what is the slope of a equation 2y = 3x + 4

The length of the mid-segment of the trapezoid is 6

The trapezium is a quadrilateral where 1 pair of sides are parallel and the sum of angle pairs between parallel lines is 180 degrees.

We have,

The vertices of a trapezoid:

E = (-3, 3)

F = (1, 3)

G = (3, -3)

H = (-5, -3)

The figure can be considered as,

            E____________F

             /                           \

      M /                                \ N

     /                                        \

H/_____________________\G

MN is the mid-segment of the trapezoid.

MN = (EF + HG) / 2

EF = √(4² + 0) = 4

HG = √(8² + 0) = 8

MN = (4 + 8) / 2

MN = 12/2

MN = 6

Thus,

6 is the length of the mid segment of the trapezoid.

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Adrian run in one hour is 5.698 km.

How to calculate speed, Distance and Time ?

Given,

Adrian ran in 1.5 hours = 8.547 km

We know, in 1.5 hours there is 90 minutes

so, in 1 min adrian ran = 8.547 / 90

                                    =  0.09496 km

We need to find the km in one hour means in 60 minutes

So, Adrian ran in 60 min = 60 * 0.09496

                                         =  5.6979 km or 5.698 km per hour

Hence, Adrian run in one hour is 5.698 km.

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The power series representation for the given function is:

1+ 9x + (9x)² + (9x)³ + .... (9x)ⁿ (where 0 ≤ n ≤ ∞).

What is the power series?

Power series is a sum of terms of the general form aₙ(x-a)ⁿ. Whether the series converges or diverges, and the value it converges to, depends on the chosen x-value, which makes power series a function.

Let u = 9x.

Return to the series above and replace each u with a 9x directly:

Where 0 n , 1 + 9x + (9x) 2 + (9x) 3 +.... (9x) n

Here, the interval of convergence is easily found. It follows that

|9x| 1 -1/9 x 1/9 because we know that geometric series must have | u | = 1

Finally, we may leverage the fact that geometric series have a sum to get the sum: S = a / (1 - u).

Here, u = 9x and a = 1

Therefore, the total is simply S = 1 /(1 - 9x).

Any sum can be calculated provided x is between -1/9 and x and less than 1/9.

Hence, The power series representation for the given function is:

1+ 9x + (9x)² + (9x)³ + .... (9x)ⁿ (where 0 ≤ n ≤ ∞).

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Answer:

y = -x + 8

Step-by-step explanation:

First find the slope (m):

m = (0-2) / (8-6) = -1

Next put one of the points (I pick (8,0)) into the point-slope formula:

y-y1 = m(x-x1)

y-0 = -1(x-8)

Now write it in slope-intercept form:

y = -x + 8

A. The graph of the absolute value function is V-shaped, with the features given as follows:

B. The transformation is that the function was shifted right two units, hence the features are given as follows:

The absolute value function, with vertex (h,k), is defined as follows:

y = |x - h| + k.

The features of the function are given as follows:

For the first item, the function is |x + 3|, hence we just have to identify the features.

For the second function, the definition if h(x) = |x - 2|, with vertex at (2,0), meaning that the function was shifted two units right from the parent absolute value function y = |x|. The shift just changes the turning point of the graph, not altering domain and range.

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The point of interaction of two circles:

(x-a)²+(y-b)² = ro²

(x-c)²+(y-d)² = r1²

The e point of interaction of the two circles is given by the formulas given below:

       D = √(c-a)²+(d-b)²

        б = √(D+r0+r2)(D+r0-r2)(D-r0+r2)(-D+r0+r2)

        X1,2 = a + c/2 + (c-a)(r0² - r1²)/2D² ± 2 b-d/D²

        X1,2 = b + d/2 + (d-b)(r0² - r1²)/2D² ± 2 a-c/D²

r0 = 935.62 ft

r1 = 959.630 ft

a = 553.7

b = 1147.86

c = 1162.93

d = 269.83

First we calculate,

                            D = √(c-a)²+(d-b)²

                               = 1980.95 ft

Lets check whether these circles intersect or not:

D<r0+r1 and D> r0-r1

r0+r1 = 2166.57 ft and D = 1980.95 ft -192.51 = 192.51 which is less than D

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The normal curve that corresponds to P (X > 37) is C, as the shaded area corresponds to the probability of 0.4207.

The normal curve is a bell-shaped curve which is used to represent a continuous probability distribution. It is used to represent the probability of a random variable X, which is normally distributed with mean μ and standard deviation σ. In this case, we have X with mean μ = 50 and standard deviation σ = 7. To compute the probability P(X > 37), we first draw a normal curve with the area corresponding to the probability shaded. Then, we can look up the area from the table of areas under the normal curve. The area corresponds to 0.4207, and the normal curve that corresponds to this probability is C, as the shaded area corresponds to the probability of 0.4207. This normal curve has the mean of 50 and the standard deviation of 7, with the area beyond 37 shaded.

P(X > 37)

= 1 - P(X ≤ 37)

= 1 - 0.4207

= 0.5793

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Situation which illustrates best the concept of absolute advantage is: Option A - A German factory can build more sports cars than foreign factories.

Absolute advantage is the potential of an individual,  a company, or a  country to produce a higher quantity of output than its competitors while using the same inputs. It means an institution with absolute advantage has more efficiency in producing a particular commodity than its rivals. It utilizes lower marginal cost (materials and labor), making its output much cheaper than others.

A factory in German has an absolute advantage because it can produce more sports car  than foreign countries. Absolute advantage makes the factory more competitive in the market than its rivals.

Therefore, the correct answer is option A.

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For the regression equation, ŷ = b₀ + b₁x where b₁ is slope of this line and it is equals to (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and b₀ is y-intercept which is equals to (∑y - b₁ ∑x)/n .

A regression line indicates the linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis. Correlation is determined by analyzing the data pattern formed by the variables.

The regression line is plotted closest to the data points in the regression plot. We use the ordinary least squares estimation method (O.L.S.E), to find the formulas to calculate the slope and intercept of the regression line, which minimizes the sum of squares due to the error. A simple linear regression model is given by y = b₀ + b₁x --(*)

where y : dependent variable

x: independent variable

b₁ --> slope of regression line

b₀ --> y-intercept

We have , regression line is ,

ŷ = (slope )x+ (y intercept)

ŷ represet the predicted value.

The formulas to compute slope(b₁) value and y-intercept (bo) value of regression line are following:

b₁ = (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and

b₀ = ŷ - b₁x = (∑y - b₁ ∑x)/n

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The area of the shaded region is 425 cm².

Let us find the area of the entire figure first and subtract the unshaded region area to find the area of the shaded region.

The given figure is of a square of side 25 cm.

Total area = 25²

=> 625 cm²

The shaded figure inserted is a rhombus.

Apart from this , we can observe four unshaded triangles of equal area.

Area of each individual triangle :

=> ½ × 5 × 20

=> 50 cm²

Area of 4 triangles ;

=> 200 cm²

Remaining area of the shaded figure :

=> 625 - 200

=> 425 cm² .

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Answer:

A

Step-by-step explanation:

A. This is true and occurred during the industrial revolution

B. The government had not started managing the economy (yet)

C. This was happening even in the 1700s

D. This was also more apparent in the 1700s with the 13 colonies, especially with cash crops such as tobacco.

cupcakes are shared

equally among four of her children, 4 Cupcakes  will each child get

what do you mean by share?

An equity ownership stake in a corporation is represented by a share. Dividends from any earnings the company makes are owed to the shareholders. They also bear the brunt of any losses the business may sustain.

Ordinary shares.

Non-voting shares.

Preference shares.

Redeemable shares.

There are a number of different types of shares including equity shares, preference shares, right shares, bonus shares, sweat equity shares (where companies issue shares at a discount or for consideration) and employees stock options plans.

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Answer:

$16.50

Step-by-step explanation:

$110 * 15% =

$110 * 15/100 =   ==> percent value is 100 times greater than the fraction

$1650/100 =  ==> multiply 110 and 15

$16.50

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Answer:

Tip=[tex]16.50[/tex]

Step-by-step explanation:

Tip%=15

Bill=$110

Tip=[tex]\frac{15}{100}[/tex]x[tex]110[/tex]

Tip=[tex]16.50[/tex]

Hope this helps u

By using  ε - δ  definition of limit, the proof of

The limit of a function exists at a cluster point c if and only if the left- and right-handed limits both exist at c and are equal

has been shown below.

What is ε - δ  definition of limit?

Let the function be f(x), cluster point be c and the limit be l. Then

the limit of a function exists at a cluster point c if

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε

Let the limit exist at a cluster point c. Let the limit be l

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that 0 < c - x < δ ⟹ |f(x) − l| < ε or

                                                                         0 < x - c < δ ⟹ |f(x) − l| < ε

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε or

                                                                         c < x < c + δ ⟹ |f(x) − l| < ε

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε  and

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that   c < x < c + δ ⟹ |f(x) − l| < ε

So the left hand and right hand limit exist and are equal.

Let the left hand and right hand limit exist and are equal.

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε  and

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that   c < x < c + δ ⟹ |f(x) − l| < ε

Let [tex]\delta_3 = min\{\delta_1, \delta_2\}[/tex]

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c ⟹ |f(x) − l| < ε  and

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that   c < x < c + [tex]\delta_2[/tex] ⟹ |f(x) − l| < ε

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c or  c < x < c + [tex]\delta_2[/tex]⟹ |f(x) − l| < ε  

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x - c| < [tex]\delta_3[/tex] ⟹ |f(x) − l| < ε  

The limit of a function exists at a cluster point c and the limit is l

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The function of the line and parabola shown in the graph is x + 6 ≤ 1 and x² + 3 > 1 respectively, so, option A is correct.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The graph of the function,

Calculate the equation of the line which is passing through (-6, 0) and (0, 5) as shown below,

y - 5 = 5 - 0 / 0 - (-6) (x - 0)

y - 5 = 5 / 6 x

6y - 30 = 5x

And the equation of the parabola can be written as,

x² + 3 = 0

From the graph, it can be seen that the solution of the line is where the line graph and parabola graph can meet,

Thus, the line will be x + 6 ≤ 1 and x² + 3 > 1.

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Answer:

The pattern is in the order of even number being added or subtracting (takes turns)

Step-by-step explanation:

12,18,10,20,8

12 to 18 is plus 6

18 to 10 is minus 8

10 to 20 is plus 10

20 to 8 is minus 12

[tex]12 + 6 = 18 \\ 18 - 8 = 10 \\ 10 + 10 = 20 \\ 20 - 12 = 8 \\ 8 + 14 = 22 \\ 22 - 16 = 6 \\ = 24 \\ = 4 \\ = 26 \\ = 2 \\ ..[/tex]

The value of x is $53.34 but cannot exceed $115, while the value of y can be as low as $160 but cannot exceed $345.

Relationships that compare two numbers or other mathematical expressions in an unequal manner are known in mathematics as inequalities. The most common use is to compare the magnitude of two numbers on a number line.

The answer to the query is

Diane will make a charitable donation "up to $460," which indicates it can be less than or equal to 460 but not more. Then,

$460 donated to charity (max)

plus $160 for educational (160 being the minimum)

Education is also stated to be three times (or greater) than City.

If x represents the city and y represents education, then

x + y = 460 . And we are aware that y 3x.

x + 3x = 4x = 460

x = 115.

This implies that she will contribute $345 to Educational when she donates 3 times (or $115) to City. The maximum value is these.

She won't provide more than $460.

Earlier, Educational had a minimal need.

When y = 160,

x equals y/3,

=> x = 160/3 = $53.34. She so gave 213.34 dollars, which is still less than $460.

As a result, x (which is City) might be anywhere between $53.34 and $115.

x, which stands for educational, might be as little as $160 or as high as $345.

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Answer:

  P/Q = (-3x +2)/(3(3x -1))

  PQ = 12/((3x -1)(-3x +2))

Step-by-step explanation:

You want the quotient and product of P(x) = 2/(3x -1) and Q(x) = 6/(-3x +2).

The quotient is found by multiplying by the inverse of the denominator:

  [tex]P(x)\div Q(x)=\left(\dfrac{2}{3x-1}\right)\div\left(\dfrac{6}{-3x+2}\right)=\left(\dfrac{2}{3x-1}\right)\times\left(\dfrac{-3x+2}{6}\right)\\\\\\\dfrac{2(-3x+2)}{6(3x-1)}=\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]

As with multiplying any fractions, the numerator is the product of the numerators, and the denominator is the product of the denominators.

  [tex]P(x)\times Q(x)=\left(\dfrac{2}{3x-1}\right)\times\left(\dfrac{6}{-3x+2}\right)=\dfrac{2\cdot 6}{(3x-1)(-3+2)}\\\\\\=\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]

__

Additional comment

Usually the simplified form would contain no parentheses. The indicated products would be multiplied out.

The number of miles Carlos drove the rental car is 88 miles.

Carlos paid a total of $64 to rent a car. The rental company charges a one-time fee of $20, with an additional charge of $0.50 per mile driven.

Therefore, the number of miles Carlos drive the rental car can be calculated as follows:

Using equation,

let

x = number of miles driven

64 = 20 + 0.50x

subtract 20 from both sides of the equation'

64  - 20 = 20 - 20 + 0.50x

44 = 0.50x

divide both sides by 0.50

Therefore,

44 / 0.50 = 0.50x / 0.50

x = 88

Therefore, the number of miles is 88 miles.

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Answer:

B

Step-by-step explanation:

[tex]3x {}^{2} - 7x + 14 + 5 {x }^{2} + 4x - 6 = 8 {x}^{2} - 3x + 8[/tex]

The value of the expression is x

From the question, we have the following parameters that can be used in our computation:

x + y = x - y

x - 2y = ?

Recall that. we have

x + y = x - y

Add y to both sides of the equation

So, we have the following representation

x + 2y = x

Add -2y to both sides of the equation

So, we have the following representation

x = x - 2y

Rewrite as

x - 2y = x

Hence, the solution of x - 2y is x

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Details scalcets,

a) If u is unit vector , then, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2 where v and w also unit vectors.

b) Exact value of angle between the vectors is 34.3803442 and Approximation value, 34.4..

c) Exact value of the angle between the vectors, a = 71 - 2j + k, b = 3i - k is 30.60889766 ~ 30.61 (approximation value).

In mathematics, a unit vector is defined as a normed vector space is a vector of length one.

a) If u is a unit vector , we have to calculate ⃗u.⃗v and ⃗u.⃗w where v and w are also unit vectors.

We know that, Angle between two vectors θ is

Cosθ = u⃗ .⃗v/|u| |v|

=> cos 60° |u| |v| = ⃗u.⃗v

=> ⃗u.⃗v = 1/2(1)(1) = 1/2

Also, Cosθ = ⃗u.⃗v/|u| |w|

=> Cosθ |u| |w| = ⃗u.⃗w

=> ⃗u.⃗w = cos 120° (1)(1)

=> ⃗u.⃗w = -1/2

So, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2

b) We have, a = (7,2), b = (3,-1)

Cosθ = a.b/|a| |b|

|a| = √(7)²+ (2)² = √49+4 = √53

|b| = √(3)²+ (-1)²= √9+1 = √10

a.b = 7×3 - 2×1 = 21 - 2 = 19

so, Cos θ = 19/√10 (√53) = 19/√530

=> θ = Cos⁻¹( 19/√530)

=> θ = 34.3803442 ~ 34.4

c) We have, a = 7i - 2j + k, b = 3i - k

Cos θ = a.b/|a| |b|

|a| = √(7)² + (-2)² +(1)² = √49+4+1 = √54

|b| = √(3)²+ 0 +(-1)² = √9+1 = √10

a.b = (7i - 2j + k).(3i - k) = 21 -0 - 1 = 20

Cosθ = 20/√10√54 = 20/√540

θ = cos⁻¹(20/√540) = 30.60889766 ~ 30.61

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Answer:

y = (-6)*x - 16

Step-by-step explanation:

The slope-intercept form of a line is given by the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

In this case, the line passes through the point (-4,8) and has a slope of -6, so we can plug these values into the equation to find the y-intercept:

y = (-6)*x + b

We know that the line passes through the point (-4,8), so we can substitute these values into the equation to solve for b:

8 = (-6)*(-4) + b

8 = 24 + b

b = -16

Therefore, the equation of the line in slope-intercept form is:

y = (-6)*x - 16

The sum of the x-coordinates of the points that lie in the region above the straight line y = 2x + 7 in coordinate plane is thirty-eight.

A point lies above the straight line , y = 2x + 7 in co-ordinate plane . If its y -coordinate is greater than two times its x-coordinate plus 7. Now, we are checking the each ordered pair one by one ,

(i) plug x = 3 and y = 10

2x + 7 = 3×2 + 7 = 13 > 10

(ii) plug x = 6 in 2x+7

=> 2× 6 + 7 = 19 < 20

(iii) x = 12

=> 2x + 7 = 2× 12 + 7 = 31 < 35

(Iv) x = 18

=> 2x + 7 = 2× 18 + 7 = 43 > 40

(v) x = 20

2x + 7 = 2×20 + 7 = 47 < 50

We see (6, 20) , ( 12,35) and (20,50) satisfy this condition. Now, we determine the sum of x-coordinates . The sum of the x-coordinates of these points is 6 + 12 + 20 = 38 . So, required sum of x-coordinates is 38.

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Complete question:

Of the five points (3, 10), (6, 20),(12, 35), (18, 40)and (20, 50), what is the sum of the x-coordinates of the points that lie in the region above the line

y = 2x + 7 in coordinate plane.

a group with at least n k 1 people such that no two members of the group are friends,We will prove this statement by inductive hypothesis.

Base Case: If n=k+1, then we can easily find a group with nk1 people such that no two members of the group are friends. We simply select the k+1 people in the room, excluding Alex. Since Alex has k friends, and no other person in the room has more than k friends, it follows that none of these k+1 people are friends.

Inductive Step: Assume that the statement is true for n=k+1. Now we must show that it is true for n=k+2.

We can select a group of k+1 people from the room, again excluding Alex. By the inductive hypothesis, we know that no two members of this group are friends. Now, we select the remaining person in the room, and add them to the group. This person cannot be friends with any of the members of the group, since Alex has k friends and no other person in the room has more than k friends. Therefore, the group we have formed has at least nk1 people, and no two members of the group are friends.

Therefore, by induction, we have proved that we can find a group with at least nk1 people such that no two members of the group are friends.

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