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3 years ago

Is this right? isn't the Directly proportional equation this. x=(1/k)y

1 answer:

7 0

It's y=kx. But 'k' is any constant. So my 'k' can easily be 1/(your k). The key is that when 'x' or 'y' increases by some factor, the other one also increases, by some constant multiple of the same factor. If so, then they're proportional.

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Simplify the following expression as much as you can use exponential properties. (6^-2)(3^-3)(3*6)^4

gtnhenbr [62]

Answer:

Simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

Step-by-step explanation:

We need to simplify the expression $(6^{-2})(3^{-3})(3*6)^4$

Solving:

$(6^{-2})(3^{-3})(3*6)^4$

Applying exponent rule: $a^{-m}=\frac{1}{a^m}$

$=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\$

Factors of $18=2\times 3\times 3=2\times3^2$

Factors of $6=2\times 3$

Replacing terms with factors

$=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\$

Using exponent rule: $(a^m)^n=a^{m\times n}$

$=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}$

Using exponent rule: $a^m.a^n=a^{m+n}$

$=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}$

Now using exponent rule: $\frac{a^m}{a^n}=a^{m-n}$

$=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108$

So, simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

7 0

3 years ago

Select all expressions that are equivalent to 64. 2 to the sixth power 2 to the eighth power 4 to the third power 8 squared 16 t

andreyandreev [35.5K]

Answer:

2 to the sixth, 4 to the third, 8 squared

Step-by-step explanation: 2*2*2*2*2*2=64 because you would have 2, 4,8,16,32,64

4*4*4=64 because you would have 4,16,64

8*8=64

3 0

2 years ago

Find each of the numbers below.

iren [92.7K]

Answer:

opposite of -7 is 7 the oppositeof 3 is -3 oppositeof -4 is 4

8 0

3 years ago

Which value is a solution of the equation 85= 120-w?

Ronch [10]

$85=120-w\\85-120=120-w-120\\-35=-w\\\frac{-35}{-1}=\frac{-w}{-1}\\35=w$

w = 35

8 0

3 years ago

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Kim and Jay leave at the same time to travel 25 miles to the beach.Kim drives 9 miles in 12 minutes.Jay drives 10 miles in 15 mi

kow [346]

Jay will arrive before kim

4 0

3 years ago

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