

Step-by-step explanation: