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2 years ago

The value of the expression 16-^3/4 is___ 8 1/8 -6 6 1/40 1/64

Mathematics

1 answer:

lorasvet [3.4K]2 years ago

5 0

Answer:

$\frac{1}{8}$

Step-by-step explanation:

Using the rules of exponents

• $a^{-m}$ ⇔ $\frac{1}{a^{m} }$

• $a^{\frac{m}{n} }$ ⇔ $\sqrt[n]{a^{m} }$

Hence

$16^{-\frac{3}{4} }$ = $\frac{1}{16^{\frac{3}{4} } }$

= $\frac{1}{\sqrt[4]{16^{3} } }$ = $\frac{1}{2^{3} }$ = $\frac{1}{8}$

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2 years ago

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2 years ago

1. Let f(x) = x + 3 and g(x) = 3x + 5. Find f(g(4)) - g(f(4)) 2. Let f(x) = 5x^2 - 5. What is f(f(x))? 3. Let f(g(x)) = 3x + 3 a

ludmilkaskok [199]

Answer:

1. f(g(4)) - g(f(4)) = -6

2. f(f(x)) = 125x^4 - 250x^2 + 120

3. a + b = 0

4. g(4) = -9

Step-by-step explanation:

First we need to find f(4) and g(4):

f(4) = 4 + 3 = 7

g(4) = 3*4 + 5 = 17

Then, we find g(f(4)) = g(7):

g(7) = 3*7 + 5 = 26

And we find f(g(4)) = f(17):

f(17) = 17 + 3 = 20

so f(g(4)) - g(f(4)) = 20 - 26 = -6

To find f(f(x)), we use the value of f(x) for every x in f(x):

f(f(x)) = 5*(f(x))^2 - 5 = 5*(5x^2 - 5)^2 - 5 = 5*(25x^4 - 50x^2 + 25) - 5

f(f(x)) = 125x^4 - 250x^2 + 120

To find f(g(x)), we use the value of g(x) for every x in f(x):

f(g(x)) = g(x) + 6 = ax + b + 6 = 3x + 3

ax + (b+6) = 3x + 3 -> a = 3 and b = -3

a + b = 3 - 3 = 0

If we assume g(x) = ax + b, we have:

g(f(x)) = a*(2x - 3) + b = 2ax - 3a + b = 5 - 4x

2a = -4 -> a = -2

-3a + b = 5

6 + b = 5 -> b = -1

g(x) = -2x - 1

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2 years ago

Find the midpoint of segment LK with endpoints L(-2, 4) and K(5,3).

fenix001 [56]

Answer: (1.5, 3.5)

Explanation:
Find the slope by using the coordinates for points L and K.

3 - 4 = -1
5 - (-2) = 7
Slope = -1/7

Then you plot your points on the graph.
But you want to half your slope to find the midpoint. So your slope would now be -0.5/3.5.

And when you follow that slope, you will plot down the coordinate (1.5, 3.5), which is the midpoint.

Hope this helped! :3
(Also don’t mind the 19 at the top left)

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2 years ago