What is the slope of the line graphed below?
(3.1)
5
5
5 (0.-5)
m=
O A. 2
O B.
2
C. -2

Answer:

The larger van has 23 seats

Step-by-step explanation:

Create a system of Equations:

1. Define variables.

> let x=small van and y=larger van

2. create 2 equations based on the information given.

> y = 6 + x

> 2x + y = 57

3. Use any method to solve

Substitution: 2x + (6 + x) = 57. x=17

                      now plug x in to the original equation to solve for y (the larger van)

                      y = 6 + 17 and y = 23

Elimination: 2y = 12 + 2x

                     y = 57 - 2x

         3y = 69  and y = 23

The function f(x) = -x² - 2x / (4x⁴ - 3) has a denominator that goes to infinity, as the highest power of x is 4. As the degree of the numerator is less than the degree of the denominator, limx→[infinity]f(x) = 0. We get:limx→−[infinity]f(x) = limx→−[infinity]-1/x⁴ / (1/x⁴ + 3/x⁴) limx→−[infinity]f(x) = limx→−[infinity]-1 / (1 + 3x⁴) = -1. Therefore, limx→−[infinity]f(x) = -1 and limx→[infinity]f(x) = 0.

To determine the limit limx→−[infinity]f(x), we first need to divide the numerator and denominator by the highest power of x that they share, which is x²:f(x) = -x² / x² - 2x / x²(4x⁴ - 3)Simplifying, we get:f(x) = -1 / (1 - (2x² / (4x⁴ - 3)))

Now we can take the limit as x approaches negative infinity: limx→−[infinity]f(x) = limx→−[infinity]-1 / (1 - (2x² / (4x⁴ - 3)))Multiplying the numerator and denominator by 1/x⁴, we get : limx→−[infinity]f(x) = limx→−[infinity]-1/x⁴ / (1/x⁴ - (2/4 - 3/x⁴)) .

Simplifying, we get:limx→−[infinity]f(x) = limx→−[infinity]-1/x⁴ / (1/x⁴ + 3/x⁴) limx→−[infinity]f(x) = limx→−[infinity]-1 / (1 + 3x⁴) = -1. Therefore, limx→−[infinity]f(x) = -1 and limx→[infinity]f(x) = 0.

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A two-bedroom apartment has a $1,643 rent each month and $2.12 is paid monthly in rent per square foot. The overall area of the apartment is 775 square footage.

Let's assume that  the total square footage of the apartment be X

Given that:

The monthly rent of the apartment  = $1,643

The monthly rent per square foot of the apartment  = $2.12

Therefore, we can say that,

X = $1,643 / $2.12

Calculating the above equation, we get:

X = 775 square footage

Therefore, the apartment's total square footage is 775.

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Answer:

4

Step-by-step explanation:

x=3

x2 means 3 square (+3)

3×3+3

=9+3

12÷3

4

Answer:

1583 in²

Step-by-step explanation:

Radius r = 12/2 = 6 inches

Height h = 14 inches

Volume = πr²h = 3.14 x 6² x 14 = 1583 in²

The solution is, Option A. Line X

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

We have to identify the line which represents the function f(x) = 3x - 5

The given equation is y = 3x -5, in which slope of the line should be 3 and y- intercept is -5.

In these lines line x is having y-intercept as -5.

Line x passes through (1, 2) and (0, -5)

So slope of the given line will be = y2 - y1/ x2 - x1

= -5-2/ 0-1

= 3

Therefore, option A : Line X is the answer.

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We want to see which statement describes the image of a triangle after a dilation of scale factor of 2/3.

We will see that the correct option is C:

"Each angle has the same measure as its corresponding angle in the pre-image."

First, if we have a given figure and we apply a dilation of scale factor K, then all the measures of the given figures are affected by that dilation.

So if the 3 sides of the original triangle measured A, B, and C.

The new measures will be:

Notice that because all the sides changed proportionally, then the internal angles produced did not change after the dilation.

From this, we can conclude that the only correct option is C:

"Each angle has the same measure as its corresponding angle in the pre-image."

This says that the angles of the dilated triangle are the same ones as the angles of the initial triangle, which is true.

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Answer:

(a)

\(\begin{array}{ccc}{} & {W} & {w} & {w} & {Ww } & {ww } & {w} & { Ww} & {ww } \ \end{array}\)

(b)

\(White = 50\%\)

\(Yellow = 50\%\)

Step-by-step explanation:

See attachment for initial punnet square

Solving (a): Complete the square

Initially, we have:

\(\begin{array}{ccc}{} & {W} & {w} & {w} & { } & { } & {w} & { } & { } \ \end{array}\)

To complete the square, we simply write the letter at the column and the letter at the row in each cell;

So, we have:

\(\begin{array}{ccc}{} & {W} & {w} & {w} & {Ww } & {ww } & {w} & { Ww} & {ww } \ \end{array}\)

Solving (b): Percentage of each

From the question, we understand that W are dominant to w.

So:

\(Ww = White\)

\(ww = Yellow\)

From (a) above

\(Ww = 2\)

\(ww = 2\)

\(Total = 4\)

So, the percentage of each is:

\(White = \frac{Ww}{Total} * 100\%\)

\(White = \frac{2}{4} * 100\%\)

\(White = 0.5 * 100\%\)

\(White = 50\%\)

\(Yellow = 100\% - White\) --- Complement rule

\(Yellow = 100\% - 50\%\)

\(Yellow = 50\%\)

There are 40 people on the team. Each van has 8 number of people, so 5 vans multiplied by 8 people each equals 40 people.

A sports team is divided equally into five vans. Each van has eight people in it. To determine the total number of people on the team, begin by counting the number of people in each van. Since each van has eight people, multiply 8 people by 5 vans to get the total number of people on the team. 8 x 5 = 40. Therefore, there are 40 people on the team. To check the answer, count the total number of people in the five vans. 8 people in each van multiplied by 5 vans equals 40 people. This confirms the answer that there are 40 people on the team.

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Answer:

165 bike

110 bus

Step-by-step explanation:

Step-by-step explanation:

the height from the 90° angle (which is y here) in a right-angled triangle is the square root of the Sergent lengths of the Hypotenuse.

y = sqrt(3×9) = 3×sqrt(3)

and x we get via Pythagoras :

x² = y² + 9² = 27 + 81 = 108

x = sqrt(108) = sqrt(36×3) = 6×sqrt(3)

so, A is correct.

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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Penelope has, 52quarters, 104 dimes, 416 nickels, and 162 pennies.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information let, 'x' be the number of quarters,

Therefore, Dimes is 2x, Nickels is 8x and Pennies is 3x.

So, x + 2x + 8x + 4x = 780.

15x = 780.

x = 52, The number of quarters.

2×52 = 104, The number of Dimes.

8×52 = 416 Nickels.

3×52 = 162 Pennies.

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Answer:

108

Step-by-step explanation:

The size of the fourth angel = 360 - ( 53 + 127 + 72 ) = 108

The optimal point values for x1, x2, λ, and μ (Lagrange multipliers) in the given problem are:

x1 = 1

x2 = 1

λ = -4

μ = 2

To solve the optimization problem using the Lagrange multipliers technique, we first construct the Lagrangian function L(x1, x2, λ) by incorporating the equality constraint:

L(x1, x2, λ) = f(x1, x2) - λ(g(x1, x2))

Where f(x1, x2) is the objective function, g(x1, x2) is the equality constraint, and λ is the Lagrange multiplier.

In this case, the objective function is f(x1, x2) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6, and the equality constraint is g(x1, x2) = x1 + x2 - 2.

The Lagrangian function becomes:

L(x1, x2, λ) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6 - λ(x1 + x2 - 2)

To find the optimal values, we need to find the critical points by taking partial derivatives of L with respect to x1, x2, and λ and setting them equal to zero. Solving these equations simultaneously, we get:

∂L/∂x1 = 4x1 - 2x2 - 6 - λ = 0

∂L/∂x2 = -2x1 + 2 + λ = 0

∂L/∂λ = -(x1 + x2 - 2) = 0

Solving these equations, we find x1 = 1, x2 = 1, and λ = -4. Substituting these values into the equality constraint, we can solve for μ:

x1 + x2 - 2 = 1 + 1 - 2 = 0

Therefore, μ = 2.

The optimal point values for the variables in the optimization problem are x1 = 1, x2 = 1, λ = -4, and μ = 2. The Lagrange multipliers λ and μ represent the rates of change of the objective function and the equality constraint, respectively, with respect to the variables. They provide insights into the sensitivity of the objective function to changes in the constraints and can indicate the impact of relaxing or tightening the constraints on the optimal solution. In this case, the Lagrange multiplier λ of -4 indicates that a small increase in the equality constraint (x1 + x2 - 2) would result in a decrease in the objective function value. The Lagrange multiplier μ of 2 indicates the shadow price or the marginal cost of satisfying the equality constraint.

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Answer: 407.67

Explanation:

(8.11×107)–(4.3×107) =

(8.11)(107)−(4.3)(107) =

         407.67

Answer:

i am pretty sure it's a.

Step-by-step explanation:

i hope this helps :)

Answer:

it's -2sqrt7

the first answer

Step-by-step explanation:

pls mark me brainliest!

We have solved the equation AB=BC for A, assuming that A, B, and C are square matrices and B is invertible, then the solution is A=C B⁻¹.

First, let's take a look at the equation AB=BC. This is an equation that involves matrices, which are essentially rectangular arrays of numbers. In this case, we have three matrices: A, B, and C. The equation tells us that the product of A and B is equal to the product of B and C.

Now, we want to solve this equation for A. This means that we want to isolate A on one side of the equation and have everything else on the other side. To do this, we can use matrix algebra.

One property of matrices is that we can multiply both sides of an equation by the inverse of a matrix without changing the solution. Since we know that B is invertible, we can multiply both sides of the equation by B⁻¹, the inverse of B:

AB B⁻¹ = BC B⁻¹

Now, we can simplify the left side of the equation, because B times its inverse gives us the identity matrix I:

A I = C B⁻¹

Again, we can simplify the left side of the equation, because anything multiplied by the identity matrix stays the same:

A = C B⁻¹

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If the area of the rectangle is 40 square centimeters and length is 7 cm less than 3 times the breadth then the length will be 8 cm and breadth will be 5 cm.

Given area of the rectangle is 40 square centimeters and length is 7 centimeters less than 3 times the breadth.

let the breadth of rectangle be x.

According to question

Length=3x-7

Breadth=x

Area of  rectangle=length* breadth

=\((3x-7)x\)

=\(3x^{2} -7x\)

Area is given as 40 square centimeters.

40=\(3x^{2} -7x\)

\(3x^{2} -7x-40=0\)

By factorization

\(3x^{2} -15x+8x-40=0\)

3x(x-5)+8(x-5)=0

(3x+8)(x-5)=0

3x+8=0

x=-8/3

x-5=0

x=5

We should neglect x=-8/3 because side cannot be negative. So we have taken x=5.

Put x=5 in 3x-7 to get length

length=3(5)-7

=15-7

=8

Hence the length will be 8 cm and breadth will be 5 cm.

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Let's move to the solution of the problem you've asked about. To use the remainder estimate for the integral test to find an upper bound for s − s100, we need to use the following formula:  Rn = sn - S`

Here, `Rn` = Remainder `sn` = The nth partial sum `S` = The actual value

We are required to find the upper bound for s − s100. We can write s − s100 as s - s1000 + s1000 - s100 By the integral test,

we have `s = int(1/(x(ln x)^p))dx ` Integrating it using u-substitution` u = ln x, du = dx/x` Substituting values,

`s = ∫du/(u^p)`= 1/(p-1)(u^(1-p)) + C = 1/(p-1)(ln x)^(1-p) + CAs p > 1, we have: `s < 1/(p-1)(ln x)^(1-p)` Therefore,

`s1000 < 1/(p-1)(ln 1000)^(1-p)`and`s100 < 1/(p-1)(ln 100)^(1-p)`  Therefore, the upper bound of

`s - s100` is `R100 < s - s100 < R1000`. The actual value of `s - s100` is equal to `R1000`.Since `R1000 > R100`, the actual value of `s - s100` is larger than the upper bound. Therefore, the actual value is greater than the estimated value.
To find an upper bound for s - s100 using the remainder estimate for the integral test, follow these steps:

1. Determine the function f(x) that represents the given series. In this case, you didn't provide the series, so let's assume it's a general convergent series with a positive, continuous, and decreasing function f(x).

2. Apply the integral test to ensure the series converges. Since the function is positive, continuous, and decreasing, the integral test can be used.

3. Calculate the integral from 100 to infinity for f(x)dx, which will give you an upper bound for the error s - s100.

4. Compare this upper bound to the actual value of s - s100. If the actual value is smaller than the upper bound, the actual value is closer to the sum of the infinite series.

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Answer:

(2) f(-2) = 3

Step-by-step explanation:

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

<95141404393>

Given:

\(\to \frac{2}{5}n+3-\frac{7}{10}n=\frac{3}{5}-3n\)

To find:

n=?

Solution:

\(\to \frac{2}{5}n+3-\frac{7}{10}n=\frac{3}{5}-3n\\\\\to \frac{2}{5}n-\frac{7}{10}n+3n=\frac{3}{5} -3\\\\\to n(\frac{4-7+30}{10})=\frac{3-15}{5} \\\\\to n(\frac{-3+30}{10})=\frac{3-15}{5} \\\\\to n(\frac{27}{10})=\frac{-12}{5} \\\\\to n=\frac{-12}{5} \times \frac{10}{27} \\\\\to n=-4 \times \frac{2}{9} \\\\\to n=-\frac{8}{9} \\\\\)

Therefore, the final answer of n is "\(-\frac{8}{9} \\\\\)".

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The drink will be F + 7.5 degrees Fahrenheit warm if left out for 30 minutes.

Let us first find the rate at which the drink is warming up.

We can use the formula,

T = T0 + k.t

where T is the temperature of the drink after time t,

T0 is the initial temperature, `

k is the rate of warming and t is the time.

Since the drink goes from F to F in 4 minutes,

we have F = F + 4k or k = 1/4.

Therefore, after 30 minutes, we have T = F + (1/4) * 30 = F + 7.5`.

Hence, the drink will be F + 7.5 degrees Fahrenheit warm if left out for 30 minutes.

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Answer:

13/7

Step-by-step explanation: YW :)

Answer:

\( \frac{13}{7} \)

Step-by-step explanation:

7×1+6/7

13/7

plz mark as brainliest

Answer:

43.68

Step-by-step explanation:

Answer:

43.68

Step-by-step explanation:

here is my work

sorry I don't know how to write with a mouse

Mr.johns invested money in each business is first business = $26909

and second business = $27909.

Given:

Last year he gained 10% on the first investment and 12% on the second if he invested $1000 more in the first business and gained a total of $6040.

Let x be the money invested in first business

From given statements:

10x/100 + (x + 1000)12/100 = 6040

multiply by 100 on both sides

10x + 12(x + 1000) = 6040*100

10x + 12x + 12000 = 604000

22x = 604000 - 12000

22x = 59200

x = 26909 invested in first business.

second business investment = 26909 + 1000 ⇒ 27909.

Therefore Mr.johns invested money in each business is first business = $26909 and second business = $27909.

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Answer:

\(a_{n}\) = 5n + 5

Step-by-step explanation:

The nth term of an arithmetic progression is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and d = a₂ - a₁ = 15 - 10 = 5 , then

\(a_{n}\) = 10 + 5(n - 1) = 10 + 5n - 5 = 5n + 5

Answer:

3x + 8

Step-by-step explanation:

Michele's ages is equivalent to x, or 1x. Then you add Kayla's age to Michele's age which now equals 3x. Finally, you add 8, which is Erica's age.