Mathematics College

[4 marks
c) log2X, log2 (X + 9), and log2 (x + 45) are three consecutive terms of an arithmetic
progression
i)
ii)
Find X
Find the 5th term as a single logarithm.
lanice​

[4 Marksc) Log2X, Log2 (X + 9), And Log2 (x + 45) Are Three Consecutive Terms Of An Arithmeticprogressioni)ii)Find

Answers

Answer 1

Answer:

1. x = 3

2. The 5th term = Log₂768.

Step-by-step explanation:

From the question given above, the following data were obtained:

Log₂x, Log₂(x + 9, Log₂(x + 45)

x =?

5th term (T₅) =.?

1. Determination of the value of x.

We shall determine the value of x as follow:

First term = Log₂x

2nd term = Log₂(x + 9)

3rd term = Log₂(x + 45)

Common difference = 2nd term – first term = 3rd term – 2nd term

Log₂(x + 9) – Log₂x = Log₂(x + 45) – Log₂(x + 9)

Recall

Log M – Log N = Log (M/N)

Therefore,

Log₂(x + 9) – Log₂x = Log₂(x + 9)/x

Log₂(x + 45) – Log₂(x + 9) = Log₂(x + 45) /(x + 9)

Thus:

Log₂(x + 9) – Log₂x = Log₂(x + 45) – Log₂(x + 9)

Log₂(x + 9)/x = Log₂(x + 45)/(x + 9)

Cancel Log₂ from both side

(x + 9)/x = (x + 45)/(x + 9)

Cross multiply

(x + 9)(x + 9) = x(x + 45)

x² + 9x + 9x + 81 = x² + 45x

x² + 18x + 81 = x² + 45x

Rearrange

x² – x² + 81 = 45x – 18x

81 = 27x

Divide both side by 27

x = 81/27

x = 3

Therefore, the value of x is 3.

2. Determination of the 5th term.

We'll begin by calculating the common difference (d)

x = 3

First term = Log₂x

First term = Log₂3

2nd term = Log₂(x + 9)

2nd term = Log₂(3 + 9)

2nd term = Log₂12

Common difference (d) = 2nd term – first term

Common difference (d) = Log₂12 – Log₂3

= Log₂(12/3)

Common difference (d) = Log₂4

Finally, we shall determine the 5th term as follow:

First term (a) = Log₂3

Common difference (d) = Log₂4

5th term (T₅) =.?

T₅ = a + 4d

T₅ = Log₂3 + 4Log₂4

Recall:

nLogM = LogMⁿ

Therefore,

4Log₂4 = Log₂4⁴ = Log₂256

T₅ = Log₂3 + 4Log₂4

T₅ = Log₂3 + Log₂256

Recall:

Log M + Log N = Log (M×N)

Thus,

T₅ = Log₂3 + Log₂256

T₅ = Log₂(3 × 256)

T₅ = Log₂768

Therefore, the 5th term is Log₂768

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1/2K-(k+1/5)=1/10(k+2)

Answers

Answer:

k=−23

Step-by-step explanation:

I hope this help if you need step by step just comment

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Quanto é 60 x 11 + 346²

Answers

Answer:

120376

Step-by-step explanation:

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Espero que isso ajude você! :)

Amy, Kareem, and Jim served a total of 123 orders Monday at the school cafeteria. Kareem served 4 times as many orders as Jim. Amy served 9 fewer orders than Jim. How many orders did they each serve?

Answers

They each served 289

picture attachment is below

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Answer:

D

Step-by-step explanation:

A rational number will either end or repeat forever like the first three, but the fourth one, pi, will go on forever and never repeat, making it irrational.

(3x +1)•2x – x^2 • 3
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Answers

Answer:

3x^2 +2x9x^2 +6x+1

Step-by-step explanation:

[tex](3x +1)\cdot 2x - x^2 \cdot 3\\\\=2x\left(3x+1\right)-3x^2\\\\\mathrm{Expand}\:2x\left(3x+1\right):\quad 6x^2+2x\\\\=6x^2+2x-x^2\cdot \:3\\\\\mathrm{Simplify}\:6x^2+2x-x^2\cdot \:3:\\\quad 3x^2+2x[/tex]

2.

[tex](3x + 1)^2\\\\\mathrm{Apply\:Perfect\:Square\:Formula}:\\\quad \left(a+b\right)^2=a^2+2ab+b^2\\\\a=3x,\:\:b=1\\\\=\left(3x\right)^2+2\cdot \:3x\cdot \:1+1^2\\\\\mathrm{Simplify}\:\left(3x\right)^2+2\cdot \:3x\cdot \:1+1^2:\\\quad 9x^2+6x+1[/tex]

If a club charges dues of $200 a year, it will have 50 members. For each $5 it raises its dues, it loses a member. USE AN EQUATION to determine what the club should charge to maximize its income from dues.

Answers

Answer:

The value is      [tex]y  =  \$ 225[/tex]

Step-by-step explanation:

From the question we are told that

   The amount charge per year is  [tex]k  =  \$ 200[/tex]

   The  number of members it will have at this amount is  [tex]n  =  50[/tex]

   The amount amount increase that will lead to the loss of a single member is   [tex]z =  \$ 5[/tex]

        Generally the total amount the club would obtain from  its members is mathematically represented as

      [tex]I  =  Amount \  due\ paid *  Number \  of members[/tex]

Now let x denote the number of member lost

Hence

      [tex]I  =  (k + zx) (n-x )[/tex]

=>    [tex]I  =  (200 + 5x) (50-x )[/tex]

=>  [tex]I  = 10000+50x-5x^2[/tex]

Thus the number of members that be removed to  give the maximum  income from dues is obtained by differentiating the above equation and equating it to zero

           [tex]\frac{dI}{dx}  =  50-10x[/tex]

=>         [tex] x   =  5[/tex]

So from  [tex]I  =  (200 + 5x) (50-x )[/tex] we have

          [tex]I  =  (200 + 5 (5)) (50-5 )[/tex]

           [tex]I  = \$ 10125 [/tex]

So the amount the club should charge is    

         [tex]y  =  \frac{10125}{50 - 5}[/tex]

         [tex]y  =  \$ 225[/tex]

         

The values in the table define the function Alx). If g(x) is the inverse of Ax), what is the value of g(1)?
xfx)
-1
-3
1
-1
4
1
6
4.
7
6

Answers

Answer: im pretty sure its D. 4

Step-by-step explanation:

Given 8x^2 – 3 + 4, what is (are) the constant(s)?

Answers

Answer:

-3 and 4

Step-by-step explanation:

[tex]-3[/tex] and [tex]4[/tex] are the constants

since they aren't multiplied a variable

-3 and 4 would be your answer

Evaluate the expression.
35 - (9+8) X 2 =?

Answers

Answer:

35-(17)×2

35-34

i think it helps you

☽------------❀-------------☾

Hi there!

~

[tex]35-(9+8)\times 2=[/tex]

[tex]= 35 - (17)(2)[/tex]

[tex]= 35 - 34[/tex]

[tex]= 1[/tex]

❀Hope this helped you!❀

☽------------❀-------------☾

What is the equation of the line that is parallel to y = 2/3x+ 4 and passes through
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Answers

Answer:

The answer is

[tex]y = \frac{2}{3} x + \frac{17}{3} [/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

The original line is y = ⅔x + 4

Comparing with the general equation above

Slope = 2/3

Since the lines are parallel their slope are also the same

Slope of parallel line = 2/3

Equation of the line using point (-7 , 1) and slope 2/3 is

[tex]y - 1 = \frac{2}{3} (x + 7) \\ y - 1 = \frac{2}{3} x + \frac{14}{3} \\ y = \frac{2}{3} x + \frac{14}{3} + 1[/tex]

We have the final answer as

[tex]y = \frac{2}{3} x + \frac{17}{3} [/tex]

Hope this helps you

Pls help i dont understand :( will mark brainliest!!

Answers

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375< y < 525

Step-by-step explanation:

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the maximum is 15 * 35 =525

He can earn any amount between these two values

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Answers

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Answers

Answer:

the probability is:

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Now to calculate the probability of A and B

you have to multiply both probabilities:

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Step-by-step explanation:)

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Answers

Answer:

738,378,886

Step-by-step explanation:

1) Add 2+99,999,999 which equals to 100,000,001

2) Then, subtract 100,000,001 with 7 which is 99,999,994

3) Finally, add 99,999,994 with 638,378,892 which is 738,378,886

Hope this helps!

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Answers

Answer: Mr. Lee’s entire face crinkles and lights up when he smiles.

Step-by-step explanation:

Mr. Lee’s entire face crinkles and lights up when he smiles. Option C is correct.

Given that,
From the sentences, we have to determine the sentence that emphasizes the engaging details.

What is engaging details?

Content created by someone who is enthusiastic about the subject they are writing about is the most engaging content. If you write with passion and explain to readers why you are passionate, you might be able to persuade them to love your company as much as you do.

Here,
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While in option C engaging sentence the smile tends to bring crinkles and lights up the face.

Thus, Mr. Lee’s entire face crinkles and lights up when he smiles. Option C is correct.

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https://brainly.com/question/17346475
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Answers

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33

Step-by-step explanation:

each upper cell is the sum of the two cells under it. For example 4 and 5 make 9 so 16+17=33

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Answers

Hey there! I'm happy to help!

A is -10 and F is -5. To find the number in between two numbers, you add them and divide by 2.

-10+(-5)=10-5=-15

-15/2=-7.5

So, the midpoint is -7.5, which is right in between C and D.

Have a wonderful day! :D

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Answers

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Step-by-step explanation:

Given: A question ask about how many hours per week do you watch television?

Total participants = 300

Since all participants are different ,  so have their own answer to this question in numerical terms.

We use proportion or percentage to summarize data if data is categorical, but here data is numerical (continuous).

here , we can use either mean or median ( if it has outliers).

For this we need to check the distribution of the data, if it is normal then Mean, standard deviation, and range would be a better option (as mean is the best measure of tendency)otherwise Median, IQR, and range would be a better option .

hence, the correct option is D. A or B depending on the distribution of the sample

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[tex] \sqrt{16} [/tex]
=x then x^2 = ​

Answers

Answer
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I hope this help you

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Answers

rational and whole, 4/16 equals 4

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Answer:

412,090

Step-by-step explanation:

math+math+brain+school

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Answers

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Answers

Answer:

x=84

Step-by-step explanation:

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plyy mark me as brainliest

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Answer:

See below

Step-by-step explanation:

1. Option D

d. -6 < x ≤ 6

2.  Option C

y = 3

3.  Option B

Travis only. Tim's graph only covers positive range

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Answer:

I think it is the option c.

please mark me as the brainliest answer and please follow me for more answers to your questions.

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3/14

Step-by-step explanation:

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