select all of the equations that are equivalent to 3x+5=20-x

Step-by-step explanation:

you don't know the Pythagoras formula yet ?

this is something you need to remember for life. this you will encounter everywhere (not just in school) :

c² = a² + b²

in a right-angled triangle c is the Hypotenuse (the side opposite of the 90° angle). a and b are the legs of the triangle.

4.

the legs of this right-angled triangle are the pole and the ground distance to the cable fixture on the ground.

the cable itself is the Hypotenuse (as the right angle is the angle between the pole and the ground distance).

so,

cable² = 8² + 6² = 64 + 36 = 100

cable = sqrt(100) = 10 m

5.

here we have a right-angled triangle with the direct distance between the points being the Hypotenuse, and the x and y coordinate differences are the legs.

so, we have

distance² = (3 - -3)² + (0 - -1)² = 6² + 1² = 36 + 1 = 37

distance = sqrt(37)

please note that since we are squaring, the direction of the differences and their signs do not matter. the square will turn positive and negative distances into positive numbers.

Carl Lewis, the popular Olympic sprinter in the 1980s and 1990s, ran a 100-meter dash that can be precisely modeled with exponential functions utilizing vmax.

Exponential functions are utilized to characterize the exponential decay of radioactive material, investment growth, or the spread of disease, among other things. It is quite crucial to understand what exponential functions are in order to understand how they can be used to model Lewis's 100-meter sprint, which can be accurately modeled with the help of vmax. The exponential function is a mathematical function with the following form:  f(x) = ab^x. Where, a and b are constants, and x is the independent variable of the function. The quantity of the function at any value of x can be calculated by plugging the value of x into the function and then solving for f(x).The vmax refers to the maximum speed of Lewis, which is a crucial component of the equation used to model his run. The equation used to model his run is V(t) = Vmax (1 - e^(-kt)).This equation can be used to determine the speed of the runner at any point in time throughout the sprint. Carl Lewis is a well-known Olympic sprinter from the 1980s and 1990s. His 100-meter sprint can be precisely modeled with exponential functions utilizing vmax. In order to understand how they can be used to model Lewis's 100-meter sprint, which can be accurately modeled with the help of vmax, it is quite crucial to understand what exponential functions are.The exponential function is a mathematical function with the following form: f(x) = ab^x. Where, a and b are constants, and x is the independent variable of the function. The quantity of the function at any value of x can be calculated by plugging the value of x into the function and then solving for f(x).The vmax refers to the maximum speed of Lewis, which is a crucial component of the equation used to model his run. The equation used to model his run is V(t) = Vmax (1 - e^(-kt)).This equation can be used to determine the speed of the runner at any point in time throughout the sprint. This model assumes that the runner accelerates smoothly from the starting line and reaches his maximum speed at some point during the race. The model also assumes that the runner maintains his maximum speed throughout the rest of the race. The model further assumes that the runner's speed gradually decreases as he approaches the finish line.

In conclusion, Carl Lewis's 100-meter sprint can be accurately modeled with exponential functions utilizing vmax. An equation V(t) = Vmax (1 - e^(-kt)) can be used to determine the speed of the runner at any point in time throughout the sprint.

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Step-by-step explanation:

an² = 182

When a = 2, n² = 182/2 = 91, n = 9.539...

When a = 5, n² = 182/5 = 36.4, n = 6.033...

Since 2 <= a <= 5, we have 6.033 <= n <= 9.539.

Therefore our possible values of n are 7, 8 and 9.

The possible values of n are 7, 8, 9

The given equation is:

an²  =  182

Make n the subject of the formula:

\(n^2=\frac{182}{a} \\n = \sqrt{\frac{182}{a}}\)

Let us consider the minimum and maximum values of a:

when a = 2

\(n = \sqrt{\frac{182}{2}}\\n = \sqrt{91} \\n = 9.54\)

When a = 5

\(n = \sqrt{\frac{182}{5}}\\n = \sqrt{36.4} \\n = 6.03\)

We can conclude that 6.03 < n < 9.54

Since n is an integer, the possible values of n are 7, 8, 9

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To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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Answer $-2

Step-by-step explanation:

CM = Cybil's Money = 0

Aunt Pays

CM = 5

Sister

5-7 = (-2)

If there exists a solution, then the vector (1, 6, 2) is a linear combination of the given vectors. We can solve this system of equations to determine the values of a, b, and c.

To determine whether the vector (1, 6, 2) is a linear combination of the vectors (1, 2, -1), (3, 1, 1), and (-4, 0, 6), we need to check if there exist scalars (constants) such that when we multiply each vector by its respective scalar and sum them up, we obtain the vector (1, 6, 2). Let's assume the scalars are a, b, and c for the three vectors respectively.

We can set up the following system of equations:

a(1, 2, -1) + b(3, 1, 1) + c(-4, 0, 6) = (1, 6, 2)

This can be written as:

(1a + 3b - 4c, 2a + b, -a + b + 6c) = (1, 6, 2)

By comparing the corresponding components, we obtain the following system of equations:

1a + 3b - 4c = 1

2a + b = 6

-a + b + 6c = 2

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The true statements are:

The lines are given as:

Lines mn, pq, mp, mn, nq and pq

From the question, the lines are either parallel lines or perpendicular lines

As a general rule,

Parallel lines have equal slope

This means that:

Lines mn and pq have the same slope

Assume two perpendicular lines have slopes m and n.

The relationship between their slopes is:

m * n = -1

This means that:

The product of the slopes of perpendicular lines mn and mp is -1

Hence, the true statements are (a) and (c)

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Complete question

Line mn is parallel to line pq, mp is perpendicular to mn, and nq is perpendicular to pq. consider each statement and determine whether it is true or false. circle the correct answer.

Pptions:

Answer:

Using the mid-term break formula for all of them.

a) x²+7x+12

= x²+3x+4x+12

= x(x+3)+4(x+3)

= (x+4)(x+3)

b) x²+6x+8

= x²+2x+4x+8

= x(x+2)+4(x+2)

= (x+4)(x+2)

c) x²+5x+6

= x²+2x+3x+6

= x(x+2)+3(x+2)

= (x=3)(x+2)

d) x²+8x+7

= x²+7x+x+7

= x(x+7)+1(x+7)

= (x+1)(x+7)

Answer:

a) the middle number is seven and the last number is 12

factorising means we want something like (x + ___) (x +__)

Which number go into the blanks?

we need 2 numbers that add together to get 7 multiplied together to get 12.

3 + 4 is equal to 7

3x4=12

Answer:

(x+3)(x+4)

b) the middle number is 6 and the last number is 8

Factoring means we want something like

(x+___)(x+___)

which number go to the blanks?

We need two numbers that add together to get 6 and multiply together to get 8

2+4=6

2x4=8

Answer:

(x+2)(x+4)

c) the middle number is 5 and the last number is 6

we need two numbers that add together to get 5 and multiply together to get 6

2 + 3 is 5 and 2 x 3=6

Answer:

(x+2)(x+3)

Answer:

d) (x+1)(x+7)

The resulting triangle after reflecting ∆PQR in the line y = -1 and rotating it 90° counterclockwise about the point R is ∆P''Q''R'' with vertices P''(5, 2), Q''(5, 2), and R''(6, -2).

To reflect the triangle ∆PQR in the line y = -1, we can find the images of each vertex by reflecting them across the line.

The reflection of a point (x, y) across the line y = -1 can be obtained by keeping the x-coordinate the same and negating the y-coordinate.

For vertex P(2, 4):

The image of P after reflection will be P' with coordinates (2, -3).

For vertex Q(2, 2):

The image of Q after reflection will be Q' with coordinates (2, -3).

For vertex R(6, 2):

The image of R after reflection will be R' with coordinates (6, -2).

Now, to rotate the reflected triangle 90° counterclockwise about the point R(6, -2), we can use the rotation formulas.

The rotation of a point (x, y) counterclockwise by 90° about the point (a, b) can be obtained using the following formulas:

x' = a + (y - b)

y' = b - (x - a)

Applying these formulas to each vertex of the reflected triangle:

For vertex P', which is (2, -3):

x' = 6 + (-3 - (-2)) = 6 + (-1) = 5

y' = -2 - (2 - 6) = -2 - (-4) = 2

The image of P' after rotation will be P'' with coordinates (5, 2).

For vertex Q', which is (2, -3):

x' = 6 + (-3 - (-2)) = 6 + (-1) = 5

y' = -2 - (2 - 6) = -2 - (-4) = 2

The image of Q' after rotation will be Q'' with coordinates (5, 2).

For vertex R', which is (6, -2):

x' = 6 + (-2 - (-2)) = 6 + (0) = 6

y' = -2 - (6 - 6) = -2 - (0) = -2

The image of R' after rotation will be R'' with coordinates (6, -2).

Therefore, the resulting triangle after reflecting ∆PQR in the line y = -1 and rotating it 90° counterclockwise about the point R is ∆P''Q''R'' with vertices P''(5, 2), Q''(5, 2), and R''(6, -2).

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Answer:

this is the answer of your question

Answer:

Step-by-step explanation:

1. \(\frac{2}{t}=\frac{12}{18}\) you have to cross multiply for you to get a value of t

2t=2x18

2t=36

t=3

note: you have to do the same with the other problems to find the value of the other.

Answer:91/4

Step-by-step explanation:
These figures appear to be similar, indicating that their sides are related by a specific ratio. To find this ratio, we divide the measurements of two sides of the figures, which are 16 and 10. By doing this, we get a scale factor of 8/5 for the quadrilaterals. To solve for x, we multiply both sides of the equation 8/5=30/(x-4) by 5(x-4). This gives us 8(x-4)=30(5). After simplifying, we find that 8X-32 is equal to 150. Adding 32 to each side, we get 8x=182. Finally, we solve for x, which is equal to 91/4.

Answer:Thus our answer is 60 miles per hour.

Step-by-step explanation:

brainliest?

To calculate the miles per gallon, or the unit rate, you divide the total distance by the total fuel used. In this example, the car uses an average of 26.8 miles per gallon of gasoline.

The unit rate represents the amount of miles a car can travel per one gallon of gasoline. To find this, we need to divide the total distance driven by the gallons of gasoline used.

Step 1: Identify the total distance and the total gallons used. Here, the total distance driven is 100.5 miles, and the gallons of gasoline used is 3.75.

Step 2: To find how many miles per gallon the car uses, divide the total miles by the total gallons used:

100.5 miles / 3.75 gallons = 26.8 miles per gallon.

So, the car uses an average of 26.8 miles per gallon of gasoline. In terms of decimals, 26.8 is the unit rate.

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Answer:

165 inches

Step-by-step explanation:

Answer:

-5^ -1 = 1/(-5) = -1/5

-1/y^(-4) = -(1/(1/y^4)) = -y^4

5^4 x 5^7 = 5^(4 + 7) = 5^11

Hope this helps!

:)

Answer:

1. -1/5

2. -y⁴

3. 5¹¹

Step-by-step explanation:

1. simplify -5^ -1

1/(-5)

-1/5

2. simplify -1/y^ -4

-1 × y⁴

-y⁴

3. simplify 5^ 4 x 5^ 7

5^(4+7)

5¹¹

Descriptive statistics are those that involve gathering, arranging, and summarizing data.

Brief informational coefficients known as descriptive statistics are used to sum up a given data set, which may be a sample of a population or a representation of the entire population. Measures of the central tendency or measures of variability make up descriptive statistics (spread).

A descriptive statistic's main function is to summarize data. Only the data set from which they were derived are statements made by descriptive statistics; they never extend further than the data you have.

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Answer:

3 3/4 or 3.75 hours.

Step-by-step explanation:

If you need to travel 300 km, assuming you are going at the speed limit, you take the total amount and divide it by that.

300 / 80 = 3.75 hours

Answer:

Step-by-step explanation:

The two x angles on the right are supplementary which means they add up to 180 degrees

5x + 12 + 7x - 24 = 180

12x - 12 = 180

12x = 192

x = 192/12

x = 18

5x + 12 and y are corresponding angles and are therefore equal

5(18) + 12 = 90 + 12 = 102

Therefore y = 102

We have to find b first: 3 = -3/2(10)+b3 = -15+b18 = bNow right the equation, your slope will be the same one....Y = -3/2x + 18

More

The red-shaded side is Y < x + 1

The blue-shaded side is x2 + y2 >= 4

You can get the points by inputing any random number into X or Y.

But the solution to the system is: ( 0.5 , 1.5 )

Answer:

The value of x = 12

Step-by-step explanation:

Here, we are to find the value of x

If the two angles are supplementary, it means that they add up to be 90 degrees

Thus;

∠GHJ + ∠MHJ = 90

6x + 18 = 90

6x = 90-18

6x = 72

x = 72/6

x = 12

Answer:

∠ABC =   52°

∠BCA =  48°

∠CAB = 80°

Step-by-step explanation:

Angle sum property of triangle: Sum of all the angles of a triangle is 180.

13x² + 12x² + 20x² = 180

Combine like terms,

                 45x²  = 180

                     x² = 180 ÷ 45

                     x² = 4

                     x = √4

                     x = ± 2

x = 2 ; -2

∠ABC = 13x² = 13*4 = 52°

∠BCA = 12x² = 12 *4 = 48°

∠CAB = 20x² = 20 *4 = 80°

The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²

The angles will be calculated as follows:-

13x² + 12x² + 20x² = 180

45x²  =  180

x²  =  4

x   =  ±2

The angles will be:-

∠ABC = 13x²  = 13 x ( 2² ) = 52

∠ACB = 12x²  = 12 ( 2² )    = 48

∠CAB = 20x²  = 20 ( 2² )  = 80

Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

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After solving given equation,

1. log 5x = log (2x+9) we get x = 3

2. log (10-4x) = log (10-3x) we get x = 0

3. log (4p-2) = log (-5p+5) cant get solution.

4. log (4k-5) = log (2k-1) we get k = 2

5. log (-2a+9) = log (7-4a) cant get solution.

6. 2log(-2r) = 0 we get  r = -1/2 and r = 1/2.

7. -10 + log(n+3) = -10 we get n = -2

8. -2log(7x-29) = -40 we get x = (29 ± \(10^{10}\)) / 7

9. -6log(x-3) = -24 we get x= 10003

10. log(x-7) - log(m+2) = 4 we get x = 10000(m+2) + 7

11. log(2+35) = log(12) - log(12v-1) we get v = 49/444

12. log(-11x+2) = log(x²+30) we get x = 4 or -7

13. log(16+2b) = log(b-4) we get b = -10

14. log(x) + log(8) = 2 + 17 we get \(x = 10^{19} /8\)

15. log(2) + log(x) = 1 we get x = 5

16. log(2) + log(4x²-1) = log(22) we get \(x = \sqrt{3}\)

17. ln(n+12) = ln(-9n-2) we get n = -7/5

18. log(x) - log(2) = 1 we get x = 20

19. log(x) + log(7) - log(3) = 2 we get x = 300/7

20. log(x+6) - log(x) = log(2) we get x = 6

21. log(x+1) - log(x) = log(29) we get x = 1/28

22. log(6) + log(2x²) = log(48) we get x = 2

23. ln(2) - ln(3x+2) = 1 we get \(x = (2/e^{-2} )/3\)

24. ln(-3x-1) - ln(7) = -2 we get \(x = -(1+7/e^2)/3\)

25. ln(x-3) - ln(x-5) = ln(5) we get x = 7

26. ln(4x+1) - ln(3) = 5 we get \(x = (3e^5-1)/4\)

1. log 5x = log (2x+9)

Setting the arguments equal to one another will allow us to answer this equation:

5x = 2x + 9

3x = 9

x = 3

So the solution is x = 3.

2. log (10-4x) = log (10-3x)

Setting the arguments equally again results in:

10-4x = 10-3x

-x = 0

x = 0

Hence, the solution is x = 0.

3. log (4p-2) = log (-5p+5)

The logarithm of a negative number is undefinable, hence the equation has no solution.

4. log (4k-5) = log (2k-1)

Setting the arguments equal:

4k-5 = 2k-1

2k = 4

k = 2

So the solution is k = 2.

5. log (-2a+9) = log (7-4a)

The logarithm cannot be defined until both arguments are true, hence this equation cannot be resolved.

6. 2log(-2r) = 0

Using the rule that \(2log(a) = log(a^2)\):

\(log((-2r)^2) = 0\)

\(log(4r^2) = 0\)

\(4r^2 = 10^0\)

\(4r^2 = 1\)

\(r^2 = 1/4\)

r = ±1/2

So the solutions are r = -1/2 and r = 1/2.

7. -10 + log(n+3) = -10

By subtracting -10 from both sides:

log(n+3) = 0

Hence, n+3 = \(10^0\) = 1, so n = -2.

8. -2log(7x-29) = -40

By dividing by -2:

\(log(7x-29)^2 = 20\)

By taking the exponential of both sides:

\((7x-29)^2\) = \(10^{20}\)

After solving for x:

7x-29 = ±\(10^{10}\)

x = (29 ± \(10^{10}\)) / 7

9. -6log(x-3) = -24

By dividing by -6:

log(x-3) = 4

Hence, x-3 = \(10^4\)

∴ x = 10003.

10. log(x-7) - log(m+2) = 4

Using the rule that log(a) - log(b) = log(a/b):

log((x-7)/(m+2)) = 4

So, (x-7)/(m+2) = 10^4,

so x-7 = 10000(m+2)

x = 10000(m+2) + 7

11. log(2+35) = log(12) - log(12v-1)

log(37) = log(12/(12v-1))

37 = 12/(12v-1)

12v-1 = 12/37

12v = 49/37

v = 49/444

12. log(-11x+2) = log(x²+30)

-11x+2 = x²+30

x²+11x-28 = 0

(x+7)(x-4) = 0

x = -7 or x = 4

13. log(16+2b) = log(b-4)

16+2b = b-4

b = -10

14. log(x) + log(8) = 2 + 17

log(8x) = 19

\(8x = 10^{19}\)

\(x = 10^{19} /8\)

15. log(2) + log(x) = 1

log(2x) = 1

2x = 10

x = 5

16. log(2) + log(4x²-1) = log(22)

log(8x²-2) = log(22)

8x²-2 = 22

8x² = 24

x² = 3

\(x = \sqrt{3}\)

17. ln(n+12) = ln(-9n-2)

n+12 = -9n-2

10n = -14

n = -7/5

18. log(x) - log(2) = 1

log(x/2) = 1

x/2 = 10

x = 20

19. log(x) + log(7) - log(3) = 2

log(7x/3) = 2

7x/3 = 100

x = 300/7

20. log(x+6) - log(x) = log(2)

log((x+6)/x) = log(2)

(x+6)/x = 2

x+6 = 2x

x = 6

21. log(x+1) - log(x) = log(29)

log((x+1)/x) = log(29)

(x+1)/x = 29

x+1 = 29x

x = 1/28

22. log(6) + log(2x²) = log(48)

log(12x²) = log(48)

12x² = 48

x² = 4

x = 2

23. ln(2) - ln(3x+2) = 1

ln(2/(3x+2)) = 1

2/(3x+2) = e

3x+2 = 2/e

\(x = (2/e^{-2} )/3\)

24. ln(-3x-1) - ln(7) = -2

ln(-3x-1) = ln(7) - 2

\(-3x-1 = 7/e^2\)

\(x = -(1+7/e^2)/3\)

25. ln(x-3) - ln(x-5) = ln(5)

ln((x-3)/(x-5)) = ln(5)

(x-3)/(x-5) = 5

x-3 = 5x-25

x = 7

26. ln(4x+1) - ln(3) = 5

ln((4x+1)/3) = 5

\((4x+1)/3 = e^5\)

\(4x+1 = 3e^5\)

\(x = (3e^5-1)/4\)

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Question- Solve each equation.

1. log 5x = log (2x+9)                          2. log (10-4x) = log (10-3x)

3. log (4p-2) = log (-5p+5)                  4. log (4k-5) = log (2k-1)

5. log (-2a+9) = log (7-4a)                   6. 2log(-2r) = 0

7. -10 + log(n+3) = -10                          8. -2log(7x-29) = -40

9. -6log(x-3) = -24                               10. log(x-7) - log(m+2) = 4

11. log(2+35) = log(12) - log(12v-1)        12. log(-11x+2) = log(x²+30)

13. log(16+2b) = log(b-4)                      14. log(x) + log(8) = 2 + 17

15. log(2) + log(x) = 1                             16. log(2) + log(4x²-1) = log(22)

17. ln(n+12) = ln(-9n-2)                          18. log(x) - log(2) = 1

19. log(x) + log(7) - log(3) = 2              20. log(x+6) - log(x) = log(2)

21. log(x+1) - log(x) = log(29)               22. log(6) + log(2x²) = log(48)

23. ln(2) - ln(3x+2) = 1                          24. ln(-3x-1) - ln(7) = -2

25. ln(x-3) - ln(x-5) = ln(5)                    26. ln(4x+1) - ln(3) = 5

Answer:

Step-by-step explanation:

1. 7x+7

2. 2y+5

Not sure about 3 or 4

5. 11x

6.5x+7

7.10x-9y

8. 5x+5y

Not sure about 9

10. 4x+4

Answer:

7x+7

2y+5

6x^2+3y

5a^3+4a^2+3a (This one is the same because none of the terms are alike)

11x

5x+7

10x-9y

5x+5y

x^2+6x

4x+4

Step-by-step explanation:

Combine like terms for all of these, meaning adding or subtracting anything that has the same variable or power of a variable attached to it.

Answer:

Step-by-step explanation:

e = 300-10(30)

e = 300 - 300

e = 0

The formula for the entries of \(M^{n}\), where n is a positive integer is \(=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right]\)  for M = \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\) .

Let us find the formula for entries of \(M^{n}\), where n is a positive integer.

Let M be a 2 x 2 matrix  \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\)

we get the eigenvalues and their associated eigenvectors as follows-

Eigenvalue : 9λ , multiplicity : 1λ, eigenvector : [ 1, 1]

Eigenvalue : 7λ , multiplicity : 1λ, eigenvector : [ 0.5, 1]

now, we have

\({\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right] }\) = \(\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]^{-1}\) \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\)  \(\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]\)

              = \(\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right]\)  \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\)  \(\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]\)

hence, \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\) = \(\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]\)  \(\left[\begin{array}{cc}9 & 0 \\0 & 7\end{array}\right]\)  \(\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right]\)

So,

\({\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]^n } & =\left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right]^n\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right]\)

                    \(= \left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{cc}9^n & 0 \\0 & 7^n\end{array}\right]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right]\)

                    \(=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right]\)

Thus, the formula for the entries of \(M^{n}\), where n is a positive integer is \(=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right]\) for M = \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\) .

Read more about matrices:

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Reason:

The first peak is at x = 0. The next peak over is at x = 1. The difference is 1-0 = 1 which is the period.

The period is the amount of time needed to repeat the cycle.

The first peak occurs at x = 0, and the next peak occurs at x = 1. The difference between these two points is  1, which represents the period of the function.

The period of a function can be determined by finding the difference between two consecutive peaks or troughs.

To determine the period step by step, we start by identifying the first peak or trough of the function. In this case, it is x = 0.

Then, check for the next peak or trough, which is x = 1.

The difference between these two points gives  the period, which is 1 unit of time.

The period represents the length of time required for the function to complete one full cycle and repeat itself. It is an important concept in understanding the periodic behavior of functions.

Learn more about periods here:

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Answer:

It is asking you what you would put as your statement for step 4.

Step-by-step explanation:

The answer by the way would be what you have clicked on - angle 1 + angle 4 = 180 degrees.

Answer:

  marked answer is correct

Step-by-step explanation:

The problem is asking you to choose an equation that should be written as statement 4 of the proof.

Statement 4 is an algebraic expression of the verbal statement 3. The marked response is correct. It expresses the relationship that is the definition of supplementary angles.

__

Often you can gain a clue in these proofs by looking at places that use similar reasons or similar statements. Lines 5 and 6 are the algebraic and verbal representations of the relation between angles 1 and 2. This matches lines 3 and 4, which are the verbal and algebraic representation of the same relationship between angle 1 anf 4.

Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer:

16.6 inches

Step-by-step explanation:

using the pythagorean theorem which is a^2 + b^2 = c^2 you can add 9^2 + 14^ together to get 277 and when you find the square root of 277 you get 16.6

Answer:

11<x<12

Step-by-step explanation: