give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles. the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are______.
a.adjascent angles
b.linear pair
c.congruent
d.intersecting

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

What is the property of slopes of parallel lines and perpendicular lines?

If two lines are given and they are parallel to each other then the slopes are equal and for perpendicular lines, the product of their slopes is equal to -1.

(7) The line AB is passing through the points (-1, 5/2) and (3/2, -1/2).

   Slope = y2 - y2/x2 - x1

              = (-1/2 - 5/2)/(3/2-(-1))

              = -6/5

   As line AB and line CD are parallel in nature so the slope of line CD is also -6/5.

(8) The line AB is passing through the points (1/2, 1) and (5/2, 5/2).

    Slope = y2 - y2/x2 - x1

              = (5/2 - 1)/(5/2-1/2)

              =3/2/2

             = 3/4

    Line CD is passing through points (1, 1) and (2, 3).

    Slope = y2 - y2/x2 - x1

              = (3 - 1)/(2-1)

              =2/2

             = 1

  As the product of their slopes is not equal to -1.

  So lines are neither parallel nor perpendicular.

(9) Slope of AB can be computed as (-2, 1) and (-5, 5)

     Slope = 5 - 1/-5 + 2

                = 4/-3.

  The slope of line passing through the point P = -4/3 as we have to draw the parallel line.

 Point P = (-1, 3)

Equation of the line :

      y - 3 = -4/3(x + 1)

    3y +9 = -4x - 4

   3y = -4x - 13

Now we can draw the line

(10) Slope of line AB = -4/3

    So the slope of the line passing through point P should be 3/4 in order to be perpendicular to line AB.

     Equation of the line passing through point P:

       y - 3 = 3/4(x - (-1))

       y - 3 = 3/4(x+1)

Hence,

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

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Answer:true, false, false, true

Step-by-step explanation:

As pre the concept of vector, div F is negative at P1 and divF is positive at P2.

In math the term vector refers the quantity that has both magnitude and direction but not position

Here we have to determine whether div F is positive or negative at P1 and at P2.

Let us consider if  div F(P)>0, the net flow is outward near P and P is called a source and if  div F(P)<0, the net flow is inward near P and P is called a sink.

Here by observing the graph of F, we have identified that the vectors end near the P1 are the larger than the vectors starts near the point P1,

So, the net flow is inward near P1 and div F is negative at P1

Where P1 is called a sink

Whereas, by observing the graph of F we have identified that the vectors end near P2 are shorter than the vectors starts near the point P2,

So, the net flow is outward and div F   is positive at P2 and the P2 is called a source

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The proof that  Δ SVW ≅ Δ UTW is given by ASA congruence criterion.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.

The symbol of congruence is’ ≅’.

Given:W is the midpoint of SU

⇒ SW = WUTU ⊥ SU and SU ⊥ SV

To prove:Δ SVW ≅ Δ UTW

Proof:In Δ SVW and Δ UTWSW = UW (given)

∠S ≅ ∠U (given)

∠ SVW ≅ ∠ UTW (vertically opposite angle)

Therefore, Δ SVW ≅ Δ UTW (by ASA congruence criterion)

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(x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

as the polynomial with rational coefficients that has zeros x=2 and x=3i

(x-2) and (x-3i) are factors of third-degree polynomial.

so ,

⇒(x-2)(x-3i)

solving (x-3i)

x = 3i

squaring both sides,

x² = -9

so , (x²+9) is a factor.

hence , (x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

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A true average strain in a way that converys information about precision and reliability (24.33, 27.67)

From given information we have:

the sample size n = 20

the mean failure strain x(bar) = 26.0

the standard deviation s = 3.4

Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.

A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.

c = 0.95 or 95%

In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.

Here, the degree of freedom :

df = 20 - 1

df = 19

and  α = (1-c)/2

          = 0.025

To find the t-value:

t_(α/2) = 2.145

Therefore, the error margin is:

E = t_(α/2) × s/√n​

E = 2.145× 3.4/√19

E ≈ 1.67

And the confidence interval would be,

(x{bar} - E, x{bar} + E) = (24.33, 27.67)

Therefore, the confidence interval is: (24.33, 27.67)

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The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.

What are domain and range?

The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

From the given question, and the above definition of domain and range,

the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value

Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.

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Answer:

I was willing to pay $20 more for the toy than I actually paid.

Step-by-step explanation:

Let us take the maximum bid be y

So,

(y × 60) ÷ 100 = 30

60y/100 = 30

60y/100 × 100 = 30 × 100

60y = 3000

60y/60 = 3000/60

y = 50

60% of $50 is $30

So,

50 - 30 = 20

Thus, I was willing to pay $20 more for the toy than I actually paid.

With all this information, and reading our question carefully, we can decipher the following:

9(n-3) = 3 + (9n + 3n)

9n - 27 = 3 + (9n +3n) (Step 1. Distributive Property)

9n - 27 = 3 + 12n       (Step 2. Combine like terms; 9n + 3n = 12n)

-9n                  -9n    (Step 3. Subtract 9n from both sides to isolate the variable)

______________

  -27 = 3 + 3n            

     -3      -3               (Step 4. Subtract 3 from both sides)

________________

-30 =       3n                        

 -----         ----

  3            3              (Step 5. Divide 3 from both sides)

________________

 -10 = n

Therefore, n = -10

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The height of the triangular cross section is equal to 2.5 cm.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H or Volume = base area × length

Where:

Next, we would determine the base area of this rectangular prism by using the formula for the area of a triangle:

Area of triangle = 1/2 × base area × height

Area of triangle = 1/2 × 4 × h

Area of triangle = 2h

Now, we can determine the height of this rectangular prism as follows;

Volume = base area × length

35 = 2h × 7

Height, h = 35/14

Height, h = 2.5 cm.

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Answer:

$8 per person

Step-by-step explanation:

32 divided by 4 is 8

32 : 4 = 8 : 1

Ф {0, [3√3/2(3√3-π)]}

The poster above has good diagrams ; so , I will just go through the calculations .

The region of integration is with in the circle x ^2+y^2=2y but outside the circle   x^2+y^2=1.

I would convert to polar . With polar , we have  x^2+y^2=r^2 ,x=rcosФ and        y=rsinФ
We thus have the first circle becomes x^2+y^2=2y ⇒r^2=2rsinФ Divide through by r,  and you get r=2sinФ(1).  
This is the upper circle in the previous posters diagrams .

The other equation of a circle becomes :
x^2 + y^2 =  1  ⇒ r^2 = 1 ⇒ r =  1   (2)      
These two curves intersect at :
r= 2sinФ =1 ⇒     sinФ=1/2  ⇒Ф= [tex]\alpha[/tex]/6 or 5[tex]\pi[/tex]/6    
From the previous poster's diagrams , we can see that there is as much mass on either side of the positive. y axis or
Ф=[tex]\pi[/tex]/2 axis in polar ; so , the X  coordinate of the center of mass is zero  
X=0 We can also see from his diagrams that the mass and moment of mass is symmetrical about the Ф=[tex]\pi[/tex]/2
we only need to integrate from Ф=[tex]\pi[/tex]/6 to Ф=[tex]\pi[/tex]/2  ( the answers from to are the same and double )
The differential of area in polar coordinates is
d A=rdrdФ  They say the area mass density is inversely proportional to the distance from the origin .

This can be written as : p=k/r. We can thus say the differential of mass is
d M=PDA=

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The probability that exactly four complaints will be received during the next eight hours is 15.41%.

A discrete probability distribution called the Poisson distribution provides the likelihood that an event will occur a specific number of times over the course of a given period of time or location. The formula for this distribution is given by [tex]P(X=x)=\frac{e^{-\mu}\times \mu ^x}{x!}[/tex] where x is the number of successes, μ is the mean, and e is Euler's number.

Given n = 8 hours then, μ = 0.7n = 0.7×8 = 5.6.

Then, the probability that exactly four complaints are received is,

[tex]\begin{aligned}P(X=4)&=\frac{e^{-5.6}\times5.6^4}{4!}\\&=0.1541\end{aligned}[/tex]

The required answer is 15.41%.

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Answer:

There is 1/32 pound food for each fish

Step-by-step explanation:

24 fish = 3/4 pound food

1 fish = (3/4)/24 pound food = 1/32 pound food

(Problem solved by using unitary method)

Answer:

Step-by-step explanation:

To find the percentage increase in the dog's weight, you can use the following formula:

percentage increase = (final value - initial value) / initial value x 100%

In this case, the initial value is 40 pounds and the final value is 48 pounds, so the percentage increase is:

percentage increase = (48 - 40) / 40 x 100% = 8 / 40 x 100% = 20%

Therefore, the dog's weight increased by 20%.

Answer: Answer is 8.47

Step-by-step explanation:

[(6x2.99)-1] ÷2

16.94 / 2

8.47

Answer:

8.47

Step-by-step explanation:

[(6x2.99)-1] ÷2  16.94 /2 =8.47

c is the answer. jdjsisiao

Error Analysis 1:(x-3)/(x+7)

Error Analysis 2:(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

Error analysis is a procedure that is usually used to identify the cause of the issue when pupils continually make mistakes. The method entails going over a student's work and looking for patterns of misinterpretation. Mathematical errors can occur for a variety of reasons and can be factual, procedural, or conceptual. The study of the kind and quantity of mistake, or uncertainty, that might be present in the solution to a problem is known as error analysis in mathematics. This issue is particularly common in practical disciplines like statistics and numerical analysis. The teacher can examine a student's errors on a worksheet, test, or progress monitoring tool to do an error analysis for mathematics. In order to grade each problem, the teacher should mark each wrong digit in the student's response, starting from the RIGHT, going to the LEFT for addition, subtraction, and multiplication problems.

Error Analysis 1:

(x²-x-6)/(x²+9x+14)

=(x-3)(x+2)/(x+2)(x+7)

=(x-3)/(x+7)

Error Analysis 2:

(x²-6x-27)/(2x²+2x)÷(x²+14x+45)/(x²)

=(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

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The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity

A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graph, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.

We are given the function;

g(x) = 2(x + 4)²/(x² - 16)

Simplifying the denominator gives;

(x² - 16) = (x + 4)(x - 4)

Thus, our function is;

g(x) = 2(x + 4)²/[(x + 4)(x - 4)]

(x + 4 ) will cancel out to give;

g(x) = 2(x + 4)/(x - 4)

Vertical asymptote:

Point in which the denominator is 0, so:

(x - 4) = 0

x = 4

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omgggg thats what she said

Answer:

y = -1/2x - 2

Step-by-step explanation:

y = mx+b, m = -1/2, and b (the y-intercept) is -2.

A widely used security technology called Transport Layer Protection, or TLS, enables privacy and data security for communications over the Internet. Encrypting communication between online applications and servers, such as when web browsers load a webpage, is one of the main applications of TLS.

When a user accesses a website through HTTPS and the browser initially starts to enquire about the website's origin server, a TLS handshake occurs

Together, the client and server will perform the following during a TLS handshake:

Indicate the TLS version (TLS 1.0, 1.2, 1.3, etc.) they'll be using.

Select the cipher suites they'll employ (see list below).

Using the server's public key and the SSL certificate authority's digital signature, confirm the server's identity.

After the handshake, generate session keys to enable symmetric encryption.

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Using the slope, the required value of k is 48.

In mathematics, the steeper direction of a line is overall processed by the slope or gradient of the line.

A line's slope can be used to determine how steep it is.

Theoretically, the gradient is calculated as "rise over run" (change in y divided by change in x).

Given is a line that crosses through the origin:

y = mx

Let,s take x = -12 and y = -2.

y = mx

-2 = -12m

m = -2/12

m = -1/6

m is the slope.

The equation now:

y = mx

y = -1/6x

Now, insert:
x = k and y = 8

y = mx

8 = -1/6x

x = 6*8

x = 48

Therefore, using the slope, the required value of k is 48.

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The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.

Given that,

Give the equation for the parabola's axis of symmetry by sketching the graph of each quadratic function using its vertex and intercepts.

We have to determine the function domain and range using the graph is f(x) = (x-1)²+2

We know that,

Its vertex A quadratic function's form is provided by

f(x) = a(x-h)²+k

So, (h,k) is the vertex of the parabola

Take

f(x) = (x-1)²+2

(1,2) is the vertex of the parabola.

Therefore, The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.

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A selective industrialization is a phenomenon in which those sectors or elements where it is desired to centralize or focus the industrialization itself are selected.

This has been a type of industrialization where industrialization is projected in sectors that are previously selected and defined.

Some of the characteristics of selective industrialization are:

¡Hope this helped!

Selective industrialization is a strategy that involves focusing on the development of specific industries or sectors in a country's economy.

This approach is often used by developing countries to promote economic growth and development by targeting key industries that have the potential to drive growth and create jobs.

In the context of an Expo, selective industrialization could refer to showcasing and promoting specific industries or sectors that a country or region specializes in or wants to develop further.

This could involve exhibiting products, technologies, and innovations related to those industries, as well as networking with potential investors, partners, and customers to explore opportunities for collaboration and growth.

stem                            leaf

0                               7, 7, 8, 8

1                                   3 , 3

2                                   5, 2

What is stem and leaf plot ?

A stem and leaf plot, also known as a stem and leaf diagram, arranges data in a way that makes it simple to see how often certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf. The stem and leaf plot key is the symbol " | " that is used to display stem and leaf values.

For instance, the stem and leaf plot key is used to represent 46 as 4 on the stem and 6 on the leaf.

in 2|5 , 2 is the stem side and 5 is the leaf side

in 0|7 , 0 is the stem side and 7 is the leaf side

in 1|3 , 1 is the stem side and 3 is the leaf side

in 0|8 , 0 is the stem side and 8 is the leaf side

in 2|2 , 2 is the stem side and 2 is the leaf side

in 0|7 , 0 is the stem side and 7 is the leaf side

in 1|3 , 1 is the stem side and 3 is the leaf side

in 0|8 , 0 is the stem side and 8 is the leaf side

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Answer:

Your answer is x = 47.

Step-by-step explanation:

First, you need to move the constant to the right-hand side and change its sign.

4x = 180 + 8

Now, you need to add the numbers.

4x = 188

Last but not least, you need to divide both sides of the equation by 4, which gets you to:

x = 47

Answer: We can set up the equation 21 stickers/pack + 24 stickers/pack + x stickers/pack = 15 stickers.

We can solve this equation to find that x, the number of stickers in each pack, is equal to 6 stickers/pack. Answer: 6

Answer: 20

Step-by-step explanation:

24 + 21 = 45

45 + 15 = 60

60 / 3 = 20