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Gala2k [10]
2 years ago
14

1/16^3x=64^2(x+8) Solve for x.

Mathematics
1 answer:
SSSSS [86.1K]2 years ago
3 0

Answer:

x = -4

Step-by-step explanation:

16 = 4*4 = 4²

64 = 4 * 4* 4 = 4³

(\dfrac{1}{16})^{3x}=64^{2*(x+8)}\\\\\\(16^{-1})^{3x}=64^{2x + 16}\\\\\\16^{-3x}=64^{2x +16}\\\\(4^{2})^{-3x}=(4^{3})^{2x+16}\\\\4^{-6x}=4^{6x +48}

As bases are same, compare exponents

6x + 48 = -6x  

Subtract 48 from both sides

6x = -6x - 48

Add '6x' to both sides

6x + 6x = -48

12x = -48

Divide both sides by 12

x = -48/12

x = -4

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Over [174]
The way we would answer the question would be to express it as

100-9(n-1) with n being the nth term of the pattern.

Why is this? We know we subtract 9 each time and START from 100.
Remember though that 100 is the first term in the sequence. So, we would have (n-1)*9 to subtract 0 from our 1st term and 9 from our second term.

Also, we have 9*(n-1) because we are just subtracting multiples of 9. It is always going to subtract by 9.


If you needed the answer here it is...

The answer to the problem would be 
100-9(13-1)
= 100-9(12)
= 100-108
= -8

5 0
4 years ago
DISTRIBUTIVE PROPERTY
11Alexandr11 [23.1K]

Answer:

1. C. 4x + 40

2. a. - 2a + 10

3. d. 13x - 45

4. 2c-7d

5. b. -2z - 12

Step-by-step explanation:

1.  4(x+10)  = 4x+4*10 = 4x+40

C


2.  -2(a - 5) = -2*a -2*-5 = -2a+10

A


3.  10x + 3 (x-15)

10x + 3x -3*15

10x+3x-45

13x-45

D


4. -5(c+d) + 7c - 2d

-5c-5d + 7c-2d

-5c+7c -5d -2d

2c-7d


5.  2(2z + 4) - 2 (3z + 10)

2*2z +2*4 -2 *3z -2*10

4z+8 -6z-20

4z-6z+8-20

-2z-12

B

8 0
4 years ago
There are 20 children in the cast of a class play, and 8 of the children are boys. of the boys, 4 have a speaking part in the pl
likoan [24]
The probability that a child with a speaking part is chosen randomly would be 2:5.
6 0
3 years ago
5 gallons of diesel weighs 37 pounds. How much does 3 gallons of diesel weigh? Do these quantities (volume and weight) vary dire
True [87]

Answer:

22.2 pounds and 1g = 7.4p

Step-by-step explanation:

Lets go in an inverse sense, finding firstly the constant variation and then the weight of 3 gallons.

The constant variation is the relation between gallons of diesel volume and pounds of diesel weight. For thise we would like to find how many pounds of diesel weights 1 gallon. We have the following equality:

5 gallons = 37 pounds

Now, lets divide both sided by 5, as we know the equality will still:

5/5 gallon = 37/ 5 pounds

1 gallon = 7.4 pounds

So, this is the constant variations: every extra gallons weights 7.4 pounds. We could also do this in terms of pounds, which means, parting from:

5 gallons = 37 pounds

Divide both sides by 37:

5/37 gallons = 1 pound

0.081 gallons = 1 pound

Every extra pound means 0.081 more gallons.

Now, as we want the weight of 3 gallons we can use our first relation and multiplying by 3:

1 gallon = 7.4 pounds

3 gallons = 22.2 pounds

5 0
4 years ago
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HACTEHA [7]

Answer:644.355

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Step-by-step explanation:

4 0
3 years ago
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