Determine the following limits: and lim 6-x-2 lim 22/3-X-1 Then the correct answers are: 3- x 2}+1 (1) 2 and -2 (2) į and - 2 (3) 6 and 3 (4) None of the above. (5) 2. Determine the following limit: - 5x² - 2x 12 + 5x + Then the correct answer is: (1) 0 (2) Does not exist (3) -5 (4) None of the above. (5) 3. Determine the following limit: lim sinºx-1 sinx-1 Then the correct answer is: (1) 12 / 2 (2) 18 MAT1512/101 (3)-1 (4) None of the above. (5) Determine the following limit: |25-xl lim -+-+*(X+5) Then the correct answer is: (1) - (2) 1 (3) Does not exist (4) None of the above. 5) (5) 5. Determine the following limit: limh(x) if x<4 (2x² -8 3 where h(x)= 2x if x24 Then the correct answer is: (1) 2 (2) 8 - (3) 8 (4) None of the above. (5) The following Questions from Question 6. below, to Question 11, below, refer to the function h below: Let h be a function defined as: 19 MAT 1512/101/0/2022 8-x if x<0 h(x)= x if 02 6. :-p Determine the following limit: limh(x) Then the correct answer is: (1) 0 (2) 8 (3) 2 (4) None of the above. (5) 7. Determine the following limit: lim h(x) Then the correct answer is: (5) (1) 0 (2) 8 (3) 2 (4) None of the above. Determine the following limit: limh(x) Then the correct answer is: 8 (1) 0 (2) 8 (3) Does not exist. (4) None of the above. (5) 9. Determine the following limit: limh(x) Then the correct answer is: (1) 2 (2) 8 (3) 6 (4) None of the above. 5 (5)

4 numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one pair of these numbers add up to 7.

The expression of a principle abstractly :

Let x and y be the finite sets and let be a function.

Given,

Set = {1, 2, 3, 4, 5, 6}

2 element pair with sum of 7 = {(1,6),(2,5),(3,4)}

Choosing 1 element from each pair = 4 [either {1,2,3,4} or {6,5,4,3}

Hence, there are 4 pairs that add to 7.

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Answer:

x+46

Step-by-step explanation:

Distribute

Combine like terms

Answer:

A is 2,8 and b is 2,3

asked my teacher

Step-by-step explanation:

Answer:

A

Step-by-step explanation

B. is slope intercept formula

Answer: it is already factored

Step-by-step explanation:

Answer:

540 minutes

Step-by-step explanation:

Create expressions to represent the costs of both service plans, where x is the number of minutes of calls:

0.12x + 27 will represent the first one

0.17x represents the second one

Then, set them equal to each other. Solve for x to find how many minutes of calls will make the prices equal.

0.12x + 27 = 0.17x

27 = 0.05x

540 = x

So, the costs of the 2 plans will be equal after 540 minutes.

Answer:

Output equals imput minus 6

Step-by-step explanation:

First, we know that -2 is 1 of the Imputs.

Then we know 8 is the second Output

8 - (-2) so that means it would be minus 6 Imput.

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Output equals input times 4 is the function rule from the values in the table.

Looking at the values in the table, we can identify the function rule by analyzing the relationship between the input and output values.

The output values are obtained by applying specific operations to the input values.

Let's examine each statement and see which one matches the given input-output pairs:

Output equals input times -4:

When we multiply the input values by -4, we get the following output values:

\(-2 \times -4 = 8\)

\(0 \times -4 = 0\)

\(1 \times -4 = -4\)

\(3 \times -4 = -12\)

This function rule matches the given input-output pairs.

Therefore, the function rule that matches the values in the table is "Output equals input times -4."

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The formula or equation used to determine the slope of a straight line is as follows:

m = (Y₂-Y₁)/(X₂-X₁)

An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

Equations can be graphed, they are used to model many problems and theories.

The straight lines are characterized by a finite succession of points, when they have an inclination they adopt a slope value different from 0, and to determine that slope it is necessary to know two points of the line and use the following equation:

m = (Y₂-Y₁)/(X₂-X₁)

Where the points are:

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Answer:

"Games played in a workplace environment to achieve status, advancement and money"

The percentage of ball that hit into the outfield would be represented by the equation = 15/8 = X/100. That is A.

The total number of balls that that where present at the battling practice by Alexis = 15.

The number of balls that hit into the outfield = 8

The number of balls that hit outside the outfield = 15-8= 7

The percentage (x) of the balls that are outside the outfield;

X = 8/15 × 100/1

x ×15 = 8 × 100

15/8 = X/100.

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Answer:

Side FG, Side DF, Side DG

Step-by-step explanation:

The angles of a triangle add up to 180° and since we know 2 of the angles add up to 110° the missing ∠G can be found by subtracting

180°-110°=70°

The opposite side of the largest angle is the largest side. The opposite is also true.

Since the angle from greatest to least is ∠D, ∠G, ∠F then the sides from greatest to least is Side FG, Side DF, Side DG

he has 90 more then he originally had

Step-by-step explanation:

The probability to the nearest hundredth that a point chosen randomly inside the rectangle is either in the circle or in the square is \(P = (πr^2 + (min(L, W))^2) / (L * W)\).

To determine the probability that a point chosen randomly inside the rectangle is either in the circle or in the square, we need to consider the relative areas of the circle and the square.

Let's assume the rectangle has dimensions of length L and width W. If the circle is inscribed inside the rectangle, its diameter will be equal to the shorter side of the rectangle (min(L, W)). The radius of the circle is then half of the diameter, which is r = min(L, W)/2.

The area of the circle is A_circle = \(πr^2\), and the area of the square is A_square = \((min(L, W))^2\).

To find the probability, we divide the sum of the areas of the circle and the square by the total area of the rectangle:

P = (A_circle + A_square) / (L * W)

Substituting the formulas for A_circle and A_square:

\(P = (πr^2 + (min(L, W))^2) / (L * W)\)

Calculating this expression will give us the probability to the nearest hundredth that a randomly chosen point inside the rectangle is either in the circle or in the square.

Therefore, to determine the probability that a randomly chosen point inside a rectangle is either in a circle or a square, we calculate the sum of the areas of the circle and the square and divide it by the total area of the rectangle.

The probability is given by \((πr^2 + (min(L, W))^2) / (L * W)\), where r is the radius of the inscribed circle and L and W are the dimensions of the rectangle. Evaluating this expression will provide the desired probability to the nearest hundredth.

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1. (1 / 5)5 * 14 = 14 because 1/5 multplied by 5 is equal to 1. I believe this is called reciprocals.

2. 6 + 4 (19 - 5) = 6 + 4(19) - 4(5) = 6 + 76 - 20 = 62. This is called the distributive property.

3. 5 (14 - 5) + 6 (3 + 7) = 5(14) - 5(5) + 6(3) + 6(7) = 70 - 25 + 18 + 42 = 105. We also used the distributive property in this question.

Answer:

m=-1/3

Step-by-step explanation:

To find the slope you have to use the equation:y₂-y₁ divided by x₂-x₁

So you would have 3-4 divided by 0-(-3)

And then you would get -1/3

Answer:

-0.33333

//////Step-by-step explanation:///////

we have the equation

6a²=5+a

group terms

6a^2-a-5=0

solve using the quadratic formula

we have

a=6

b=-1

c=-5

substitute

the solutions are

a=1 and

a=-10/12=-5/6

therefore

answer is

Percentage change expresses the ratio of the change in the amount of an initial quantity to the initial quantity as a percentage.

Mathematically, the formula for percentage change, C, can be presented as follows;

\(C = \dfrac{x_{2} - x_{1} }{ x_{1} } \times 100\)

Where:C = The percentage change

\(x_{1} \) = The original value

\(x_{2} \) =The new value

Graphically, percentage change can be presented as follows;

When the number of fruits that drops from a three each month, changes from 10 to 8, the percentage change is therefore;

\( C = \dfrac{10-8}{10} = 20\% \)The percentage change is 20%

Initial number of fruits that drops monthly from the tree;

##########

The new number of fruits that drops from the tree on the specified month;

########

The difference in the number of fruits that drops from the tree is 2, which corresponds to the 20 % calculated for the percentage change.

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Answer:

She will learn 15 appetizer recipes.

Step-by-step explanation:

Here's why........because 2 weeks equals 5 so if you divide 6 and 2 you will get 3 and multiply that by 5 you get 15.

The Six Sigma process is a quality management approach that aims to reduce the number of defects in a process by identifying and eliminating the causes of variation. True.

It is a data-driven approach that seeks to improve the quality of products or services by reducing variability and increasing process efficiency.

One of the defining characteristics of the Six Sigma process is that it requires the specification limits to be set at least six standard deviations away from the mean of the process.

This means that the process is designed to produce products or services that are within the specifications with a high degree of certainty, as the chances of the output falling outside of the specification limits are very low.

The Six Sigma approach involves several steps, including defining the problem, measuring the process, analyzing the data, improving the process, and controlling the process.

It is a rigorous approach that requires the involvement of all levels of the organization and relies on statistical tools and techniques to identify and eliminate the causes of variation in the process.

The Six Sigma process has been widely adopted by many organizations in various industries, including manufacturing, healthcare, finance, and services, to improve their processes, reduce defects, and increase customer satisfaction.

It has proven to be an effective approach for improving the quality of products and services, reducing costs, and increasing profitability.

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Answer:

Option A will be your answer

Step-by-step explanation:

hope it helps ..

have a great day!!

The third equation and substituting a1 in terms of \(a0\), we can solve for \(a3\)in terms

To find the power series solution of the given differential equation (x² + 1)y" + xy' - y = 0 about the ordinary point x = 0, we assume that the solution can be written as a power series:

y(x) = \(a0 + a1x + a2x² + a3x³ + ...\)

We can then differentiate this power series twice to find expressions for y' and y'':

\(y'(x) = a1 + 2a2x + 3a3x² + ...\)

\(y''(x) = 2a2 + 6a3x + ...\)

We can then substitute these expressions into the differential equation and equate the coefficients of like powers of x to obtain a set of recursive equations for the coefficients. Specifically, we have:

(x^2 + 1)(2a2 + 6a3x + ...) + x(a1 + 2a2x + 3a3x² + ...) - (a0 + a1x + a2x² + a3x³ + ...) = 0

Expanding the terms and equating coefficients, we get:

\(a0 + 2a2\) = \(0\)

\(a1 - a0\) = \(0\)

\(2a2 + a1\) = \(0\)

\(6a3 + a2\) = \(0\)

Using the first equation, we can solve for \(a2\) in terms of \(a0\):

\(a2\) = -\(a0/2\)

Using the second equation, we can solve for \(a1\) in terms of \(a0\):

\(a1\) = \(a0\)

Using the third equation and substituting \(a2\) in terms of \(a0\), we can solve for \(a1\) in terms of \(a0\):

\(a1 = -a0/2\)

Using the fourth equation and substituting \(a2\) in terms of \(a0\), we can solve for \(a3\) in terms of \(a0\):

\(a3 = a0/24\)

Thus, the power series solution of the differential equation about x = 0 is:

y(x) = a0(1 -\(x^2/2\) + \(x^4/24\) - \(x^6/720\) + ...)

where a0 is an arbitrary constant.

To use the power series method to solve the initial-value problem y" – xy' - y = 0, y(0) = 2, y'(0) = -1, we assume that the solution can be written as a power series:

\(y(x) = a0 + a1x + a2x² + a3x³ + ...\)

We can then differentiate this power series twice to find expressions for y' and y'':

\(y'(x) = a1 + 2a2x + 3a3x² + ...\)

\(y''(x) = 2a2 + 6a3x + ...\)

We can then substitute these expressions into the differential equation and equate the coefficients of like powers of x to obtain a set of recursive equations for the coefficients. Specifically, we have:

\(2a2 + a0 = 0\)

\(a1 - a0 = -1\)

\(6a3 - a1 = 0\)

\(2a4 - 6a3 - a2 = 0\)

Using the first equation, we can solve for a2 in terms of a0:

\(a2 = -a0/2\)

Using the second equation, we can solve for a1 in terms of a0:

\(a1 = a0 - 1\)

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Answer:

m

Step-by-step explanation:

A graph which represents the solutions to this equation x² + 8x = -20 include the following: B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8).

In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.

Next, we would re-write the given quadratic function in standard form by equating it to zero (0) as follows;

x² + 8x = -20

Adding 20 to both sides of the linear-quadratic equation, we have the following:

x² + 8x + 20 = -20 + 20

x² + 8x + 20 = 0

In this scenario, we would use an online graphing calculator to plot the graph of the given quadratic function and then determine the point of intersection and vertex.

y = x² + 8x + 20

By critically observing the graph of the given quadratic function, we can logically deduce that the solutions and vertex are as follows;

x = -6, y = 8.

x = -2, y = 8.

Vertex = (-4, 4).

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Answer:

y = 3

Step-by-step explanation:

Linear Function:

y = mx + b

When X = 2, Y should equal 3

(2, 3)

When X = 4, Y should also equal 3

(4, 3)

Another way to ask this question if you are curious:

"Write a linear equation that passes through the points (2, 3) and (4 , 3)

Using the points though, we can use the slope formula equation to get the slope:

y2 - y2

----------

x2 - x1

-plug in the numbers from the points-

3 - 3

------

4 - 2

=

0 / 2

So the slope is going to be 0.

y = 0x + 3

y = 3

The pair adjacent angles are CAD and DAE

The pair of complimentary angles are BAC and CAD.

The pair of supplementary angles are BAD and DAE

The pair of vertical angles are BAC and FAE.

Adjacent angles are two angles which have common side and a common vertex.

Complementary angles are when two angles add up to 90 degrees.

Supplementary angles are when two angles add up to 180 degrees.

Therefore,

Adjacent angles are CAD and DAE

Complimentary angles are BAC and CAD.

Supplementary angles are BAD and DAE

Vertical angles are BAC and FAE.

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