Line passes (-5, -1) and (10, -7)

Answer:

c a those are the answers in order

Answer:

D, C, C, A, B, C

Step-by-step explanation:

Answer:

B and E

Step-by-step explanation:

A.

-6(2x - 1)
Distribute the -6.

-12x + 6

B.

6(2x - 1)
Distribute the 6.

12x - 6

C.

6x(2 - 1)

Subtract inside parenthesis.

6x(1)
Multiply.

6x

D.

-6x(2x - 1)
Distribute the -6x.

-12x² + 6x

E.

-6(-2x + 1)
Distribute the -6.

12x - 6

F.

6x(-2x + 1)

Distribute the 6x.

-12x² + 6x

The distance between Ray-Ann and Steve, using the law of cosines, is given as follows:

11.5 feet.

The law of cosines states that we can find the length of the missing side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

The parameters of the equation are given as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the distance between Ray-Ann and Steve is obtained as follows:

c² = 6²+ 7² - 2 x 6 x 7 x cos(124)º

c² = 132

c = square root of 132

c = 11.5 feet.

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Gaussian Elimination and Gauss-Jordon Elimination are two methods of solving linear systems of equations.
A-x=3, y=2, z=-2,B-x=4, y=-2, z=15 C-x=2, y=-2, z=2.

An equation is a mathematical statement that states two expressions are equal. It consists of two expressions separated by an equals sign (=) and can use any of the operations of arithmetic such as addition, subtraction, multiplication, division and exponents. An equation can be solved to find the value of one or more variables that make the equation true.

Question 1:

Using Gaussian Elimination:

2x+y + 2z = 1

4x + 3z = -5

5y + 4z = 13

Step 1: Subtract 2 times the first equation from the second equation.

0x+3y+z=-6

Step 2: Subtract 5 times the first equation from the third equation.

0x+2y+3z=10

Step 3: Subtract 2 times the second equation from the third equation.

x+y=4

Step 4: Subtract 4 times the second equation from the first equation.

x=3

Step 5: Substitute x = 3 in the second equation.

3+2y+z=-6

Step 6: Subtract 3 times the fifth equation from the fourth equation.

y=2

Step 7: Substitute y = 2 in the fifth equation.

3+4+z=-6

Step 8: Solve for z.

z=-2

Answer: x=3, y=2, z=-2

Question 2:

Using Gauss-Jordan Elimination:

2x+y+z=13

x+2y+z= 11

x + 3y + 3z = 19

Step 1: Subtract 2 times the first equation from the second equation.

-x+3y=2

Step 2: Subtract x times the first equation from the third equation.

2y+2z=6

Step 3: Subtract 3 times the second equation from the third equation.

x=4

Step 4: Substitute x=4 in the second equation.

4+3y=2

Step 5: Solve for y.

y=-2

Step 6: Substitute y=-2 in the first equation.

2x+(-2)+z=13

Step 7: Solve for z.

z=15

Answer: x=4, y=-2, z=15

Question 3:

Using Gaussian Elimination:

-3x+2y-6z = 6

5x + 7y - 5z = 6

x + 4y = 2z = 8

Step 1: Subtract 5 times the first equation from the second equation.

2x+9y-z=0

Step 2: Subtract 2 times the third equation from the first equation.

-5x+2y-2z=-2

Step 3: Subtract 2 times the first equation from the third equation.

3x+7y=2

Step 4: Subtract 3 times the second equation from the third equation.

x=2

Step 5: Substitute x=2 in the second equation.

4+9y-z=0

Step 6: Solve for y.

y=-2

Step 7: Substitute y=-2 in the fifth equation.

2+(-2)-z=0

Step 8: Solve for z.

z=2

Answer: x=2, y=-2, z=2

Conclusion:

Gaussian Elimination and Gauss-Jordon Elimination are two methods of solving linear systems of equations. Both methods rely on manipulating the equations to create a triangular form, which allows for the easier determination of the variables. By using both methods, we were able to solve each of the three linear systems of equations given in the question.

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Answer:

A

Step-by-step explanation:

< means "less than". The number must be smaller than 45 to be true.

Answer:

X=44

Step-by-step explanation:

Hops this helps

The function is an exponential growth function

The function is given as

y=2(1.06)^9

We can begin by rewriting the given equation as:

y = 2 * 1.06t

So, we have

y = 2 * (1 + 0.06)^t

Now we can see that the equation is in the form y = a*b^t,

where a = 2 and b = 1.06^9

This equation represents exponential growth because the base of the exponent, b = 1.06, is greater than 1.

We can re-write it in the form y = a(1+r)t,

we can find the value of r by subtracting 1 from 1.06 which is 0.06 and the value of a is 2.

so we have y = 2(1+0.06)^t

So, the equation represents exponential growth with a = 2 and r = 0.06

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The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.

Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.

The discriminant is described below:

Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d²      (1)

Where:

If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:

Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²

Δ = - 1024

The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

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Answer:

21/100 is the correct answer.

Hope it helps.....

Answer:

\(\frac{21}{100}\)

Step-by-step explanation:

When adding fractions, make sure that both denominators are the same

To do this multiply \(\frac{1}{10}\) by 10 to make it into \(\frac{10}{100}\)

\(\frac{10}{100} + \frac{11}{100}\) = \(\frac{21}{100}\)

The maximum number of pieces of drywall that can be installed before running out of screws is 0.

To determine the number of pounds of drywall that can be installed before running out of screws, we need to consider the weight of both the drywall and the screws.

Given:

12 screws are required per piece of drywall.

Each piece of drywall weighs 30 lbs.

Each screw weighs 0.011 lbs.

The company received a bulk order of 100 lbs of screws.

Let's denote the number of pieces of drywall as "x".

The weight of the screws can be calculated as:

Weight of screws = Number of screws × Weight per screw

Weight of screws = 12 screws × 0.011 lbs/screw

Weight of screws = 0.132 lbs

Now, we can calculate the maximum number of pieces of drywall that can be installed based on the weight of the screws:

Maximum number of pieces of drywall = Weight of screws / Weight per drywall piece

Maximum number of pieces of drywall = 0.132 lbs / 30 lbs

Maximum number of pieces of drywall ≈ 0.0044 pieces

Since it doesn't make sense to have a fraction of a drywall piece, we can round down the result. Therefore, the maximum number of pieces of drywall that can be installed before running out of screws is 0.

In conclusion, with the given bulk order of 100 lbs of screws, the company cannot install any drywall before running out of screws.

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The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Answer:

6.12

Step-by-step explanation:

Have a nice day

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

9 - 3 = 6

Average rate of return for 3D Printer is 4% and for Truck is 9%.

Average income = Estimated total income/ useful life.

For 3D Printer,

Average Income = 4160/ 4

Average Income = $1040

For Truck,

Average Income = 15120/ 7

Average Income = $2160

Average Investment = (Investment + residual value)/ 2

For 3D Printer,

Average Investment = (52000 + 0)/ 2

Average Investment = $26000

For Truck,

Average Investment = (48000 + 0)/ 2

Average Investment = $24000

Average rate of return = Average Income/ Average Investment

For 3D Printer,

Average rate of return = 1040/26000

Average rate of return = 4%

For Truck,

Average rate of return = 2160/24000

Average rate of return = 9%

Hence, average rate of return for 3D Printer is 4% and for Truck is 9%.

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Answer:

C) (-2, 4), (6,8) is the correct answer.

Step-by-step explanation:

Given that line segment AB:

A (-3, 6) and B (9, 12) is dilated with a scale  factor 2/3 about the origin.

First of all, let us calculate the distance AB using the distance formula:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Here,

\(x_2=9\\x_1=-3\\y_2=12\\y_1=6\)

Putting all the values and finding AB:

\(AB = \sqrt{(9-(-3))^2+(12-6)^2}\\\Rightarrow AB = \sqrt{(12)^2+(6)^2}\\\Rightarrow AB = \sqrt{144+36}\\\Rightarrow AB = \sqrt{180}\\\Rightarrow AB = 6\sqrt{5}\ units\)

It is given that AB is dilated with a scale factor of \(\frac{2}{3}\).

\(x_2'=\dfrac{2}{3}\times x_2=\dfrac{2}{3}\times9=6\\x_1'=\dfrac{2}{3}\times x_1=\dfrac{2}{3}\times-3=-2\\y_2'=\dfrac{2}{3}\times y_2=\dfrac{2}{3}\times 12=8\\y_1'=\dfrac{2}{3}\times y_1=\dfrac{2}{3}\times 6=4\)

So, the new coordinates are A'(-2,4) and B'(6,8).

Verifying this by calculating the distance A'B':

\(A'B' = \sqrt{(6-(-2))^2+(8-4)^2}\\\Rightarrow A'B' = \sqrt{(8)^2+(4)^2}\\\Rightarrow A'B' = \sqrt{64+16}\\\Rightarrow A'B' = \sqrt{80}\\\Rightarrow A'B' = 4\sqrt{5}\ units = \dfrac{2}{3}\times AB\)

So, option C) (-2, 4), (6,8) is the correct answer.

Answer:

forebrain

Step-by-step explanation:

Answer:

Cerebrum???

Step-by-step explanation:

HOPE THIS HELPEDDD:)))

Answer:

Quadrilaterals

Step-by-step explanation:

Answer:

?⋅3=4.5 or 3⋅?=4.5

The measure of a central angle of a decagon is 36 degrees.

the 1/2 central angle = 18 degrees

Apothem ≈ 16.93

Area of the decagon ≈ 931.15

The figure has ten sides hence a decagon

To find the measure of a central angle of a decagon, we need to use the formula:

Central angle = 360 degrees / number of sides

Substituting the value for a decagon, we get:

Central angle = 360 degrees / 10 sides

Central angle = 36 degrees

To find the 1/2 central angle, we simply divide the central angle by 2:

1/2 central angle = 36 degrees / 2

1/2 central angle = 18 degrees

To find the apothem, we use the formula:

Apothem = (Side length) / (2 x tan(180 / number of sides))

Substituting the given values, we get:

Apothem = (11) / (2 x tan(18 degrees))

Apothem ≈ 16.93

To find the area of the decagon, we first need to find the perimeter using the formula:

Perimeter = (Number of sides) x (Side length)

Perimeter = 10 x 11

Perimeter = 110

Now, we can use the formula for the area:

Area = (1/2) x Apothem x Perimeter

Area = (1/2) x 16.93 x 110

Area ≈ 931.15

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Answer:

324

Step-by-step explanation:

We can use a proportion.

12/8 = x/216

8x = 12 × 216

8x = 2592

x = 324

Any proper CDF \(F(x)\) has the properties

• \(\displaystyle \lim_{x\to-\infty} F(x) = 0\)

• \(\displaystyle \lim_{x\to+\infty} F(x) = 1\)

so we have to have a = 0 and b = 1.

This follows from the definitions of PDFs and CDFs. The PDF must satisfy

\(\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1\)

and so

\(\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0\)

\(\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1\)

In every 10 minutes an average of 3 customers will arrive to the pizza station

Given,

The number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour.

We have to find the average number of customers arrives in each 10 minutes.

Here,

The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:

P (X = x) = (e^-μ × μ^x) / x!

Where,

The number of successes is x.

The Euler number is e = 2.71828.

μ is the average over the specified range.

Now,

Rate of 18 customers per hour;

μ = 18 n

n is the number of hours.

Number of customers arrive in each 10 minutes

10 minutes = 10/60 = 1/6

Then,

μ = 18 x 1/6 = 3

That is,

In every 10 minutes an average of 3 customers will arrive to the pizza station.

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Answer:

C = 1.5m+6

Step-by-step explanation:

The numbers of miles that we ride, we are charged 1.5 based on that. Hence, 1.5m. And we are anyway charged with 6 dollars, so plus 6.

The tax revenue is $ 9000 and Deadweight loss is $500.

We have,

Hotel rooms in Smalltown go for $100, and 1,000 rooms are rented on a typical day.

So, The tax revenue is calculated by :

Tax revenue = Tax Imposed × Quantity sold

= 10 x 900

= $ 9000

Now, The deadweight loss is calculated as:

= 1/2 × Tax imposed × change in quantity sold

= 1/2 x 10 x (1000-900)

= $500

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