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hichkok12 [17]
3 years ago
13

3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtrcted by 6

Mathematics
1 answer:
hichkok12 [17]3 years ago
5 0

Answer:

x = -0.5

Step-by-step explanation:

Here we have the sentence:

"3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtracted by 6"

The first part:

"3 to the power 2x+3 is subtracted by 9..."

This can be written as:

3^{2x + 3} - 9

"... is equal to 2 times 9 to the power x+1 and is subtracted by 6"

3^{2x + 3} - 9 = 2*9^{x + 1} - 6

Let's solve this for x.

First, we can add 9 in both sides:

3^{2x + 3}  = 2*9^{x + 1} - 6 + 9 =  2*9^{x + 1} + 3

We also know the relations:

a^n*a^b = a^{n + b}

and

(a^n)^m = a^{n*m}

We can write the left part as:

3^{2x + 3} = 3^{2x}*3^3 = (3^2)^x*3^3 = 9^x*27

And the right side as:

2*9^{x + 1} + 3 = 2*9^x*9 + 3 = 18*9^x + 3

Then the equation becomes:

27*9^x = 18*9^x + 3

Now let's move both terms with 9^x to the left side:

27*9^x - 18*9^x = 3\\

(27 - 18)*9^x = 3

9*9^x = 3

9^x = 3/9 = 1/3

Now remember that:

Ln(a^b) = b*Ln(a)

Then if we apply the Ln( ) function to both sides, we get:

Ln(9^x) = Ln(1/3)

x*Ln(9) = Ln(1/3)

x = \frac{Ln(1/3)}{Ln(9)} = -0.5

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Sam and Mary collect marbles. “If you give me 5 marbles I’ll have twice as many as you.” said Sam to Mary.
ivann1987 [24]

Answer:

54 marbles

Step-by-step explanation:

The question is a word problem leading to a simultaneous equation

Let 'x' represent the initial number of marbles with Sam, and let 'y' represent the initial number of marbles with Mary,

If Mary gives Sam 5 marbles, we have;

x + 5 = 2 × (y - 5)...(1)

If Sam gives Mary 4 marbles, we get;

x - 4 = y + 4...(2)

From equation (1), we get;

x + 5 = 2 × (y - 5) = 2·y - 10

x = 2·y - 10 - 5 = 2·y - 15

x = 2·y - 15...(3)

From equation (2), we have;

x - 4 = y + 4

∴ x = y + 4 + 4 = y + 8

x = y + 8...(4)

Equating the two values of 'x' in equation (3), and equation (4), we get;

2·y - 15 = y + 8

2·y - y = 8 + 15 = 23

∴ y = 23

From equation (4), we get;

x = y + 8 = 23 + 8 = 31

x = 31

The total number of marbles they have altogether = x + y

However, x + y = 23 + 31 = 54

Therefore;

The total number of marbles they have altogether = 54 marbles.

7 0
3 years ago
Albert bought some fish at a grocery store at $2 per pound for salmon and $4 per pound for catfish. He spent a total of $12 on s
Gemiola [76]

Albert bought 2 pounds of catfish and 2 pounds of salmon

Let c represent the amount of catfish in pounds and s represent the amount of salmon in pounds.

He spent a total of $12 on salmon and catfish and bought a total of 4 pounds.  Hence:

c + s = 4    (1)

4c + 2s = 12    (2)

Solving equations 1 and 2 simultaneously gives:

c = 2, s = 2

Albert bought 2 pounds of catfish and 2 pounds of salmon

Find out more on equation at: brainly.com/question/2972832

7 0
2 years ago
Please please please help me!! I'll give 5 stars and thanks!
ipn [44]
F(1) = -2

hope it helps

---------------------------------
4 0
3 years ago
Let f(x) = ............
34kurt

Answer:

So first lets find g(-1)

so we plug in the answers:

-2 * -1 ^2 -4

-2*1-4 = -2-4 =

-6

Now lets solve for f(-2)

-2^2-3

4-3=1

-6+1 = 5

3*5 = 15

Im getting answer of 15 but it shows -15 or something, so I dont know if I got it wrong or if its like a dash then the answer.

3 0
3 years ago
I need help with this!!!
7nadin3 [17]

Answer:

6

Step-by-step explanation:

cancel out 5 by multiplying its by 5, what you do to one side you do to the other.   so you also multiply 12 by 5. and you should get 60

3 0
3 years ago
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