Please answer correctly

Please Answer Correctly

Answers

Answer 1

By direct comparison we conclude that the graph of g(x) is the graph of f(x) compressed vertically and reflected over the x-axis. (Correct choice: C)

How to compare two quadratic functions according to rigid transformations

In this question we must compare two functions in terms of characteristics associated with rigid transformations. Rigid transformations are transformations applied on functions such that Euclidean distance is conserved. Two common operations are shown below:

Stretching

h'(x) = k · h(x)     (1)

Where k is the stretch factor, where 0 < k < 1 indicates a contraction and k > 1 indicates a stretch.

Reflection over the x-axis

h'(x) = - h(x)     (2)

By direct comparison we conclude that the graph of g(x) is the graph of f(x) compressed vertically and reflected over the x-axis. (Correct choice: C)

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Related Questions

Please help with this math problem ASAP!! Its due tonight!! I will give branliest!! :)

Please help with this math problem ASAP!! Its due tonight!! I will give branliest!! :)

Answers

Answer:

I’m not sure but I think it’s 5.88

Step-by-step explanation:

Easy! Please help! Giving BRAINLIEST
Look at the question on the picture <3​

Easy! Please help! Giving BRAINLIEST Look at the question on the picture &lt;3

Answers

Answer:

2134

Step-by-step explanation:

Answer:

Its not what the first person said its 321

Step-by-step explanation:

First you multiply the stuff in the parenthesis which gets you 125-30 in the parenthesis

Then you multiply 3 to 125 and 30 to get 375-90

Multiply 4 and 3 to the second power which is 9 and you will get

375-90+36 and you will subtract 375 and 90 to get 285 then add 36 to get the final answer of 321

I am not 100% sure this is right but you can try it

If A is 3x3 and det(2A−1)=5=det[(A)2(BT)−1, find det(A) and det(B).

Answers

In this case, det(A) = 3/4 and det(B) = 1458/4096.

How to determine the value of det(A)

If A is 3x3 and det(2A−1)=5=det[(A)2(BT)−1], we have to find det(A) and det(B).

Firstly, let's write out the determinant property of 2A - 1. By expanding the determinant, we get:

det(2A - 1) = 5⟺ 8 det(A) - det(I) = 5⟺ 8 det(A) - 1 = 5⟺ 8 det(A) = 6⟺ det(A) = 3/4

Now let's consider the second equation.

We have:

det[(A)2(BT)−1] = 5

We know that det(A) = 3/4.

Therefore, we can rewrite the above equation as:

det[(A)2] × det(BT)−1 = 5

Taking the determinant of the transpose of B is the same as taking the determinant of B

Therefore,

det[(A)2] × det(B)−1 = 5⟺ [det(A)]6 × det(B)−1 = 5⟺ (3/4)6 × det(B)−1 = 5⟺ (729/4096) × det(B)−1 = 5⟺ det(B)−1 = 4096/1458⟺ det(B) = 1458/4096

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100. Hardison drives his 6-wheeled truck 7,700
miles in 20 days. (There are 5,280 feet in a
mile.) If each of the 6 wheels of his truck
has a radius of 12 inches, approximate the
number of revolutions each tire made per
day, on average, by using for .
F. 53,900
G. 323,400
H. 646,800
J. 1,940,400
K. 6,468,000

Answers

Answer:the answer is 53 900

Step-by-step explanation:

if you  you have to add subtract an then divid

Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y=-8
y=6

Answers

Answer:

They're parallel.

Step-by-step explanation:

The reason is that any equation only with a y coordinate is a horizontal line. As they're both horizontal, they'd be parallel.

please answers this​

please answers this

Answers

Answer:

shusidvxxosbsbzbz

Step-by-step explanation:

usjzkdofjfbf

Answer:

50 degree for X look at pic attached

please answers this

Need help on these 2 questions please??? 14 points ?

Need help on these 2 questions please??? 14 points ?

Answers

Answer:

8 is congruent 9 isnt

Step-by-step explanation:

Answer: 8. is Congruent and 9. Isn't Congruent

Step-by-step explanation:

Which phase of inferential statistics is sometimes considered to be the most crucial because errors in this phase are the most difficult to correct?

Answers

The phase of inferential statistics which is sometimes considered to be the most crucial because errors in this phase are the most difficult to correct is "data gathering".

What is inferential statistics?

Inferential statistics are frequently employed to compare treatment group differences.

Some characteristics of inferential statistics are-

Inferential statistics compare treatments groups and make conclusions about the greater population of participants using measures from the experiment's sample of subjects.Inferential statistics aids in the development of explanations for a condition or phenomenon. It enables you to draw conclusions on extrapolations, which distinguishes it from descriptive statistics, which simply summarize the information that has been measured.There are numerous varieties of inferential statistics, each with its own set of research design & sample characteristics. To select the correct statistical test of their experiment, researchers should reference the numerous texts about experimental design and statistics.

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Show the calculating process by the restoring-division
algorithm for the following division case:
Divisor 00011
Dividend 1011

Answers

The quotient is 1111. The process continues until the result is less than the divisor.

To perform the division using the restoring-division algorithm with the given divisor and dividend, follow these steps:

Step 1: Initialize the dividend and divisor

Divisor: 00011

Dividend: 1011

Step 2: Append zeros to the dividend

Divisor: 00011

Dividend: 101100

Step 3: Determine the initial guess for the quotient

Since the first two bits of the dividend (10) are greater than the divisor (00), we can guess that the quotient bit is 1.

Step 4: Subtract the divisor from the dividend

101100 - 00011 = 101001

Step 5: Determine the next quotient bit

Since the first two bits of the result (1010) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

Step 6: Subtract the divisor from the result

101001 - 00011 = 100110

Step 7: Repeat steps 5 and 6 until the result is less than the divisor

Since the first two bits of the new result (1001) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100110 - 00011 = 100011

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100011 - 00011 = 100001

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100001 - 00011 = 011111

Since the first two bits of the new result (0111) are less than the divisor (00011), we guess that the next quotient bit is 0.

011111 - 00000 = 011111

Step 8: Remove the extra zeros from the result

Result: 1111

Therefore, the quotient is 1111.

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the students of 3 sections of a class have to stand in rows each row has an equal number of students if there are 24 , 36 , and 60 students in 3 sections find the maximum number of students in each row​

Answers

The maximum Number of  scholars in each row is 12. This means that the  scholars can be arranged in rows with an equal number of  scholars, and each row can have a  outside of 12  scholars.

To find the maximum number of  scholars in each row, we need to determine the  topmost common divisor( GCD) of the total number of  scholars in each section. The GCD represents the largest number that divides all the given  figures unevenly.  

Given that there are 24, 36, and 60  scholars in the three sections, we can calculate the GCD as follows    Step 1 List the  high factors of each number  24 =  23 * 31  36 =  22 * 32  60 =  22 * 31 * 51    

Step 2 Identify the common  high factors among the three  figures  Common  high factors 22 * 31    Step 3 Multiply the common  high factors to find the GCD  GCD =  22 * 31 =  4 * 3 =  12  

 thus, the maximum number of  scholars in each row is 12. This means that the  scholars can be arranged in rows with an equal number of  scholars, and each row can have a  outside of 12  scholars.

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the weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3996 grams and a variance of 111,556 . if a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4664 grams. round your answer to four decimal places.

Answers

Rounding to four decimal places, we get the probability that the weight will be less than 4664 grams as 0.9991.

Let X be the weight of a newborn baby boy born at the local hospital. We know that X follows a normal distribution with mean μ = 3996 grams and variance σ² = 111,556 grams².

We want to find the probability that the weight will be less than 4664 grams. That is, we need to find P(X < 4664).

To standardize X, we can use the z-score formula:

z = (X - μ) / σ

Substituting the given values, we get:

z = (4664 - 3996) / √111556

z = 3.1217

Using a standard normal table or calculator, we can find that the probability of a standard normal random variable being less than 3.1217 is approximately 0.9991.

Therefore, P(X < 4664) = P(Z < 3.1217) ≈ 0.9991.

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-0.72x + 0.42x = 8.4
solve for x

Answers

You first have have to add -0.72 and 0.42 because they both have like terms. Then you will get -0.3x. Then you will divide both sides by -0.3 because you have to get x alone. When you do that you’ll get -28. That’s your answer -28.

What is ""statistical conclusion validity""? what was the main threat to statistical conclusion validity discussed in class?

Answers

Statistical conclusion validity is the extent to which inferences and conclusions drawn from statistical data are valid.

The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not.

Statistical conclusion validity is a measure of how valid the conclusions drawn from statistical data are. This is important because it allows us to draw valid inferences from the data. The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not. For example, a study may show that there is a correlation between ice cream sales and crime rate, when in fact it is merely a coincidence that both variables increase during the summer months. By controlling for other variables and using appropriate statistical tests, it is possible to identify and avoid spurious correlations.

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write the equation in the slope intercept form of the line shown on the graph​

write the equation in the slope intercept form of the line shown on the graph

Answers

y=3x+6
3 is the slope (rise over run)
6 is the y intercept (the point where the line meets the y axis)

Dena owes her aunt $12. Her aunt takes away $3 of the debt. In the discussion box, answer these questions:

How much does Dena still owe her aunt?
Is this a problem you could model using counters or a number line? Explain why or why not.

Answers

Answer:

9 dollars that dena owes the aunt,and no you could not

Step-by-step explanation:

because u cant express on the numberline

A(n+1)=A(n)+4 for n21 and A(1)=-6*
Helllllp

Answers

9514 1404 393

Answer:

  74

Step-by-step explanation:

The recursive definition is for an arithmetic sequence with a first term of -6 and a common difference of 4.

The general term of such a sequence is ...

  a(n) = a(1) +d(n -1)

This sequence is ...

  a(n) = -6 +4(n -1) = 4n -10

Then for n = 21, the term is ...

  a(21) = 4(21) -10 = 84 -10

  a(21) = 74

Can u guys PLEASE answer this question ASAP. THIS IS EXTREMELY URGENT. Twenty circular pieces of pastry, each of diameter 4 cm, are cut from a rectangular layer of pastry 20 cm long and 16 cm wide. What is the area, correct to two decimal places, of pastry remaining after the 20 pieces are removed?

Answers

Answer:

68,67 cm^2

Step-by-step explanation:

Let's calculate first the total area of pastry that we have.

Let A be that area.

The pastry has rectangular form so its area is:

● A = width × length

The width here is 16 and the length is 20

● A = 20 × 16

● A = 320 cm^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's calculate the are of the 20 pastry circles

Let A' be the area of one circle.

● A' = Pi × r^2

r is the radius wich is the diameter over 2.

● d/2 = 4/2 = 2 cm

● A' = Pi × 2^2

● A' = 4Pi cm^2

The area of 20 pastry circles is 20A'

● 20A'= 20 × 4 × Pi

● 20A'= 80Pi

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let A" be the area of the remaining pastry

● A" = A-20A'

● A" = 320 - 80Pi

● A" = 68.67 cm^2

What is the IQR of the aged, in years?

What is the IQR of the aged, in years?

Answers

The IQR of the ages, in years include the following: B. 16.

How to interpret the box-and-whisker plot?

Based on the information provided about the given box plot or box-and-whisker plot, the five-number summary for the given data set include the following:

Minimum (Min) = 12.First quartile (Q₁) = 22.Median (Med) = 32.Third quartile (Q₃) = 38.Maximum (Max) = 44.

How to calculate the interquartile range (IQR)?

In Mathematics and Statistics, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of data set = Q₃ - Q₁

Interquartile range (IQR) of data set = 38 - 22

Interquartile range (IQR) of data set = 16.

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.When developing groups, there will almost always be disagreements and conflicts as members work to develop a common understanding. This stage of group development is called○ forming.○ norming.○ performing.○ storming.○ adjourning.

Answers

The stage of group development that is characterized by disagreements and conflicts is called storming. During this stage, group members may have different ideas and opinions about how to approach tasks and goals, and they may struggle to find a common understanding.

Conflict can arise as individuals compete for leadership roles or try to assert their ideas over others. However, this stage is important for groups to progress towards their goals as it allows for open communication and the airing of different perspectives. Eventually, through negotiation and compromise, groups move on to the norming stage where a common understanding is established and roles are defined. From there, groups move on to performing, where they are able to work together effectively towards their goals.

Finally, the adjourning stage is where the group disbands after reaching their goals or completing their tasks.

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Help please. I dont know how to do this :((

Help please. I dont know how to do this :((

Answers

Answer:

You need the distance of all four sides so that is:

2 * (5y +1) + 2 * (2y -3) which equals

10y + 2 + 4y -6 and that equals

14y -4

Step-by-step explanation:

marcus wants to include the month of the year in the analysis as categories. how many dummy variables will be needed?

Answers

11 dummy variables will be needed.

A dummy variable is a numerical variable used in regression analysis to represent subgroups of the sample in your study. In research design, a dummy variable is often used to distinguish different treatment groups.

we know that,

dummy variable formula = K- 1,

here, K = 12 (months in a year)

this implies, K - 1 = 12 - 1 = 11

Therefore, no. of dummy variables needed = 11.

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A certain basketball player practices shooting free throws over and over again. The shots are independent, with probability p of success.
a) In n shots, what is the expected number of streaks of 7 consecutive successful shots? (Note that, for example, 9 in a row counts as 3 streaks.)
b) Now suppose that the player keeps shooting until making 7 shots in a row for the first time. Let X be the number of shots taken. Sow the E(X) <= 7/p^7.

Answers

The expected number of streaks of 7 consecutive successful shots in n shots = (n - 6) * p7, where n is the number of shots and p is the probability of success.The probability of making 7 consecutive successful shots in exactly k shots is given by Pk = (1-p)k-7 * p7. The expected value of X is given by E(X) = [k=7,] k. We can use the formula for the sum of an infinite geometric series to simplify the expression and evaluate the numerator of the expression. Thus, E(X)  7 / p7.

a) In n shots, the expected number of streaks of 7 consecutive successful shots is given by the formula below:The expected number of streaks of 7 consecutive successful shots in n shots = (n - 6) * p^7, where n is the number of shots and p is the probability of success. In other words, for each block of 7 shots, we have a probability of p^7 of making 7 consecutive successful shots, and there are (n-6) blocks of 7 shots in n shots. Therefore, the expected number of streaks of 7 consecutive successful shots is the product of these two values.

b) We know that X is the number of shots taken until the player makes 7 consecutive successful shots for the first time. Therefore, X is a random variable that follows the geometric distribution with parameter p. The probability of making 7 consecutive successful shots in exactly k shots is given by:Pk = (1-p)^{k-7} * p^7Therefore, the expected value of X is given by:E(X) = Σ[k=7,∞] k * PkWe can use the formula for the sum of an infinite geometric series to simplify this expression:

\(E(X) = Σ[k=1,∞] k * (1-p)^{k-1} * p^7 / (1 - (1-p)^7)\) We can also use the formula for the sum of a geometric series to simplify the denominator:

\(E(X) = Σ[k=1,∞] k * (1-p)^{k-1} * p^7 / (p^7 + Σ[j=1,6] (1-p)^j * p^7)\)

\(E(X) = (p^7 * Σ[k=1,∞] k * (1-p)^{k-1}) / (p^7 * (1 + Σ[j=1,6] (1-p)^j))\)

\(E(X) = (1 / p^7) * (Σ[k=1,∞] k * (1-p)^{k-1}) / (1 + Σ[j=1,6] (1-p)^j)\)

We can use the formula for the derivative of a geometric series to evaluate the numerator of this expression:

\(Σ[k=1,∞] k * (1-p)^{k-1} = d/dp\)

Σ[k=1,∞] (1-p)^k

= d/dp (1-p) / (1 - (1-p))²

= 1 / p^2

Therefore, \(E(X) = (1 / p^7) * (1 / (1 + Σ[j=1,6] (1-p)^j)) * (1 / p^2) ≤ (1 / p^7) * (1 / (1 + Σ[j=1,6] (1-p)^j)) * (1 / p^7) = 1 / p^{14} ≤ 7 / p^7\)

Thus, \(E(X) ≤ 7 / p^7.\)

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Serena is ordering lunch from Tony's Pizza Parlor. John told her that
when he ordered from Tony's last week, he paid $34 for two 16-inch
pizzas and two drinks. Jodi told Serena that when she ordered one
16-inch pizza and three drinks, it cost $23.
Write two equations to represent the two statements that Serena hears.

Answers

The cost of each pizza is $14 and the cost of each cool drink is $3.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, John told Serena that when he ordered from Tony's last week, he paid $34 for two 16-inch pizzas and two drinks.

Let the cost of each pizza be x and the cost of each cool drink be y.

Now, 2x+2y=34

x+y=17 -------(i)

Jodi told Serena that when she ordered one 16-inch pizza and three drinks, it cost $23.

x+3y=23 -------(ii)

Subtract equation (i) from (ii), we get

x+3y-(x+y)=23-17

2y=6

y=3

Substitute y=3 in equation (i), we get

x=14

Therefore, the cost of each pizza is $14 and the cost of each cool drink is $3.

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at a 25% off sale you buy a game for 45$ what was the original price

Answers

Answer:

$60

Step-by-step explanation:

Let x = the original cost

x - .25x = 45

.75x = 45  Divide both sides by .75

x = 60

Two trains leave a city at the same time. One train goes west at a constant rate of 60 mph. The other goes east at a rate of 50 mph. How long will it take the trains to be 550 miles apart?
A. 5 hours
B. 7 hours
C. 9 hours
D. 11 hours

Answers

Lets t be the time that needed for trains to be 550 mi apart.

1st train will go (60*t) mi

2nd train will go (50 *t) mi

Altogether
(60t +50t), at the same time this distance equals 550 mi.

So, we can write

60t +50t =550
110t = 550
t=550/110
t=5 h

We have now proven that it would take 5 hours for the two trains to be 550 mile apart.
Hope this would help you.!!:)

Answer:

A. 5 hours

Step-by-step explanation:

For each of the following system, use the poincare and
bendixson's criterion to show that the system has a periodic
orbit
(4) \( \quad \dot{x}_{1}=x_{1}+x_{2}-x_{1} h(x), \quad \dot{x}_{2}=-2 x_{1}+x_{2}-x_{2} h(x) \) In the fourth system, \( h(x)=\max \left\{\left|x_{1}\right|,\left|x_{2}\right|\right\} \).

Answers

Following the same steps as in Case 1, we find the fixed points by setting ( \dot{x}{1} = \dot{x}{2} = 0 ):

To apply the Poincaré-Bendixson criterion to the given system:

( \dot{x}{1} = x{1} + x_{2} - x_{1} h(x) )

( \dot{x}{2} = -2x{1} + x_{2} - x_{2} h(x) )

where ( h(x) = \max \left{ \left| x_{1} \right|, \left| x_{2} \right| \right} ), we need to determine if there exists a periodic orbit.

The Poincaré-Bendixson criterion states that if a system's trajectory is bounded and does not approach a fixed point or a limit cycle, then it must contain a closed trajectory (a periodic orbit).

To analyze the system, let's consider the region where ( h(x) ) is at its maximum. This occurs when either ( \left| x_{1} \right| ) or ( \left| x_{2} \right| ) is larger.

Case 1: ( \left| x_{1} \right| > \left| x_{2} \right| )

In this case, ( h(x) = \left| x_{1} \right| ), so the system becomes:

( \dot{x}{1} = x{1} + x_{2} - x_{1} \cdot \left| x_{1} \right| )

( \dot{x}{2} = -2x{1} + x_{2} - x_{2} \cdot \left| x_{1} \right| )

Case 2: ( \left| x_{2} \right| > \left| x_{1} \right| )

In this case, ( h(x) = \left| x_{2} \right| ), so the system becomes:

( \dot{x}{1} = x{1} + x_{2} - x_{1} \cdot \left| x_{2} \right| )

( \dot{x}{2} = -2x{1} + x_{2} - x_{2} \cdot \left| x_{2} \right| )

Now, let's analyze each case separately.

Case 1: ( \left| x_{1} \right| > \left| x_{2} \right| )

In this case, the system becomes:

( \dot{x}{1} = x{1} + x_{2} - x_{1} \cdot \left| x_{1} \right| )

( \dot{x}{2} = -2x{1} + x_{2} - x_{2} \cdot \left| x_{1} \right| )

To find potential fixed points, we set ( \dot{x}{1} = \dot{x}{2} = 0 ):

( x_{1} + x_{2} - x_{1} \cdot \left| x_{1} \right| = 0 )

( -2x_{1} + x_{2} - x_{2} \cdot \left| x_{1} \right| = 0 )

Simplifying the equations, we have:

( (1 - \left| x_{1} \right|)x_{1} + x_{2} = 0 )

( (-2 - \left| x_{1} \right|)x_{1} + (1 - \left| x_{1} \right|)x_{2} = 0 )

From these equations, we can see that the fixed points occur when either ( x_{1} = 0 ) or ( x_{2} = 0 ). However, in both cases, the system is not globally asymptotically stable, and trajectories can escape to infinity.

Since the system is not globally asymptotically stable, we cannot conclude the existence of a periodic orbit in Case 1.

Case 2: ( \left| x_{2} \right| > \left| x_{1} \right| )

In this case, the system becomes:

( \dot{x}{1} = x{1} + x_{2} - x_{1} \cdot \left| x_{2} \right| )

( \dot{x}{2} = -2x{1} + x_{2} - x_{2} \cdot \left| x_{2} \right| )

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factor the polynomial 24x^3 - 78x^2 + 45x

Answers

Answer:

3x ( 4x-3 )( 2x - 5 )

Step-by-step explanation:

24x^3 - 78x^2 + 45x

factor out biggest common values

3x ( 8x^2 - 26x + 15 )

3x ( 4x-3 )( 2x - 5 )

Fill in the blank to correctly complete the sentence. One way of solving the following system by elimination is to multiply equation (2) by the integer to eliminate the y-terms by direct addition. 14x+13y=71 2x+y=19

Answers

One way of solving the following system by elimination is to multiply equation (2) by 2 to eliminate the y-terms by direct addition.

To solve the given system of equations, we can use the method of elimination. The goal is to eliminate one variable by adding or subtracting the equations in a way that allows us to solve for the remaining variable. In this case, we want to eliminate the y-terms. To do this, we can multiply equation (2) by **2** to make the coefficients of the y-terms the same in both equations.

Multiplying equation (2) by 2, we get:

2 * (2x + y) = 2 * 19

4x + 2y = 38

Now we have two equations:

14x + 13y = 71

4x + 2y = 38

By multiplying equation (2) by 2, the coefficients of the y-terms in both equations are now the same, namely **2**. We can proceed to eliminate the y-terms by subtracting the second equation from the first equation.

Subtracting equation (2) from equation (1), we get:

(14x + 13y) - (4x + 2y) = 71 - 38

14x + 13y - 4x - 2y = 33

10x + 11y = 33

Now we have a new equation:

10x + 11y = 33

We can now solve this equation simultaneously with one of the original equations to find the values of x and y.

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(c) prove that for any positive integer n, 4 evenly divides 11n - 7n.

Answers

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. tan 82° = ___

Answers

When we calculate the value of tan82 then we have to round off to hu ndreth place.

\(\tan (82\text{degre}e)=7.1153\)

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