What is the area of a circle with a circumference of 36.68 units

The equation y = 11x + 1 is a linear equation. All three ordered pairs, (0, 1), (1, 12), and (-1, -10), satisfy this equation.

The equation y = 11x + 1 represents a linear equation. To determine which ordered pairs satisfy this equation, we substitute the x and y values into the equation and check if the equation holds true. Let's check each option:

Based on the calculations, we can see that all three ordered pairs are valid solutions for y = 11x + 1.

Answer:

59.5

Step-by-step explanation:

The middle number of the number set is 59.5 because the number in between 59 and 60 is 59.5

The median of the data set: 46, 88, 28, 73, 63, 55  is 59.

Arranging in ascending order :  28, 46,55, 63, 73,88,

A number of terms are odd, then the median is the middle number i.e., 59.

⇒(55+63)/2=59

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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Answer:

B [tex]log_{2} 42[/tex]

Step-by-step explanation:

Due to the product rule of logarithms, we can combine them as such. Then it will simplify to our answer.

[tex]log_{2} 6+log_{2} 7=log_{2} (6*7)\\\\log_{2} 42[/tex]

The single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex]  is [tex]log_{2} 42[/tex]. The correct answer is option B.

To express [tex]log_2^{6} + log_2^{7}[/tex] as a single logarithm, we can use the logarithmic identity log a + log b = log ab.

Applying this identity to the given expression, we get:

[tex]log_2^{6} + log_2^{7}[/tex] = [tex]log_{2} (6 * 7)[/tex]

Simplifying the expression within the logarithm, we get:

[tex]log_{2} (6 * 7)[/tex] = [tex]log_{2} 42[/tex]

Therefore, the single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex] is [tex]log_{2} 42[/tex]. The correct answer is option B.

Logarithms are used to simplify complex mathematical calculations involving large numbers. They allow us to break down a number into its constituent parts and perform operations on those parts more easily. In this problem, we are asked to express the sum of two logarithms as a single logarithm. To do this, we use the logarithmic identity log a + log b = log ab.

Applying this identity to the given expression, we get:

[tex]log_2^{6} + log_2^{7}[/tex] = [tex]log_{2} (6 * 7)[/tex]

We simplify the expression on the right-hand side of the equation to get:

[tex]log_{2} (6 * 7)[/tex] = [tex]log_{2} 42[/tex]

Therefore, the single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex] is [tex]log_{2} 42[/tex].

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Answer:

I'd say C Sets 2 and 3 contain outliers.

Step-by-step explanation:

Set 2 has an outlier of 90, while set 3 has an outlier of 40. 40 isn't as much of an outlier as 90 is, so I'm not absolutely sure. Cmakes the most sense though.

Answer: Third option.

Step-by-step explanation:

The standard deviation increases as we have more values that are far away from the mean.

For example, in data set 2, we can see that most of hour points are between 38 and 49, but we also have a point with a value of 90, so we may expect that this data set has a big standard deviation.

The data set 3 is similar, most of our points are between 24 and 31, and we have a value that is on 40, so again we have an outlier that increases the value of the standard deviation.

Noticing it we can conclude that data set 2 and data set 3 have a greater standard deviation than set 1.

The correct option is the third option.

Answer:

8/15

Step-by-step explanation:

Well to add fractions you have to have the same denominator so you would multiply your 1/3 by 5 to be 5/15 then you can add.

3/15 + 5/15 = 8/15

1 over 3 would change to 5 over 15 to make the denominators equal then you add the numerators and you get 8 over 15

Answer:

C

Step-by-step explanation:

Answer:

The correct option is 3.

Step-by-step explanation:

The difference of squares is defined as

[tex]a^2-b^2=(a-b)(a+b)[/tex]

In option 1,

[tex](-7x+4)(-7x+4)=(-7x+4)^2[/tex]

This expression is a perfect square, therefore this is not the difference of squares. Option 1 is incorrect.

In option 2,

[tex](-7x+4)(4-7x)=(-7x+4)(-7x+4)=(-7x+4)^2[/tex]

This expression is a perfect square, therefore this is not the difference of squares. Option 2 is incorrect.

In option 3,

[tex](-7x+4)(-7x-4)=(-7x)^2-(4)^2[/tex]

This expression is the difference of squares., therefore Option 3 is correct.

In option 4,

[tex](-7x+4)(7x-4)=-(-7x+4)(-7x+4)=-(-7x+4)^2[/tex]

This expression is a perfect square, therefore this is not the difference of squares. Option 4 is incorrect.

Answer:

C

Step-by-step explanation

The mapping diagram which shows the inverse of R(x) is Option (C).

A function is a special type of relation in which each element of the domain is paired with exactly one element in the range . A mapping diagram shows how the elements are paired. Its like a flow chart for a function, showing the input and output values. A mapping diagram consists of two parallel columns.

To identify the mapping diagram for inverse of a function, we simply just change the values of first set of columns into the second set of columns.

This is because if [tex]f(x) = y[/tex] , then  [tex]f^{-1}(y) = x[/tex]

For the given function R(x) , values are 6,7,8,9 in first column and 9,10,11,12 in the second column . Thus for the inverse function,  6,7,8,9  will be in the second column and 9,10,11,12 will be in the first column.

From the given Options, Option (C) is the correct mapping of inverse of R(x).

Thus, the mapping diagram which shows the inverse of R(x) is Option (C).

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Answer:

0

Step-by-step explanation:

Between -6 and 9 are 15 units.

2/5 of 15 units is 6 units.  Add this to -6 to obtain 0.

0 is the answer to this question

Step-by-step explanation:

I'm not sure but I think its like the distance between -6 and 9 is 15 or something and 15 divided by 5 is 3 and 2/5 is 6 so 6-6 is 0 and that's that point.

B is the correct answer

Answer:

-3

Step-by-step explanation:

The x-intercept is the plot point where y = 0.

Answer:

-3

Step-by-step explanation:

the x-intercept is the point on the graph where the ploted line crosses the x axes  

Answer:

18x-30-10x-35=25

8x-65=25

8x-65+65=25+65

8x=90

Divide by 8 for 8x and 90

x=90/8 or 45/4 or 11 1/4 ( Answers)

The x - determinant of the equation is [tex]\left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right][/tex]

The y - determinant of the equation is [tex]\left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right][/tex]

The system determinant is [tex]\left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right][/tex]

How to find the determinants of x, y and the entire system?

The given system of equation include the following;

2x - y = 0

x + y = - 3

The x - determinant of the equation will be obtained by replacing coefficient of x with the constant terms.

[tex]\Delta x = \left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right][/tex]

The y - determinant of the equation will be obtained by replacing coefficient of y with the constant terms.

[tex]\Delta y = \left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right][/tex]

The system determinant is obtained by removing the constant term and writing only the x and y coefficient in the matrix;

[tex]\Delta = \left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right][/tex]

Answer:

The correct answer option is (5, -6).

Step-by-step explanation:

We know that the following are the coordinates of a point:

[tex] ( - 5 , - 6 ) [/tex]

If this point is reflected through y axis, we are to find the coordinates of its image?

If a point is reflected through y-axis, the sign of the x coordinate is changed so we get:

[tex] ( - 5 , -6 ) [/tex] [tex] \implies [/tex] (5, -6)

Answer:  12

Step-by-step explanation:

2/3  = 8/12

1/4 = 3/12

8/12 + 3/12 + 11/12

amy & anna ate 11 and david had 1

Answer:

There were 12 donuts in the box.

Step-by-step explanation:

We are given the following information in the question:

Let x be the number of donuts in the box.

Then, according to the question

Number of donuts eaten by Amy = [tex]\frac{2x}{3}[/tex]

Number of donuts eaten by Anna = [tex]\frac{x}{4}[/tex]

Number of donuts eaten by David = 1

Total number of donuts =

Number of donuts eaten by Amy + Number of donuts eaten by Anna + Number of donuts eaten by David

[tex]\Rightarrow \frac{2x}{3} + \frac{x}{4} + 1 = x[/tex]

Solving the above equation:

[tex]11x + 12 = 12x\\x =12[/tex]

Thus, there were 12 donuts in the box.

Answer:

10/24 and 15/36, more answers possible

Step-by-step explanation:

if you multiply both the numerator and denominator by the same number, it will always be equivalent to 5/12, as you can simplify it back to that fraction.

5/12, multiply both by two, and you have 10/24

5/12, multiply both by three, and you have 15/36

10/24 and 15/36 are fractions equivalent to the given fraction.

10/24: This is equivalent to 5/12 because it can be reduced to 5/12 by dividing both the numerator and the denominator by 2.

15/36: This is another fraction equivalent to 5/12 since it can be reduced to 5/12 by dividing both the numerator and denominator by 3.

ANSWER

y=10

x=5

EXPLANATION

The base angles of an isosceles triangle are equal.

This implies that:

8y-7=73°

Add 7 to both sides:

8y=73+7

8y=80°

y=10°

Interior angles of a triangle sums up to 180°

73+73+6x+4=180

150+6x=180

6x=180-150

6x=30

Divide both sides by 6

x=5

Answer:

Step-by-step explanation:

[tex]METHOD\ \#1\\\\\text{Put b = 3 to each equation and check equality:}\\\\A.\ 3-24b=75\\L_s=3-24(3)=3-72=-69\\R_s=75\\L_s\neq R_s\\\\B.\ 65+9b=38\\L_s=65+9(3)=65+27=92\\R_s=38\\L_s\neq R_s\\\\C.\ -2b+30=24\\L_s=-2(3)+30=-6+30=24\\R_s=24\\L_s=R_s\\\\D.\ 102b-21=-55\\L_s=102(3)-21=306-21=285\\R_s=-55\\L_s\neq R_s[/tex]

[tex]METHOD\ \#2:\\\\\text{Solve each equation:}\\\\A.\\3-24b=75\qquad\text{subtract 3 from both sides}\\-24b=72\qquad\text{divide both sides by (-24)}\\b=-3\neq3\\\\B.\\65+9b=38\qquad\text{subtract 65 from both sides}\\9b=-27\qquad\text{divide both sides by 9}\\b=-3\neq3\\\\C.\\-2b+30=24\qquad\text{subtract 30 from both sides}\\-2b=-6\qquad\text{divide both sides by (-2)}\\b=3\\\\D.\\102b-21=-55\qquad\text{add 21 to both sides}\\102b=-34\qquad\text{divide both sides by 102}\\b=-\frac{1}{3}[/tex]

Answer: This is some information I have gathered to help you since I cannot answer this directly sin θ + (cot θ)(cos θ)  

= sin θ + (cos θ / sin θ)(cos θ)  

= sin θ + cos² θ / sin θ  

Since cos² θ = 1 - sin² θ,  

= sin θ + (1 - sin² θ) / sin θ  

= sin θ + 1 / sin θ - sin θ  

= 1 / sin θ  

= csc θ ∎ Sin(x) = tan(x) / [sqrt(1 + tan^2(x)]  

Sin(theta) =3/4 / sqrt[1 + .75^2]

Sin(theta) =0.75 / sqrt[ 1.5625 ]

Sin(theta) =0.75 / 1.25

Sin(theta) = 0.60

Depending on the country, most democracies use taxes for:

-public programs (any governmentally run or funded services)

-infrastructure (roads, bridges, etc)

-the military

-schools

-governmental departments (EPA, Department of Homeland Security, etc)

-government employee paychecks

And SOMETIMES:

-universal healthcare

-college/university

-etc.

Taxes are used to fund government services, reduce income inequalities, and support state and local government activities.

Taxes are used for a variety of purposes. They are primarily used to fund government services such as military, police, education, infrastructure, and social security. Taxes are also used to reduce income and wealth inequalities by transferring income to lower income groups. Additionally, taxes are used to support state and local government activities and services.

For example, in the United States, the federal government raises revenue through income taxes, corporate earnings taxes, and sales taxes on goods such as gasoline, alcohol, and tobacco. State and local governments also collect taxes, including income, property, and sales taxes, which fund activities like maintaining public parks and providing a police force.

Overall, taxes play a crucial role in financing government operations and essential public services that benefit communities.

ANSWER

(C) d=1

EXPLANATION

The given equation is

[tex] \frac{ - 3d}{ {d}^{2} - 2d - 8} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]

Factor the first fraction to get,

[tex] \frac{ - 3d}{(d + 2)(d - 4)} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]

Multiply through by (d+2)(d-4)

[tex] - 3d + 3(d + 2) = - 2(d - 4)[/tex]

Expand:

[tex] - 3d + 3d + 6 = - 2d + 8[/tex]

[tex] 6 = - 2d + 8[/tex]

[tex]6 - 8= - 2d[/tex]

[tex] - 2 = - 2d[/tex]

divide both sides by -2

[tex]d = 1[/tex]

The correct answer is (B) [tex]\( d = -2 \)[/tex] and [tex]\( d = 4 \)[/tex].

To find the solution to the given quadratic equation, we can factor it or use the quadratic formula. The equation is not provided in the conversation, but based on the options given, it seems that the equation could be in the form [tex]\( (d - a)(d - b) = 0 \)[/tex], where [tex]a[/tex] and [tex]b[/tex]are the roots of the equation.

The quadratic equation can be written as [tex]\( d^2 - (a+b)d + ab = 0 \)[/tex]. To have the sum of the roots [tex]\( a + b \)[/tex] equal to 0 and the product of the roots [tex]\( ab \)[/tex] equal to -8, we can set up the following system of equations:

1. [tex]\( a + b = 0 \)[/tex]

2. [tex]\( ab = -8 \)[/tex]

From equation 1, we can express [tex]\( b \)[/tex] in terms of [tex]\( a \): \( b = -a \).[/tex]

Substituting [tex]\( b \)[/tex] into equation 2, we get:

[tex]\( a(-a) = -8 \)[/tex]

[tex]\( -a^2 = -8 \)[/tex]

[tex]\( a^2 = 8 \)[/tex]

Taking the square root of both sides, we find:

[tex]\( a = \pm\sqrt{8} \)[/tex]

[tex]\( a = \pm2\sqrt{2} \)[/tex]

Since [tex]\( b = -a \),[/tex] we have:

[tex]\( a = 2\sqrt{2} \) and \( b = -2\sqrt{2} \)[/tex]

[tex]\( a = -2\sqrt{2} \) and \( b = 2\sqrt{2} \)[/tex]

However, these are not the exact values given in the options. We need to find the exact integer values for [tex]a[/tex] and [tex]b[/tex]. Since the product [tex]\( ab \)[/tex] is -8, we can look for two numbers that multiply to -8 and add up to 0. These numbers are -2 and 4.

Therefore, the solutions to the equation are [tex]\( d = -2 \)[/tex] and [tex]\( d = 4 \)[/tex], which corresponds to option (B).

Step-by-step explanation:

[tex]8^{2x-4}=8^{5x+1}\iff2x-4=5x+1\qquad\text{add 4 to both sides}\\\\2x=5x+5\qquad\text{subtract 5x from both sides}\\\\-3x=5\qquad\text{divide both sides by (-3)}\\\\\boxed{x=-\dfrac{5}{3}}\\\\================================[/tex]

[tex]2^{x+6}=16^{3x+4}\\\\2^{x+6}=(2^4)^{3x+4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{x+6}=2^{4(3x+4)}\iff x+6=4(3x+4)\qquad\text{use the distributive property}\\\\x+6=(4)(3x)+(4)(4)\\\\x+6=12x+16\qquad\text{subtract 6 from both sides}\\\\x=12x+10\qquad\text{subtract 12x from both sides}\\\\-11x=10\qquad\text{divide both sides by (-11)}\\\\\boxed{x=-\dfrac{10}{11}}\\\\================================[/tex]

[tex]\left(\dfrac{1}{2}\right)^x=2^{x+3}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^{-1})^x=2^{x+3}\\\\2^{-x}=2^{x+3}\iff -x=x+3\qquad\text{subtract x from both sides}\\\\-2x=3\qquad\text{divide both sides by (-2)}\\\\\boxed{x=-\dfrac{3}{2}}\\\\================================[/tex]

[tex]36^{2x}=216^{3x-1}\\\\(6^2)^{2x}=(6^3)^{3x-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\6^{(2)(2x)}=2^{3(3x-1)}\iff(2)(2x)=3(3x-1)\qquad\text{use the distributive property}\\\\4x=(3)(3x)+(3)(-1)\\\\4x=9x-3\qquad\text{subtract 9x from both sides}\\\\-5x=-3\qquad\text{divide both sides by (-5)}\\\\\boxed{x=\dfrac{3}{5}}\\\\================================[/tex]

[tex]p\%=\dfrac{p}{100}\\\\100\%-12.6\%=87.4\%=\dfrac{87.4}{100}=0.874\\\\8\ years\to(0.874)^4\approx0.584\to58.4\%\\\\\text{After 8 years, the car will be worth 58.4}\%\ \text{of the initial price.}[/tex]

The answer is:

The correct options are:

A)  [tex]y-2=-0.75(x-3)[/tex]

and

D) [tex]y-5=-0.75(x+1)[/tex]

To find the correct answers, we need to find a equation that meet the following charactheristics:

From the graph we can se that the function:

- Has a negative slope (is decreasing)

- Pass throught the points: (-1,5) and (3,2)

Now, discarding from the given options, we have:

[tex]y-2=-0.75(x-3)[/tex]

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

[tex]5-2=-0.75(-1-3)[/tex]

[tex]3=-0.75(-4)[/tex]

[tex]3=3[/tex]

Evaluating (3,2):

[tex]2-2=-0.75(3-3)[/tex]

[tex]0=-0.75(0)[/tex]

[tex]0=0[/tex]

We have that the equation is satisfied, so,  the line pass  through the given points.

Hence, we have that the equation A is an equation of the line shown.

[tex]y-5=-0.75(x-1)[/tex]

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

[tex]5-5=-0.75(-1-1)[/tex]

[tex]0=-3.5[/tex]

Hence, we have that since the equation is not satisfied, the line shown is not passing  through the point (-1,5) meaning that the equation is not an equation of the line shown.

So,  we have that the equation B is not equation of the line shown.

[tex]y-3=-0.75(x-2)[/tex]

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

[tex]5-3=-0.75(-1-2)[/tex]

[tex]2=-0.75(-3)[/tex]

[tex]2=2.25[/tex]

Hence, we have that since the equation is not satisfied, the line shown is not passing  through the point (-1,5) meaning that the equation is not an equation of the line shown.

So, we have that the equation B is not equation of the line shown.

(assuming you committed a mistake writing the options and the equality sign is missing)

[tex]y-5=-0.75(x+1)[/tex]

We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).

Evaluating the points, we have:

Evaluating (-1,5)

[tex]5-5=-0.75(-1+1)[/tex]

[tex]0=-0.75(0)[/tex]

[tex]0=0[/tex]

Evaluating (3,2)

[tex]2-5=-0.75(3+1)[/tex]

[tex]-3=-0.75(4)[/tex]

[tex]-3=-3[/tex]

We have that the equation is satisfied, so,  the line pass  through the given points.

Hence, we have that the equation B is an equation of the line shown.

Finally, we have that the correct options are:

A)  [tex]y-2=-0.75(x-3)[/tex]

and

D) [tex]y-5=-0.75(x+1)[/tex]

Have a nice day!

Answer:

x = ± 2[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Given

16 - 2x² = - 64 ( subtract 16 from both sides )

- 2x² = - 80 ( divide both sides by - 2 )

x² = 40 ( take the square root of both sides )

x = ± [tex]\sqrt{40}[/tex] = ± [tex]\sqrt{4(10)}[/tex] = ± 2[tex]\sqrt{10}[/tex]

Answer:

[tex]P = 0.201[/tex]

Step-by-step explanation:

If the discrete random variable X represents the number of correct Colin responses then X can be represented by a binomial distribution with parameters p, n, x.

In this case p represents the probability that colin gets a correct answer, n represents the number of questions.

So the probability that Colin receives x correct questions is:

[tex]P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}[/tex]

Where:

[tex]p=\frac{1}{5}[/tex]

[tex]n=10[/tex]

[tex]x=3[/tex]

[tex]P(x=3) = \frac{10!}{3!(10-3)!}*(\frac{1}{5})^3*(1-\frac{1}{5})^{10-3}[/tex]

[tex]P(x=3) = \frac{10!}{3!*7!}*\frac{1}{125}*(\frac{4}{5})^{7}[/tex]

[tex]P = 0.201[/tex]

Answer:

True

Step-by-step explanation:

The numbers 20, 21, and 29  are a Pythagorean triplet and can be the dimensions of a right triangle.

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.

A triangle with sides of lengths 20, 21, and 29 is a right triangle.

Three numbers can be the sides of a triangle if the sum of two of them is greater than the third. So, since

20+21 > 29,

20+29 > 21, and

21+29 > 20

Are trivially true, they can be the sides of a triangle.

The given numbers are a Pythagorean triplet and can be the dimensions of a right triangle.

20,21 and 29 is a Pythagorean triplet, since

[tex]20^2+21^2=29^2[/tex]

So you also know that they form a right triangle.

Hence, the numbers 20, 21, and 29  are a Pythagorean triplet and can be the dimensions of a right triangle.

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Answer:

7:2:8.

Step-by-step explanation:

The income form the raffle = £350

Income from the quiz = 14*4 = £56 + £44 = £100

Income from membership fees = 20*20 = £400.

The ratio of raffle : quiz : fees

= 350:100:400

Dividing each number by 50:

= 7:2:8   in simplest form.

Answer:

A ratio the income from the raffle to the income from the quiz to the income from membership fees is 7:2:8.

Step-by-step explanation:

Given : The table shows a darts club's income in 2017 from a raffle, a quiz and membership fees.

To find : Express as a ratio the income from the raffle to the income from the quiz to the income from membership fees ?

Solution :

The raffle amount is £350.

Quiz, entry fees is 14 at £4 each and refreshment is £44.

The quiz amount is £[tex]14\times 4[/tex]+£44=£56+£44=£100

Membership fees=20 at £20 each.

The membership amount is £[tex]20\times 20[/tex]=£400

Now, the ratio of income from the raffle to the income from the quiz to the income from membership fees is

The ratio of raffle : quiz : membership

[tex]R= 350:100:400\\\\R= 35:10:40\\\\R=7:2:8[/tex]

Therefore, a ratio the income from the raffle to the income from the quiz to the income from membership fees is 7:2:8.

Answer:

a) 3,6,9,12,15,..

b) Common Ratio is 3

c) Recursive Formula : aₙ= aₙ₋₁ + d where a₁=3 and d= 3

Step-by-step explanation:

a) Create your own arithmetic sequence. Write out the first 3 terms.

Consider the sequence: 3,6,9,12,15,..

a₁ = 3

a₂ = 6

a₃ = 9

b) What is the common difference of your sequence?

6-3 = 3

9-6 = 3

12 -9 =3

So, common difference is 3

c) Write the recursive formula representing your sequence.

a₁ = 3

a₂ = aₙ₋₁ + d

   = a₁ + d

   = 3+ 3 = 6

a₃ = aₙ₋₁ + d

    = a₂ + d

   = 6+3 = 9

so, recursive formula is aₙ = aₙ₋₁ + d where a₁ = 3 and d= 3

An example of an arithmetic sequence can be created with a starting value (a1) of 2 and a common difference (d) of 3. The sequence's terms would be 2, 5, 8, etc. Its recursive formula would be a1 = 2; a_n = a_(n–1) + 3.

Let's create an arithmetic sequence, starting with the first term (a1) of 2 and a common difference (d) of 3. So, the first three terms of the sequence would be 2, 2+3=5, and 5+3=8.

The common difference of this arithmetic sequence is 3 as each term is 3 greater than the previous term.

The recursive formula for this sequence is a1 = 2; a_n = a_(n–1) + 3. What this formula means is that the first term is 2, and each subsequent term (an) is the previous term (an-1) added to the common difference (3).

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x=1/4 because, 1/4 will multiply with 4 to cancel out to have an exponent of 1

[tex]\bf (9^4)^{?}=9^1\implies 9^{4\cdot ?}=9^1\implies \stackrel{\textit{same base, the exponents must also be the same}}{4?=1\implies ?=\cfrac{1}{4}}[/tex]

Answer:

the answer on e2020 is 12.

The required answer is,

f(x) + f(x) + f(x) = 3ax² + 3bx + 3c

3f(x) = 3ax² + 3bx + 3c

3f(2) = 12a  + 6b + 3c

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Now let the function be,

f(x) = ax² + bx + c

To find,

f(x) + f(x) + f(x)

we have,

f(x) + f(x) + f(x) = (ax² + bx + c) +  (ax² + bx + c) +  (ax² + bx + c)

⇒ f(x) + f(x) + f(x) = 3(ax² + bx + c)

or, f(x) + f(x) + f(x) = 3ax² + 3bx + 3c

Similarly,

3f(x) = 3(ax² + bx + c)

or, 3f(x) = 3ax² + 3bx + 3c

now to find f(2), put x =  2 in f(x). we get,

f(2) = a2² + b2 + c

or, f(2) = 4a + 2b + c

Therefore,

3f(2) = 3(4a + 2b + c)

or, 3f(2) = 12a  + 6b + 3c

hence, the required answer is,

f(x) + f(x) + f(x) = 3ax² + 3bx + 3c

3f(x) = 3ax² + 3bx + 3c

3f(2) = 12a  + 6b + 3c

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Step-by-step explanation:

If you lost "y" in the first equation.

[tex]\underline{+\left\{\begin{array}{ccc}2x-3y=14\\-x+3y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\\\.\qquad x=8\\\\\text{Put the value of x to the first equation:}\\\\2(8)-3y=14\\16-3y=14\qquad\text{subtract 16 from both sides}\\-3y=-2\qquad\text{divide both sides by (-3)}\\y=\dfrac{2}{3}\\\boxed{x=8,\ y=\dfrac{2}{3}}[/tex]

If first equation is correct.

[tex]2x-3=14\qquad\text{add 3 to both sides}\\2x=17\qquad\text{divide both sides by 2}\\x=8.5\\\\\text{Put the value of x to the second equation:}\\-8.5+3y=-6\qquad\text{add 8.5 to both sides}\\3y=2.5\qquad\text{divide both sides by 3}\\y=\dfrac{2.5}{3}\\y=\dfrac{25}{30}\\y=\dfrac{5}{6}\\\\\boxed{x=8.5,\ y=\dfrac{5}{6}}[/tex]