For which value of x is line L parallel to line M?

Notice that

a + ar³ + ar⁶ + ar⁹ + ... = a + r³ (a + ar³ + ar⁶ + ...)

but the grouped sum on the right side is the same as the sum on the left side. This means that, if the sum we want to compute

a + ar³ + ar⁶ + ar⁹ + ...

converges to S, then

S = a + r³ S

Solve for S :

S - r³ S = a

(1 - r³) S = a

S = a/(1 - r³)

Similarly, knowing the value of the first sum, we have

a + ar + ar² + ar³ + ... = a + r (a + ar + ar² + ...)

but we know

a + ar + ar² + ... = 15

so

15 = a + 15r

and knowing the value of the second sum, we have

a + ar² + ar⁴ + ... = a + r² (a + ar² + ar⁴ + ...)

so

9 = a + 9r²

Solve these two equations for a and r :

15 = a + 15r   ⇒   a = 15 - 15r

9 = a + 9r²   ⇒   9 = 15 - 15r + 9r²   ⇒   3r² - 5r + 2 = (3r - 2) (r - 1) = 0

⇒   r = 2/3 or r = 1

We cannot have r = 1, since that would mean

a + a + a + ... = 15

since the left side is adding infinitely many copies of some constant; such a sum can never converge to a finite number. So it must be that r = 2/3, and it follows that a = 15 - 15 (2/3) = 5.

Then the sum we want has a value of

S = 5/(1 - (2/3))³ = 135/19

Answer:

Step-by-step explanation:

  a + ar¹ + ar² + ar³ + ... = 15       #1

r(a + ar¹ + ar² + ar³ + ...) = 15r

       ar¹ + ar² + ar³ + ... = 15r      #2

subtract #2 from #1

a = 15 - 15r

     a + ar² + ar⁴ + ar⁶ + ... = 9         #3

r²(a + ar² + ar⁴ + ar⁶ + ... )= 9r²

         ar² + ar⁴ + ar⁶ + ... = 9r²       #4

subtract #4 from #3

a = 9 - 9r²

15 - 15r = 9 - 9r²

9r² - 15r + 6 = 0

3r² - 5r + 2 = 0

r = (5 ±√(5² - 4(3)(2))) / (2(3)

r = (5 ± 1) / 6

r = 1

or

r = 4/6 = 2/3

if r = 1 then a = 15 - 15(1) = 0 and a series of zeros added together can never equal 15 so r = 2/3 must be true.

a = 15 - 15(2/3) = 5

   a + ar³ + ar⁶ + ar⁹ + ... = C           #5

r³(a + ar³ + ar⁶ + ar⁹ + ...) = Cr³

         ar³ + ar⁶ + ar⁹ + ... = Cr³          #6

subtract #6 from #5

a = C - Cr³

a = C(1 - r³)

C = a/(1 - r³)

C = 5/(1 - (2/3)³)

C = 5/(1 - 8/27)

C = 5/(19/27)

C = 5(27/19)

C = 135/19 = 7.1052631578947368....

[tex]\rule{2000pt}{1000000pt}[/tex]

Answer:

-8(10x-3) = -80x+24 = A

Step-by-step explanation:

yr welcome

The expression can be used to determine how much more money Club A will cost than Club B after x months is 7 - 4x

A linear equation is in the form:

y = mx + b;

where y, x are variables,  m is the rate of change and b is the initial value of y.

Let y represent the total cost for x months.

Club A charges a $35 joining fee, plus $19 per month. hence:

y = 19x + 35

Club B charges a $28 joining fee, plus $23 per month. hence:

y = 23x + 28

Club A will cost than Club B:

19x + 35 - (23x + 28)

= 7 - 4x

The expression can be used to determine how much more money Club A will cost than Club B after x months is 7 - 4x

Find out more on linear equation at: https://brainly.com/question/14323743

Answer:

3

Step-by-step explanation:

4x+2=5x-1

4x - 5x = -1 -2

x = 3

Answer:

2000

Step-by-step explanation:

1 dm =1000

2dm =?

2dm x 1000

1dm

2000

Answer:

Expression D

Step-by-step explanation:

all other answers are above 15! hope this helps :D

Answer:

The answer is 54.

Step-by-step explanation:

You add all these numbers up.

Answer:

24 pints

Step-by-step explanation:

if 1 gallon is = to 8

then 3 gallons is 24

There are 24 pints in 3 gallons.

To determine how many pints are in 3 gallons, we can use the conversion factor provided: 1 gallon equals 8 pints.

Step 1: Calculate the number of pints in 1 gallon.

Since 1 gallon equals 8 pints, we can write this as 1 gallon = 8 pints.

Step 2: Multiply the number of pints in 1 gallon by the number of gallons.

To find the number of pints in 3 gallons, we multiply the number of pints in 1 gallon (8 pints) by 3 gallons:

3 gallons × 8 pints/gallon = 24 pints.

Therefore, there are 24 pints in 3 gallons.

Learn more about conversion factor click;

https://brainly.com/question/30567263

#SPJ6

Step-by-step explanation:

We use the power rule a^(x+y) = a^x * a^y:

3^(2x+1) = 3^(2x) * 3

We can re-write 3^(2x) as (3^x)^2, and we know that 3^x = a, so:

3a^2 is the final answer. There is not exact value, it's all just about re-writing.

[tex]3a^2 [/tex] is a required answer.

Answer:

solution given:

[tex]3^{2x+1}=? [/tex]

if [tex] 3^x=a[/tex]

By using power rule, we can write

[tex]3^{2x+1}[/tex] as

[tex]3^{2x+1}=(3^x)^2*3^1 [/tex]

[tex]a^2*3=3a^2 [/tex]

Answer:

2

Step-by-step explanation:

the first number is one .then you write number two twice . The next number is the summation of the three previous numbers .then you write number two twice and the next number is the summation of the three previous numbers .and you do that regularly

Answer:

112cm^3

Step-by-step explanation:

Formula for volume of a cone is:

[tex] \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]

r = radius and h = height

To find the radius you divide the diameter by 2:

12.9 ÷ 2 = 6.45

Now substitute values into the formula:

[tex] \frac{1}{3} \times \pi \times {6.45}^{2} \times 16.6[/tex]

Which equals 112cm^3

Answer:

can't see the pic properly

The number that can be added to 17/4 to make 5 is 3/4

Given

Add to 17/4 to make 5

let

x + 17/4 = 5

x = 5 - 17/4

x = (20-17) / 4

x = 3/4

Learn more about fraction:

https://brainly.com/question/11562149

Answer:

I don't know

Step-by-step explanation:

plus all of them = Answer

Answer:

Step-by-step explanation:

False    Line of symmetry is x = -1

False   The maximum of f(x) = 3  

we can find the maximum of f(x) by putting it in vertex form (y - 3) = - 1(x + 7)² which tells us that the vertex is at (-7, 3)

True     -7 < -1

Answer:

  2

Step-by-step explanation:

x-values in the table increase by 1, while y-values increase by 2. The rate of change is ...

  m = slope = rate of change = (change in y)/(change in x) = 2/1 = 2

The rate of change is 2.

Answer:2

Step-by-step explanation:

Answer:

unfortunately i cannot tell you the exact answers; however, i can suggest something instead. my suggestion is that if there's any math notes that are available, maybe you could look over them-then apply that to the problems.

Step-by-step explanation:

I hope this helps you!

Answer:

Below in bold.

Step-by-step explanation:

1. 165/3.3 = 50 meters/second.

2. In 4 seconds the skydiver will fall 4*50 = 200 meters.

Answer:

4.546, rounded

Step-by-step explanation:

pls mark brainliest!

Answer:

f(0) = 3

f(-2) = -15

Step-by-step explanation:

You just have to plug in the value in f(b) into the b of the equation.

So for f(0) --> 2(0)^3 - |0-4| + 7

2(0) - |-4| + 7

0 - 4 + 7 = 3

------------

for f(-2)

2(-2)^3 -|-2-4| + 7

2(-8) - 6 + 7

-16 -6 + 7 = -15

Answer:

32 and 37

Step-by-step explanation:

Because the difference between the values is 5.

assuming the fraction is 1/11, the denominator shows how many parts the WHOLE was sliced into, namely 11 parts.

Answer:

-32>x

Step-by-step explanation:

-16>x÷2

-16×2>x

-32>x

Answer:

first option

Translate seven left followed by mirror over y = 2

Step-by-step explanation:

The solution is Option A.

The translation of triangle MNP to triangle STR is a translation of 7 units to the right and a reflection along R = 2

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the triangle be represented as MNP

Now , the transformed triangle be STR

Now , the translation is given as

Step 1 :

The coordinates of triangle is MNP

M = M (-5 , 2 )

N = N ( - 8 , 5 )

P = P ( -2 , 4 )

Now , the translation of 7 units to the right will result in

M' = M' ( 2 , 2 )

N' = N' ( -1 , 5 )

P' = P' ( 5 , 4 )

Step 2 :

The coordinates of the translated triangle M'N'P' is

M' = M' ( 2 , 2 )

N' = N' ( -1 , 5 )

P' = P' ( 5 , 4 )

Now , on reflection of triangle M'N'P' by R = 2 , we get

S = S ( 2 , 2 )

T = T ( -1 , -1 )

R = R ( 5 , 0 )

Hence , the translation of triangle MNP to triangle STR is a translation of 7 units to the right and a reflection along the R = 2

To learn more about transformation of function click :

https://brainly.com/question/26896273

#SPJ2

Answer:

Should be 3 units away from the picture

Step-by-step explanation:

I hope this helps! ;)

The coordinates of the image of EFG under the dilation with scale factor 3/2 and center of dilation (0, 0) are E(-3,3), F'(-3,-3) and G'(3,-3).

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

The image of EFG under the dilation with scale factor and center of dilation has to be drawn.

The coordinates or the triangle are E(-2,2), F(-2,-2) and G(2,-2). The new points after the dilation are,

[tex]E'(-2\times\dfrac{3}{2},2\times\dfrac{3}{2})=E'(-3,3)\\F'(-2\times\dfrac{3}{2},-2\times\dfrac{3}{2})=F'(-3,-3)\\G'(2\times\dfrac{3}{2},-2\times\dfrac{3}{2})=G'(3,-3)[/tex]

The dilated image of triangle EFG is attached below.

Thus, the coordinates of the image of EFG under the dilation with scale factor 3/2 and center of dilation (0, 0) are E(-3,3), F'(-3,-3) and G'(3,-3).

Learn more about the dilation of the figure here;

https://brainly.com/question/3457976

#SPJ2

The maximum number of bags is an illustration of the greatest common factor

The maximum number of bags John can make is 8

The given parameters are:

[tex]Chocolate=48[/tex]

[tex]Peanut=56[/tex]

Start by expressing 48 and 56 as a product of their factors.

[tex]Chocolate = 1 \times 2 \times 2 \times 2 \times 2 \times 3[/tex]

[tex]Peanut = 1 \times 2 \times 2 \times 2 \times 7[/tex]

The product of the common factors between the above products is:

[tex]Factors = 1 \times 2 \times 2 \times 2[/tex]

Multiply

[tex]Factors = 8[/tex]

The above represents the greatest common factor of 48 and 56.

Hence, the maximum number of bags John can make is 8

Read more about greatest common factor at:

https://brainly.com/question/219464

Step-by-step explanation:

To determine the maximum number of bags John can make, we need to find the greatest common divisor (GCD) of the two quantities: 48 chocolate chip cookies and 56 peanut butter cookies.

The GCD is the largest number that divides both quantities without leaving a remainder. It represents the maximum number of bags that can be made, with each bag containing an equal number of cookies of each type.

Let's find the GCD of 48 and 56:

Step 1: List the divisors of each number:

Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Divisors of 56: 1, 2, 4, 7, 8, 14, 28, 56

Step 2: Identify the common divisors in both lists:

Common divisors of 48 and 56: 1, 2, 4, 8

Step 3: Determine the greatest common divisor (GCD):

The greatest common divisor of 48 and 56 is 8.

So, John can make a maximum of 8 bags, with each bag containing an equal number of chocolate chip and peanut butter cookies.

PLEASE MARK AS BRAINLIEST IF SATISFIED WITH THIS ANSWER PLEASE