Write the equation for the linear function shown in the table

Answer:

Length = 7.83, Width = 3.83

Step-by-step explanation:

Assign variables. Let x represent the width

Area (L x W) = 30 m²

(4 + x)(x) = 30

4x + x² = 30

x² + 4x - 30 = 0

Apply Quadratic Formula

[tex]\frac{-4 + \sqrt{4^2 - 4(1)(-30)}}{(2)(1)}[/tex]

Solve

x = -2 ± √34

x = 3. 83... or x = -7.83 (reject this one)

Width = 3.83

Length = x + 4 = 7.83

The bank routing number on a check is a 9-digit code used to identify a financial institution in a transaction. It is also known as an ABA routing number, an RTN, and a routing transit number.

In order to determine the routing number on a check:

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Answer:

Step-by-step explanation:

(a) No solutions when r ≠ 6 and s ≠ 5. (b) Exactly one solution when r = 6 and s = 5. (c) Infinitely many solutions when r = 6 and s is arbitrary.

For the system of equations to have (a) no solutions, both r and s must have values that do not satisfy the equations. For example, if r ≠ 6 and s ≠ 5, then the equations cannot both be true. For the system to have (b) exactly one solution, both r and s must have values that satisfy the equations. For example, if r = 6 and s = 5, then the equations are both true and have one unique solution. For the system to have (c) infinitely many solutions, one of the variables must have a value that satisfies the equations, while the other variable may take on any value. For example, if r = 6 and s is arbitrary, then the equations are both true and have infinitely many solutions.

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The angles in the given triangle are ∠2=65°,∠5=100°,∠6=100°,

∠7=35°,∠8=145°,∠9=115°.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

Given ∠4=115°,∠1=35°

∠2+∠4=180  ( supplementary angles)

∠2=180-115=65°

∠1+∠2+∠3=180 (sum of angles of a triangle=180°)

∠3=180-65-35=80°

∠3+∠5=180

∠5=180-80=100°

∠5=∠6=100°  (opposite angles)

∠1=∠7=35° (opposite angles)

∠7+∠8=180 (supplementary angles)

∠8=180-35=145°

∠4=∠9=115°  (opposite angles)

Hence,

           The angles in the given triangle are ∠2=65°,∠5=100°,∠6=100°,

∠7=35°,∠8=145°,∠9=115°.

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The graph of the equation is attached, and the coordinates are (0, 2), (2, -3), (1, -0.5), and (-2, 7).

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given equation, 2y = 4 - 5x

let's find the coordinates for the graph,

when x = 0

2y = 4

y = 2

(0, 2)

when x = 2

2y = 4 - 5*2

2y = -6

y = -6/3

y = -3

(2, -3)

when x = 1

2y = 4 - 5

2y = -1

y = -0.5

(1, -0.5)

when x = -2

2y = 4 - 5(-2)

2y = 14

y = 7

(-2, 7)

coordinates for the graph are (0, 2), (2, -3), (1, -0.5), (-2, 7).

Hence graph lies in coordinates (0, 2), (2, -3), (1, -0.5), (-2, 7).

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The number of distinct initial possible pairings for a single-elimination ping-pong tournament with n players that result in distinct tournament brackets is 2^(log2(n) - 1).

What is logarithm ?

The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

In a single-elimination ping-pong tournament, each player plays one match in each round until a champion is determined. For n players, there are log2(n) rounds in the tournament, and in each round half the players are eliminated.

For n = 2, there is only 1 player left after the first round, so there is only 1 distinct pairing and 1 distinct tournament bracket.

For n = 4, there are 2 players left after the first round, and they play in the final. There are 2 possible pairings for the first round, which result in 2 distinct tournament brackets.

For n = 8, there are 4 players left after the first round, and there are 4 possible pairings for the first round. These pairings result in 4 distinct tournament brackets.

So the number of distinct initial possible pairings for a single-elimination ping-pong tournament with n players that result in distinct tournament brackets is 2^(log2(n) - 1).

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Answer:

Below

Step-by-step explanation:

Standard form of a circle =     (x-h)^2  + (y-k)^2 = r^2

   where h,k is the center  

for this circle h,k = 2,-1     and radius, r= 4

so the equation would be

(x-2)^2 + (y+1)^2 = 4^2

The balance after 2 years would be $4482.25

What exactly is compound interest?

Compound interest is when you earn interest on both your savings and your interest earnings.

The formula for finding the amount in a continuously compounded account is: A = P * e^(rt), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.718.

Using this formula, we have:

            [tex]A = $4000 * e^(0.057 * 2) = $4000 * e^0.114\\\\A = $4000 * 1.12061367\\\\A = $4482.25[/tex]

So the balance after 2 years would be $4482.25

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The area of the figure ( a regular hexagon ) is 314.37 square millimeters     .

A regular hexagon which is inscribed in a circle consist of 6 equilateral triangle. All angle is equal.

So side length of the regular hexagon will be same with the radius of circle.

From the question we have following information :

1. Regular hexagon inscribed in a circle

2. Radius of circle is 11 millimeters.

To find the area of the hexagon we can use following formula

A = (3√3) / 2 * [tex]r^{2}[/tex]

Substituting r = 11mm into the equation for the area of the hexagon,

A = (3√3) / 2 * [tex]11^{2}[/tex] = (3√3) / 2 * 121 = 314.367 square millimeters

So the area of the figure is approximately 314.37 square millimeters (rounded to two decimal places).

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subtract e^2/4 from both sides of the equation to get x = (e^2 - 8)/4. This is the final answer of the equation.

e^2 - 4x = 8

4x = e^2 - 8

x = (e^2 - 8)/4

To solve for x in this equation, the first step is to subtract 8 from both sides of the equation. The next step is to divide both sides of the equation by 3.This results in the equation:  x = 4.Once 8 is subtracted from both sides, the equation becomes e^2 - 4x = 0. Then, divide both sides of the equation by 4, which gives 4x = e^2/4. Finally, subtract e^2/4 from both sides of the equation to get x = (e^2 - 8)/4. This is the final answer of the equation.

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The correct conclusion is:

a. f opens down on the interval 0.987 < x < 1

To determine the conclusion about the behavior of the function f, we can use the tangent line approximation and whether it overestimates or underestimates the actual value of f(0.987).

Given that the tangent line approximation at x = 1 is 2.37, and if this approximation is an overestimate of the actual value of f(0.987), it means that the function lies below the tangent line in the interval 0.987 < x < 1.

Since the tangent line has a positive slope (given that f'(1) = 4), if the function f lies below the tangent line, it must be decreasing in the interval 0.987 < x < 1.

Therefore, the correct conclusion is:

a. f opens down on the interval 0.987 < x < 1

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Complete question =

For f differentiable such that f(1) = 3 and f'(1) = 4, the tangent line approximation of (0.987) = 2.37.

If this is an overestimate, what conclusion can be made about f ??

a. f opens down on the interval 0.987 x < x < 1

b. f opens up on the interval 0.987 x < x < 1

c. f opens down at x =  0.987

d. f opens up at x = 1

The most common answer to this question is that people would suggest splitting the fare equally i.e. each person contributes $40.

Each stranger should contribute to the total fare based on the distance traveled, so the fare would be divided as follows -

Bob: 10 miles * $2/mile = $20

Sally: 20 miles * $2/mile = $40

Mike: 30 miles * $2/mile = $60

Total fare: $20 + $40 + $60 = $120

Therefore, each stranger should contribute $120/3 = $40 to the total fare.

The most common answer to this question is that people would suggest splitting the fare equally, i.e. each person contributes $40, regardless of the distance traveled. This is because it is a simpler and fairer solution, as each person benefits from the shared ride and the cost savings, regardless of the distance traveled.

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Answer:

-----------------------------------

The vertical change is the difference of the y-coordinates.

The y- coordinates are 0 and 2, their difference is:

Answer:

[tex](1+\sin(x))(\sec(x)-\tan(x))=\cos(x)[/tex]

Step-by-step explanation:

We are going to use the Pythagorean trigonometric identity:

[tex]\sin^2(x)+\cos^2(x)=1[/tex]

and the following relationships between trigonometric functions:

[tex]\sec(x)=\frac{1}{\cos(x)}\\\tan(x)=\frac{sin(x)}{cos(x)}[/tex]

We can transform the expression as follows:

[tex](1+\sin(x))(\sec(x)-\tan(x))=(1+\sin(x))(\frac{1}{\cos(x)}-\frac{\sin(x)}{\cos(x)})=(1+\sin(x))\frac{1-\sin(x)}{\cos(x)}=\frac{(1+\sin(x))(1-\sin(x))}{\cos(x)}[/tex]

Using the formula for the difference of two squares, we can write

[tex](1+\sin(x))(1-\sin(x))[/tex]

as

[tex]1-\sin^2(x)[/tex]

which, according to the Pythagorean trigonometric identity, is equal to

[tex]\cos^2(x)[/tex]

Now we can simplify the original expression to

[tex]\frac{\cos^2(x)}{\cos(x)}=\cos(x)[/tex]

The following are the respective measures of angles and lengths of the rectangle ABCD:

m∠1 = 49°, m∠2 = 41°, m∠3 = 41°, m∠ADC = 90°, AB = 6.9, BD = 10, and CE = 5.

Considering the triangle AEB, angles A and B are base angles of a the isosceles triangle AEB so;

2(m∠ABE) + 98 = 180° {sum of interior angles of a triangle}

m∠ABE = (180 - 98)/2

m∠ABE = 41°

m∠1 = 90° - 41° {complementary angles of a rectangle}

m∠1 = 49°

angles m∠2 and m∠BAC are alternate angles and are equal so;

m∠2 = 41°

m∠ADC is one of the four interior angles of a rectangle so m∠ADC = 90°

Considering the right triangle ∆ABD and the tangent of angle B = 41°, we can solve for the length of AB as follows:

tan 41° = 6/AB {opposite/adjacent}

AB = 6/tan41° {cross multiplication}

AB = 6.9022.

m∠3 and m∠ABD are alternate angles so;

m∠3 = 41°

lines AC and BD are diagonals of the rectangle and they bisect each other, since EB = 5 then;

BD = 2 × 5 = 10

CE = 5

Therefore, the following are the respective measures of angles and lengths of the rectangle ABCD:

m∠1 = 49°, m∠2 = 41°, m∠3 = 41°, m∠ADC = 90°, AB = 6.9, BD = 10, and CE = 5.

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Answer: Sebastián bought 18 figurines.

Data :

We must bear in mind that Javier bought 3 envelopes of 6 figurines each. Calculate the total number of figurines by adding 6 + 6 + 6 therefore:

[tex]\bf \: 6 + 6 + 6 = \boxed{ \bf18}[/tex]

Rpt: Sebastián bought 18 figurines.

Answer: Alan would have to sell exactly 180 boxes.

Step-by-step explanation:

The general solution to the separable differential equation 9yy′ = x, with the initial condition y(9) = 5.

The given differential equation is 9yy′ = x. This is a separable equation, meaning it can be solved by separating the variables and integrating both sides. To solve the equation, we start by dividing both sides by 9y to get y′ = x/9y. Now, we can solve for y by integrating both sides with respect to x. This gives us y = (1/9)∫xdy + c, where c is a constant of integration.

To determine c, we can use the initial condition given, y(9) = 5. We substitute 9 for x, and 5 for y to get 5 = (1/9)∫9dy + c. We can solve for c by subtracting (1/9)∫9dy from both sides, giving us c = 5 - (1/9)∫9dy.

Finally, we can substitute c into our equation to get the solution, y = (1/9)∫xdy + (5 - (1/9)∫9dy). This is the general solution to the separable differential equation 9yy′ = x, with the initial condition y(9) = 5.

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As per the regression equation, the value of intercept coefficient is 1.5707

Regression is a statistical technique used to determine the relationship between an independent variable and a dependent variable.

In this case, the regression statistics provided in table 6 show the results of estimating the model

=> Δln (Sales t) = b0 + b1Δln (Sales t −1) + εt,

where Δln (Sales t) is the change in the natural log of sales for Cisco Systems quarterly observations from 3Q:1991 to 4Q:2000.

The R-squared value of 0.0661 indicates that only about 6.61% of the variation in the change in the log of sales can be explained by the change in the log of sales from the previous quarter.

The standard error of 0.4698 indicates the average deviation between the actual and predicted change in the log of sales.

If the results show that the specification is correct, then the long-run change in the log of sales toward which the series will tend to converge can be determined by the intercept coefficient, which in this case is 1.5707.

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By using the Root Test on the series "∑n" , we found that the series is Divergent and diverges to infinity .

The Root Test states that, if the limit of nth root of the absolute value of the nth term of a series is less than 1, then the series converges. and

If the limit is greater than or equal to 1, the test is inconclusive.

In the series ∑n , the nth term of the series is "n" ,

So, the nth root of the absolute value of nth term is the nth root of |n|, which is = n^(1/n).

we see that as n approaches infinity, the nth root : n^(1/n) approaches 1, So,  the limit of the nth root of the absolute value of the nth term is equal to 1. Which means that the Root Test is inconclusive for this series.

Therefore , the series ∑n diverges, it is a known series called as Harmonic series, which diverges to infinity.

The given question is incomplete , the complete question is

Use the Root Test to determine whether the series convergent or divergent.  ∑n , where n is from 1 to infinity .

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Elena will likely use a measure of central tendency, such as the mean or median, to summarize her data in a single score.A measure of central tendency is a statistical value that summarizes a set of data.

It is accomplished by assigning a representative score, usually the most common value in a dataset. Elena's statistics course assignment requires her to utilise either the mean or the median to summarise the link between money and happiness.

The mean is computed by summing all of the values in a dataset and dividing by the total number of values. When a set of data is ordered numerically, the median is the midway value. Both of these metrics generate a single score that reflects the full dataset, making it easier to comprehend and make inferences from it.

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Answer:

hhyýuhhhí7 and Pakistan were colonized together so the britains could no win the fight with india therefore

Step-by-step explanation:

because at that time india and Pakistan were colonized together so the britains could no win the fight with india therefore Britain's plan to intimidate

Answer:

See below

Step-by-step explanation:

I am assuming you need help only for the bottom questions as the top is VERY simple (the top of the cross is literally multiplication of the numbers and the bottom of the cross is addition). This questions needed to be worth more points, with that being said

1. [tex]4y^3 - 2y + 3y^2 - 5y - y^2[/tex]

Combine like terms

[tex]4y^3 - 2y^2 - 7y[/tex]

2. [tex](2x^2 - x + 1) - (x+1)[/tex]

Remove numbers from brackets by distribution property (just imagine a one on the outside of the bracket)

[tex]2x^2 - x + 1 -x - 1\\2x^2 - 2x\\2x(x - 1)[/tex]

3. [tex]-2p^3(-2p^4 + 5p^2 - p)[/tex]

This is just distribution property, multiple the outside by inside (you add the exponents when you multiply)

   [tex]4p^7 - 10p^5 + 2p^4[/tex]

4. [tex](3y-6)(2y+3)[/tex]

You multiply each term on the inside of one bracket with the ones on the inside of the other bracket

[tex]6y^2 + 6y -12y -18\\6y^2 - 6y - 18\\6(y^2 - y -3)[/tex]

5. [tex](x+6)(x-6)[/tex]

Same as above but honestly its much quicker if you know the b term in ax^2 + bx + c = 0 always equals 0 in this case

[tex]x^2 -6x + 6x -36\\x^2 - 36[/tex]

The conjectures which you can make about a point on the perpendicular bisectors of a segment and a point of a bisector of an angle include the following below:

Th line that divides something into two equal parts and it is usually applied to the line segments and angles.

The following relationships between them is that if there is a point which lies on the perpendicular bisector of a segment, then it is most likely to be equidistant from the endpoints of the segment when scrutinized thereby making it the correct choice.

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I am pretty sure the answer would be (2,3)

Parallel lines have the same slope.

The slope of y = 9x + 9 is 9, because of the 9 in 9x.

The slope of a parallel line would also be 9.

The segments DF and AB are parallel, as they have the same slope.

A segment is composed by two endpoints, and then the slope is calculated as the change in y divided by the change in x of these points.

The endpoints of segment AB are given as follows:

A(-5,2) and B(1,-2).

Hence the slope is of:

m = (-2 - 2)/(1 - (-5)) = -4/6 = -2/3.

The endpoints of segment DF are given as follows:

D(-4,-2) and F(-1,-4).

Hence the slope is of:

m = (-4 - (-2))/(-1 - (-4)) = -2/3.

As the segments have the same slope, they are parallel.

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Answer:

The picture won't show. are there answer options?

Step-by-step explanation:

Small room (S) - hold 3 people

Large room (L)- hold 4 people

Hudson reserved twice as many large rooms = 2x Large room #

2L + S = 66

So,

Let S = Small room

Let L = Large room

I hope this can make things slightly easier for you. I tried to make it more visible for you. Please comment if you need more help.