Find the 7th term of the geometric sequence whose common ratio is 2/3 and whose first term is 6.

Answer:

k = ±2√5 + 3

Step-by-step explanation:

[tex]k=3+2\sqrt5\ or\ k=3-2\sqrt5[/tex]

[tex]k^2-6k=11[/tex]

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[tex]k^2-6k+(6\times\frac{1}{2})^2=11+(6\times\frac{1}{2})^2[/tex]

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[tex]k^2-6k+3^2=11+3^2[/tex]

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[tex](k-3)^2=11+3^2[/tex]

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[tex](k-3)^2=11+9[/tex]

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[tex](k-3)^2=20[/tex]

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[tex]k-3=\sqrt{20}\ or\ k-3=-\sqrt{20}[/tex]

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                                 [tex](k-3=\sqrt{20})[/tex]

[tex]k=\sqrt{20}+3\\ k=2\sqrt{5}+3[/tex]

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                               [tex](k-3=-\sqrt{20})[/tex]

[tex]k=\sqrt{20}+3\\ k=-2\sqrt{5}+3[/tex]

_____________________________________________________

[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]

_____________________________________________________

[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]

_____________________________________________________

I hope this helps you

:)

Answer:

if it is just the 10+36-6 then that is 40 but then if it is 2/5 10+36-6 then that would be 16

Step-by-step explanation:

add 10 and 36 which is 46 then subtract 6 which is 40 then get the 2/5 which would be 16 hope this helps you

Answer:  She observed older fossils that contained many of the same minerals as the newer ones

Step-by-step explanation:

Answer:

chaupapi

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Step-by-step explanation:

Answer:

y = 71

z = 18

x = 14

Step-by-step explanation:

Figure on the right is simply figure on the left but flipped on its side. we know this because the question tells us the shapes are congruent (which means equal, the same)

Step-by-step explanation:

(2x - 3)×4

random number multiplied by 2, then minus 3 from that result, and multiply that result by 4.

Answer:

that's 4 and 7 .............

Answer:

C. 5%

Step-by-step explanation:

if u count the shaded part it is 5 shaded out of 100 so that fraction is 5/100 which is .05 as a decimal and 5% as a percent

Answer:

Third option

Step-by-step explanation:

Given the following question:

[tex]7x-4=5x+15[/tex]

To find the answer we need to use inverse of operations to simplify the equation in till we isolate the variable and find the value of x.

[tex]7x-4=5x+15[/tex]
[tex]-4+4=0[/tex]
[tex]15+4=19[/tex]
[tex]7x=5x+19[/tex]
[tex]5x-5x=0[/tex]
[tex]7x-5x=2x[/tex]
[tex]2x=19[/tex]
[tex]2x\div2=x[/tex]
[tex]19\div2=\frac{19}{2}[/tex]
[tex]=\frac{19}{2}[/tex]

Your answer is the third option or "19/2."

Hope this helps.

Answer:

A, C, E,

Step-by-step explanation:

A)Surveying the boys in the freshman class.

C)Surveying all the students in her math class.

E)Surveying the students in the chess club.

Answer:

872 square in.

Step-by-step explanation:

The formula for the surface area of a rectangular prism is:

[tex]A=2(wl*wh*lh)[/tex]

Where w is the width of the prism, l s the length of the prism, h is the height of the prism, and A is the surface area.

Plugging in the numbers given, you get the following equation:

[tex]A=2((20*18)*(20*2)*(18*2))[/tex]

Which when calculated out, is 872 square in.

The capacitance between two parallel plates of area s and separation of d is;

[tex]\rm Capacitance = \varepsilon _0\dfrac{s}{d}[/tex]

Capacitance is the limitation of the body to store the electric charge. Every capacitor has its capacitance.

The typical parallel-plate capacitor consists of two metallic plates of area s, separated by the distance d.

The capacitance between two parallel plates of area s and separation of d is given by the following formula;

[tex]\rm Capacitance = \varepsilon _0\dfrac{s}{d}[/tex]

The capacitance of a parallel plate capacitor depends on the area of the plates s and their separation d.

According to Gauss's law, the electric field between the two plates is: Since the capacitance is defined by one can see that capacitance is: Thus you get the most capacitance when the plates are large and close together.

To know more about capacitance click the link given below.

https://brainly.com/question/14746225

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Answer:

90 students

Step-by-step explanation:

So, if you have 100 students to start and it decreases by 10% then take the 100 and multiply it by .10. You should get 10. Then, subtract 10 from 100 and you end up with 90.

Answer:

hello

2010 = 100 students

2011 = 100 x 0.9 = 90

2012 =  90 x 1.1 =  99  

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

30% of 90 can be written as 30% × 90

= 30/100 × 90

= 27

The fraction of the compact disks ordered  by the owner of the music store that are Soft Rock is 13/28.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above while the denominator is the number below.

1 - (1/4 + 2/7)

1 -[ (7 + 8) /28]

1 - 15/28 = 13/28

What is k ? (k = y/x)

     If y is dollars earned and x is hours worked,

k = y/x

k = 150 dollars /20 hours

k = 7.50 dollars per hour

What is the equation for the direct variation situation? (y = kx)

y = kx

y = (7.50)(60)

y = 450

How much will she earn for working 60 hours?

y = $450

       She will earn $450 after working for 60 hours.

The possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.

It should be noted that a persuasive speech simply means a speech that is used to convince an individual to agree to a particular perspective.

In this case, the possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.

Learn more about speech on:

https://brainly.com/question/25887038

Answer:

constant = - 3

Step-by-step explanation:

[tex]\frac{x}{2}[/tex] - 3 = [tex]\frac{1}{2}[/tex] x - 3

the number without letters attached is the constant - 3

Answer:

-3

Step-by-step explanation:

The answer is -3 because 2 has a letter attached to it which is x/2 -3 is without a letter.

hope dis helps):

Answer:

The answer is 15

Step-by-step explanation:

the answer is c (x=15)...

[tex]\large\bold\color{pink}{{★ƛƝƧƜЄƦ ↦}}[/tex]

[tex]\\ \large \rm{↠Given \: triangle \: is \: right \: angled \: triangle .}[/tex][tex]\\\rm{Pythagorean \: Theorem \: states \: that} \\ \\ \large \rm{↠Hypotenuse = \sqrt {Altitude^{2} + Base ^{2} } } [/tex]

[tex]\blue{\rule{15mm}{3.9pt}} \red{\rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex]

Here,

[tex]\blue{\rule{15mm}{3.9pt}} \red{\rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex]

[tex]\rm{↠Substituting \: values }[/tex]

[tex] \large\rm{↠AC= \sqrt {AB^{2} + BC ^{2} } } \\ \\ \large\rm{↠x = \sqrt{12 ^{2} + 9 ^{2} } } \\ \\ \large\rm{↠x = \sqrt{144 + 81} } \\ \\ \large\rm{↠x = \sqrt{225} } \\ \\ \large\rm{↠x =15 }[/tex]

[tex] \underline{\rule{100mm}{3.2pt}}[/tex]

[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]

Answer:

66 (no other answer)

Step-by-step explanation:

The number can be divided by 2 so its even. Its a multiple of 11. It is between 20 and 79. it is a multiple of 3.

The equation [tex]y = x^2 - 8x + 3[/tex] is an illustration of a quadratic equation

The vertex of the quadratic equation [tex]y = x^2 - 8x + 3[/tex] is (4,-13)

The equation is given as:-

[tex]y = x^2 - 8x + 3[/tex]

A quadratic equation is represented as:

[tex]y = ax^2 + bx + c[/tex]

By comparison, we have:

a = 1; b = -8; c = 3

The x-coordinate of the vertex is:
[tex]x = -\frac b{2a}[/tex]

So, we have:

[tex]x = \frac 8{2*1}[/tex]

[tex]x = 4[/tex]

Substitute 4 for y in [tex]y = x^2 - 8x + 3[/tex]

[tex]y = 4^2 - 8 * 4 + 3[/tex]

[tex]y = -13[/tex]

When x = 2 and 3, we have:

[tex]y = 2^2 - 8 * 2 + 3 = -9[/tex]

[tex]y = 3^2 - 8 * 3 + 3 = -12[/tex]

When x = 5 and 6, we have:

[tex]y = 5^2 - 8 * 5 + 3 = -12[/tex]

[tex]y = 6^2 - 8 * 6 + 3 = -9[/tex]

So, the table of values is:

x       y

2      -9

3      -12

4      -13

5      -12

6      -9

Read more about quadratic functions at:

https://brainly.com/question/18797214

Answer:

5

Step-by-step explanation:

Answer:

The mean absolute deviation would be 10.

Step-by-step explanation:

I calculated the answer in Microsoft excel. I used a bunch of excel formulas. I do not know how to insert some of the math symbols neccessary to show you my steps. Here is a picture of the formula.

Answer:

yes I can help you with this but I don't know it

Answer:

4.61

Step-by-step explanation:

Step-by-step explanation:

[tex] = 4 \frac{2}{4} + \frac{1}{9} \\ = \frac{4 \times 4 + 2}{4} + \frac{1}{9} \\ = \frac{18}{4} + \frac{1}{9} [/tex]

Find the LCM

[tex] = \frac{18}{4} \times \frac{9}{9} + \frac{1}{9} \times \frac{4}{4} \\ = \frac{162}{36} + \frac{4}{36} \\ = \frac{166}{36} [/tex]

Convert into lowest term

[tex] \frac{83}{16} \\ [/tex]

Answer: a 5/24

Step-by-step explanation:

3 + 5 + 1 = 9

First = Pop Song     P = 3/9  = 1/3

Seconed = Hip Hop Song       P2 =  5/9-1   = 5/8

So P = 1/3 x 5/8 = 5/24

So that makes A the correct answer

Answer:

2100

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of thesquares on the other two sides, that is

x² + 8² = 9²

x² + 64 = 81 ( subtract 64 from both sides )

x² = 17 ( take square root of both sides )

x = [tex]\sqrt{17}[/tex]

Answer:

⠀

Step-by-step explanation:

⠀

We'll solve this using the Pythagorean Theorem.

⠀

Let,

⠀

We know that,

[tex]{ \longrightarrow \pmb{\qquad \: (AB) {}^{2} +( BC) {}^{2} = (AC) {}^{2} }}[/tex]

[tex]{ \longrightarrow \sf \qquad \: (8) {}^{2} +( x) {}^{2} = (9) {}^{2} } [/tex]

[tex]{ \longrightarrow \sf \qquad \: ( x) {}^{2} = (9) {}^{2} - (8) {}^{2}} [/tex]

[tex]{ \longrightarrow \sf \qquad \: ( x) {}^{2} = 81 - 64} [/tex]

[tex]{ \longrightarrow \sf \qquad \: ( x) {}^{2} = 17} [/tex]

[tex]{ \longrightarrow \it \qquad \pmb {x = \sqrt{17 \: \: } } }[/tex]

⠀

Therefore,