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The equation which correctly represents the explicit formula for the nth term of the given sequence is; a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.

As evident in the task content; the given sequence is a geometric sequence and the common ratio of the sequence can be determined as;

r = 3 / 9 = 9 / 27 = 1 / 3.

On this note, since the common ratio of the consecutive terms of the sequence is; 1/3 it follows that the required explicit formula which represents the nth term , a (n) is;

a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.

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The standard way to solve 3 linear equations with 3 variables is to use elimination or substitution.

-Elimination: To solve the 3 equations using elimination, add or subtract equations together to eliminate one of the variables. Keep repeating this process until you are left with one equation with one variable. Solve the equation and then use the value of the variable to substitute back into the other equations to find the values of the other variables.

-Substitution: To solve the 3 equations using substitution, pick one of the equations and solve it for one of the variables. Then substitute the value of the variable into the other equations. Keep repeating this process with the other equations and variables until you have a system of equations with one variable that you can solve. Once you have the value of the variable, substitute it back into the other equations to find the value of the other variables.

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The values of x and y, given the angles in the diagram, can be found to be :

The angles given above are called vertical angles and they are such that the two corresponding angles are equal to each other.

This means that ( 8 x + 7 ) ° is equal to ( 9 x - 4 )° and 5 y° is equal to  ( 7y - 34 )°.

The value of x is :

8 x + 7 = 9 x - 4

9x - 8x = 7 + 4

x = 11

The value of y is :

5 y = 7y - 34

7y - 5y = 34

2 y = 34

y = 34 / 2

y = 17

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Answer:  y=7,x=3

Steps:

y = 2x + 1

3x + y = 16

Substitute y = 2x + 1

3x + 2x + 1 = 16

Simplify

5x+1=16

Isolate x for 5x + 1 = 16: x = 3

For y = 2x + 1

Substitute x = 3

y = 2 · 3 + 1

Simplify

y = 7

The solutions to the system of equations are:

y = 7, x = 3

Hope This Helps!

Answer: 54 inches squared

Step-by-step explanation:

Since it is a scale drawing, when we scale one variable up or down, we have to scale the other value the same amount because they are proportional. For example, if we divide one value by 3, we have to divide the other value by 3 also.

In this case, the real length is 30 feet, and the scale drawing length is 15 in. We divided by 2, so we have to divide the width by the same amount. 24/2 = 12 inches, so the width would be 12 inches or 1 foot.

Answer: The answer is 10x2

Step-by-step explanation:

The increase was 250% over the original price.

percentage, a relative value indicating hundredth parts of any quantity.

let 'x' represent the original price, then 'x+0.25x' represents the first increase of 25%

six times greater, converted to a percentage:

(x+0.25x)×2×100 a second increase of six-fold

1.25x×2×100

250

The increase was 250% over the original price.

Hence, the increase was 250% over the original price.

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Step-by-step explanation:

First, find the slope from the first 2 points, then use the value of the slope and either one of the first 2 points to find y in the 3rd point.

m = (8 - 4)/(3 - 1) = 4/2 = 2

2 = (y - 4)/(6 - 1)

Answer: E. All hemlock trees in the forest from which the 200 trees were selected

Step-by-step explanation:

When we generalize data, it needs to be about a sample that is as specific as possible so that the generalization has a better chance of holding true.

The best group of trees to generalize the data on is the trees in the forest where the hemlock trees were found. This is a specific population and has a higher chance of being right because the trees used in research could not have been the only ones suffering.

Answer:

Pretty sure is 90 degrees

Step-by-step explanation:

Answer:

[tex] {a}^{2} = {100}^{2} - {80}^{2} \\ {a}^{2} = 10000 - 6400 \\ {a}^{2} = 3600 \\ a = \sqrt{3600} = 60mi[/tex]

About what percentage of people had a score between Janine's and Laura's scores?

Answer:

Its D) 36%

Number of pens  x=10.

Number of pencils  y=30.

The Five Principles are: freedom, efficiency, mutuality, responsibility, and quality. Victoria that she always incorporates The Five Principles into her conversations with other businesses, government officials, and other partners and leaders. The writing core is tougher and leaves a lighter trace on the paper as the number increases.

Let number of pens =x

And number of pencils =y

⇒ x+y=40

⇒(5+y)+(x−5)=4x

⇒3x=y

Substituting in above equations ;

⇒x+3x=40

⇒x=10

⇒y=30

∴number of pens =x=10

⇒number of pencils =y=30

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Answer:

i think it is 68 degree i think

Answer:

D 91

Step-by-step explanation:

Add 3 +2 =68 +23=91

Sum of any angle in atringle is 180 (rule)

Then 180-91 =89 (the missing angle in the traingle)

Since the sum of any straight angle is 180 (Therom)

180 - 89 =91

Or

The some of 2 interior angle in a triangle equal to the opposite exterior angle (Therom)

So 68 +23 = 91

Answer:

D: I and IV only.

Step-by-step explanation:

We can go through each statement and examine its validity.

I) All congruent triangles are similar.

For congruent triangles, all of its corresponding sides and angles are congruent.

Since all angles are congruent, this fulfills the AA Similarity criterion. Thus, I is true.

II) All similar triangles are congruent.

Congruence guarantees similarity, but similarity does not guarantee congruence.

Two triangles need only two congruent angles to guarantee similarity, while two congruent angles does guarantee congruence. II is false.

III) All right triangles are similar.

Triangles are similar through the AA criterion. One angle of a right triangle must be 90, so this leaves 90 for the two remaining angles. Since these two angles can be anything that sum to 90, we are not guaranteed similarity. For example, 20 - 70 - 90 and 30 - 60 - 90 triangles. They are both right triangles, but are not similar. III is false.

IV) All isosceles right triangles are similar.

Again, since we have a right triangle, one angle is 90, which leaves two remaining angles that must sum to 90.

However, since it is isosceles, the two remaining angles must measure the same. Only one solution exists then: both angles must be 45.

Since all angles must be 45 - 45 - 90, it fulfills the AA Criterion. Thus, all isosceles right triangles are similar. IV is true.

The correct statements are I and IV.

Answer:

The fuel economy is 36 miles per gallon. For each mile 1/36 gallon will be used.

Initial volume is 13,2 gallons and x is the number of miles.

Our equation is:

or

The general rule is power of power. It can be represented by (x^m)^n = x^mn.

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Now complete the given table:

Problem to           First repeated        second repeated               Power of

simplify                 multiplication         multiplication              the form of a^n

(2²)³                         2²×2²×2²               2×2×2×2×2×2                           2⁶

(5³)⁴                     5³ × 5³ × 5³ × 5³      5×5×5×5×5×5×5×5×5×5×5×5    5¹²

(7³)⁴                     7³ × 7³ × 7³ × 7³      7×7×7×7×7×7×7×7×7×7×7×7        7¹²

((3x)²)³                   (3x)²×(3x)²×(3x)²    3x×3x×3x×3x×3x×3x                    (3x)⁶

(4y²)³                   (2y)²×(2y)²×(2y)²    2y×2y×2y×2y×2y×2y                    (2y)⁶

The general rule is  (x^m)^n = x^mn. The name of the rule is power of power.

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Answer:

y = -5/3x + 20

Step-by-step explanation:

y = -5/3x + b

-5 = -5/3(15) + b

-5 = -25 + b

20 = b

y = -5/3x + 20

Answer:

In other words.. The fourth option D.

Step-by-step explanation:

EDGE2022

i like your cut g

Answer:

C. But be careful. It depends if you have been told what I was having trouble with.

Step-by-step explanation:

The question is a little unclear. If the actual interest is constant for all situations, the answer is C. The more times you compound, the more interest you will accumulate. Banks don't do it that way. It they compound every three months, then they cut the interest rate by a quarter.

So the interest would look like (1 + 0.022/4)*principle. Whoever made the question has to make clear what is going on. My guess is the intended answer is C.

Answer:

58

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle

x + 56 = 114 subtract 56 from both sides

x = 58

On solving the provided question, we can say that - here in the equation, [tex]x^2- x = 4[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

so, x = 2

therefore

[tex]x^2- x \\6-2\\4[/tex]

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Answer:

14, 22

Step-by-step explanation:

x+y = 36

2×x - y = 6

=> x = 36 - y

=> 2×(36 - y) - y = 6

72 - 2y - y = 6

-3y = -66

3y = 66

y = 22

=> x = 36 - 22 = 14

Answer:

C.

Step-by-step explanation:

The mean at Belmont is 16.75, the median is 15.5, and the mode is 13.

The mean at Tyler is 10.9, the median is 10.5, and the mode is 13, 10, and 6.

Answer:

E

Step-by-step explanation:

Let

A = # of slices Alice got

B = # of slices Bob got

C = # of slices Charles got

D = # of slices Darwin got

First, write equations based on given information:

A = 0

B = 2C

5C = D

D = C + 8

5C = D -> D = 5C

Now that we have two equations for D, we can set them equal to each other:

5C = C + 8

4C = 8

C = 2

Now just plug in the rest:

A = 0

B = 2(2) = 4

C = 2

D = 2 + 8 = 10

Add all solutions together to get (E) 16 slices

Approximately $2.40 per kilogramme is the average rate that the total cost rises as the order size does, from 100 to 600 kg.

The average rate of change is the average change rate of one thing in respect to another. Simply explained, a computation that divides the amount of change in one thing by the comparable amount of change in another is known as an average rate of change function.

Divide the y-value change by the x-value change to determine the average rate of change. When analyzing changes in observable parameters like average speed or average temperature, finding that average rate of change is especially helpful.

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So the expression evaluates to 14 when x = 2.

To evaluate the expression, we first substitute x = 2 into the expression:

5(2 - 6 + 3*2)^2 - 6

There are two methods for solving simultaneous linear equations: graphical methods and algebraic methods. The algebraic technique includes the substitution method as one of its categories.

The value of one variable from one equation is substituted in the second equation using the substitution method. In this manner, a pair of linear equations is reduced into a single linear equation with only one variable, which can then be solved quickly.

Next, we simplify the expression inside the parentheses:

=5(2 - 6 + 6)^2 - 6

=5(2)^2 - 6

=5*4 - 6

=20 - 6

=14

So the expression evaluates to 14 when x = 2.

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Answer:

y-5=-1/7(x-4)

Step-by-step explanation:

The equation of the line in point-slope form is y-5=-1/7(x-4)

Answer:

y = -1/7 x + 39/7

Step-by-step explanation:

An equation in point slope form is

y = mx+b  where m is the slope and b is the y intercept

We are given the slope

y = -1/7 x + b

Substitute in the point for x and y and solve for b

5 = -1/7(4) +b

5 = -4/7 +b

5 + 4/7 = b

5*7/7 + 4/7 = b

35/7 + 4/7 = b

39/7 = b

The equation is

y = -1/7 x + 39/7

[tex]\\ \sf\longmapsto f(n)=2^n[/tex]

#a

[tex]\\ \sf\longmapsto f(1)=2(1)=2Amoebas[/tex]

#b

[tex]\\ \sf\longmapsto f(2)=2^2=4Amoebas[/tex]

#c

[tex]\\ \sf\longmapsto f(6)=2^6=64Amoebas[/tex]

#d

[tex]\\ \sf\longmapsto f(24)=2^24Amoebas[/tex]

Answer:

slope = 5

Step-by-step explanation:

slope of a line = y2 -y1 / x2 - x1          

where x1 =4.5 x2 =2                    y1= 2.5             y2 = -10

slope = -10 - 2.5 /   2 - 4.5

slope = -12.5 / -2.5

slope = 5