Which expression can be written as
[tex]k \sqrt{3} [/tex]where k is an integer?

a.
[tex] \sqrt{63} [/tex]

b.
[tex] \sqrt{108} [/tex]

c.
[tex] \sqrt{144} [/tex]

d.
[tex] \sqrt{150} [/tex]

​

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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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

To find the endpoint we have to calculate the distance between the known midpoint to the known endpoint. To calculate the midpoint we add two points and divide them by 2.

The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2.

Substituting in the two x-coordinates and two y-coordinates from the endpoints.

Putting it together,

The endpoint formula is:

(x a ,ya)= ((2xm−xb),(2ym−yb))

( x a , y a ) = ( ( 2 x m − x b ) , ( 2 y m − y b ) ).

The end of a line at a point that is equally distant from both ends, a time interval between an event's beginning and end.

The point on a graph or figure where the figure stops might be referred to as the endpoint. It can be the point joining the sides of a polygon (the vertex), the common endpoint of two rays making an angle, the two extreme points of a line segment, the one end of a ray.

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On using the distribution method the value could be  [tex]e ^ {t^{2}[/tex]/ 2

What is the Gamma Distribution  ?

A distribution which is described as two parameters – shape parameter and inverse scale parameter, having continuous probability distributions.

Given,

Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).

Using the distribution method, find the pdf of U = Z 2.

And Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution.

Suppose e Z ∼ N (0, 1),  then

mZ (t) = 1√2πetxe−x2/2dx

= et2/21/√2π

[tex]e ^ {-(x-t)^{2} /2[/tex] dx

= [tex]e ^ {t^{2}[/tex]/ 2

hence, on using the distribution method the value could be [tex]e ^ {t^{2}[/tex]/ 2

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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

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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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

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: 7

Step-by-step explanation:

Answer:

$80.438.11

Step-by-step explanation:

the formula for calculating future value when there is continuous compounding is : A x e^r x N A= amount e = 2.7182818 N = number of years r = interest rate

$5,000  x (2.7182818 ^0.07) x 15 = $80.438.11

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

Answer:

Its D) 36%

Answer: The answer is 10x2

Step-by-step explanation:

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

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)

[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:

22.5

Step-by-step explanation:

125

x 18

---------

1. first set up your problem

2 4

125

x 18

------

1000

2. next multiply the 8 by 5 getting 40, drop the 0 anf move the 4 to the top above 2.

3. multiply 8 by 2 getting 16, then add the 4 you have ontop of the 2 to the 16 getting 20. Drop the 0 and bring the 2 over and place it above the one.

4. multiply 8 by 1 getting 8 then add the 2 above the 1 to 8 getting 10. Then put the ten infront of the tw zeros. 1000

125

x 18

--------

1000

0

Next add a 0 as a place filler under the 0 at the end.

125

x 18

-------

1000

1250

Then multiply the 1 by 5, then 1 by 2, then finnaly 1 by 1, getting you 1250.

1000

+1250

add together

getting 2250

then move 2 decimal places over to get 22.5

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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The easiest way to find the slope of a line is converting the line equation into the slope-intercept form.

There are 3 forms of line equations:

- slope intercept form, the equation is given by:

 y = mx + b

Where:

m = slope

- point slope form, the equation is given by:

y − y₁ = m (x - x₁)

Where:

m = slope

- standard form: Ax + By = C

The easiest way to find the slope of a line is to convert it into a slope-intercept form.

Example:

Line equation in standard form:

2x + 4y = 6

We will convert it into  slope-intercept form.

4y = -2x + 6

y = (-2/4) x + 6

y =  (-1/2) x + 6

Hence, the slope is  (-1/2)

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Answer:

Calculate the value of x. Give your answer ... Hyp. 5.8 m. Opp. 1. Adi. Diagram NOT accurately drawn. POR is a triangle. Angle Q = 90° ... the value of x. Give your answer correct to 1 decimal place. ... a. Diagram NOT accumtely drawn. 9,6 cm. 6.4 cm. A. Hyp. To. Aaj. LMN is a right-angled triangle. MN = 9.6 cm. ... x = ton​-14.5.

Step-by-step explanation:

please be right

Answer:

he arrived at school at 7:18

Step-by-step explanation:

Time = distance/speed  = 3mi/30mph

= 3/30

= 0.1 hour

= 6 minutes

= 00:06:00

Answer:

Step-by-step explanation:

We need to transform the given x^2 - 19x + c into the form

                                                      (x - a)^2 + d

by completing the square:

1.  Take half of the coefficient (-19) of x, obtaining -19/2.

2.  Square this result, obtaining 361/4.

3.  Add this to x^2 - 19x, and then immediately subtract it:

    x^2 - 19x + c becomes x^2 - 19x + 361/4 - 361/4+ c

4.  Replace the first three terms with (x - 19/2)^2:

     x^2 - 19x + 361/4 - 361/4+ c  =>  (x - 19/2)^2 - 361/4 + c

5.  Put this into final form: (x - 19/2)^2 - (361/4 - c)

Marla is 30 years old.

Let marla age be x and Darla age be y

Given : Marla is four years less than twice as old as Darla

What is equation ?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Marla is four years less than twice as old as Darla can be represented as : 2y - x = 4

sum of their ages is 47 can be represented as : x + y = 47

Solving both the equation using addition we got ,

3y = 51

y = 17

Substituting the value of y in x + y =47 , we get

x + 17 = 47

x = 47 -17

x = 30

Hence , Marla is 30 years old.

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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:

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

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:

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.