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3 years ago

3^x-3^(x-2)=A*3^x solve for A

Mathematics

1 answer:

ale4655 [162]3 years ago

3 0

Answer:

$a=\frac{8}{9}$

Step-by-step explanation:

$3^x-3x^{x-2} =a3^x$

Divide both sides by $3^x$ :

$3^{x-x}-3^{x-x-2}=a$

Simplify:

$3^0-3^{-2}=a\\a=1-\frac{1}{9} \\a=\frac{8}{9}$

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Could it be a proportional function?

Kipish [7]

Y=mx+b. I think because +b gives it away which never goes through the origin, and we just reviewed this at school.

5 0

3 years ago

A sequence is defined by the explicit formula an=3n+4 Which recursive formula represents the same sequence of numbers?

fomenos

Answer:

Option (3)

Step-by-step explanation:

Explicit formula of the sequence is,

$a_n=3^n+4$

From this explicit formula,

First term of the sequence will be,

$a_1=(3^1)+4$

$a_1=7$

Second term of the sequence,

$a_2=(3^2)+4$

$a_2$ = 13

3rd term of the sequence,

$a_{3}=(3^3)+4$

= 31

Sequence formed,

7, 13, 31 ..........

From the given options,

Recursive formula,

$a_n=3a_{n-1}-8$

$a_2=3(a_1)-8$

$a_2=3(7)-8$

$a_2=21-8$ = 13

$a_3=3a_2-8$

$a_3=3(13)-8$

= 39 - 8

= 31

Sequence formed from this recursive formula will be,

7, 13, 31........

Therefore, Option (3) will be the answer.

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3 years ago

Scott's gas tank is 1/3 full. After he buys 12 gallons of gas, it is 7/9 full. How many gallons can Scott's tank hold?

Bumek [7]

Answer: We start with the variable "x". Let's call "x" Dan's full tank.

So we know that right now he has 1/3x or 1/3 of a full tank.

After adding 12 gallons, at the end, he has 7/9x, or 7/9 of a full tank

So we start with

(1/3)x + 12 = 7/9x

Let's subtract 1/3x from both sides

12 = 7/9x - 1/3x

Remember, we need to use common denominators to subtract, so 1/3 becomes 3/9

12 = 7/9x - 3/9x

Now we simplify to get

12 = 4/9x

Multiply the reciprocal of 4/9 to both sides which is 9/4

12 * 9/4 = x

Answer is 27 gallons.

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3 years ago

9. What is the likelihood that a randomly selected couple's relationship survived between 90 and 150 days

andrew-mc [135]

Answer:

0.5818

Step-by-step explanation:

Suppose the average teenage romantic relationship is normally distributed with a mean number of 100 days with a standard deviation of 30 days.

Answer:

The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if it is negative then it is below the mean. It is given by:

$z=\frac{x-\mu}{\sigma}\\ \\where\ \mu=mean,\sigma=standard\ deviation, x=raw\ score$

Given that:

$\mu=100\ days,\sigma=30\ days\\\\For\ x=90\\\\z=\frac{90-100}{30} =-0.33\\\\For\ x=150\\\\z=\frac{150-100}{30} =1.67$

Therefore, from the normal distribution table, P(90 < x < 150) = P(-0.33 < z < 1.67) = P(z < 1.67) - P(z < -0.33) = 0.9525 - 0.3707 = 0.5818

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3 years ago

Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function be written using

kozerog [31]

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Given

9x + 3y = 12

We require to rearrange expressing y in terms of x

Subtract 9x from both sides

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4

Expressed in functional notation by replacing y by f(x), that is

f(x) = - 3x + 4

8 0

3 years ago