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AURORKA [14]
3 years ago
5

Please solve i got 3 but i’m not sure

Mathematics
1 answer:
GuDViN [60]3 years ago
7 0
Short answer x = 11/3
Step One

Change 64 to a power of 4
\text{64  = 4}^{4}

Step Two
Include 2x - 4 as part of your power. So far you are only working on the right side of the problem.

(x^{4*(2x - 4)}

Step Three
The bases are the same so you can equate the powers.
2x + 6   = 4(2x - 4) 

Step Four
Remove the brackets on the right.
2x + 6 = 8x - 16 

Step five
Collect like terms.     Begin by adding 14 to both sides.
2x + 6 + 16 = 8x       Subtract 2x from both sides.
22 = 8x - 2x
22 = 6x                     Divide by 6
22/6 = x
x = 3.666333 or 3 2/3 or 11/3

Check
Left hand side
4^(2*11/3 + 6) 
4^(22/3 + 6)
4^(22/3 + 18/3)
4^(40/3) 

Right Side
64^(2*11/3 - 4)
64^(22/3 - 4)
64^(22/3 - 12/3)
64^(10/3)    There is something we can do without figuring out what this is.
64 = 4^4
4^(4*10/3)
4^(40/3) which is the same as the left side

Answer x = 11/3 <<<<<
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what is te discontinuity of the function f(x) = the quantity of x squared plus 6x plus 8 all over x plus 4?
seropon [69]

Answer:

A hole at x=-4.

Step-by-step explanation:

This is a fraction so we have to worry about division by zero.

The only time we will be dividing by 0 is when x+4 is 0.

Solving the equation

x+4=0 for x:

Subtract 4 on both sides:

x=-4

So there is either a vertical asymptote or a hole at x=-4.

These are the kinds of discontinuities we can have for a rational function.

If there is a hole at x=-4, then x=-4 will make the top zero and can be cancelled out after simplification.

If is is a vertical asymptote, x=-4 will make the top NOT zero.

Let's see what -4 for x in x^2+6x+8 gives us:

(-4)^2+6(-4)+8

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Top and bottom are 0 when x=-4.

Let's see what happens after simplication.

We are going to factor a^2+bx+c if factorable by finding two numbers that multiply to be c and add up to be b.

So what 2 numbers together multiply to be 8 and add up to be 6.

I hoped you said 4 and 2 because (4)(2)=8 where 4+2=6.

\frac{x^2+6x+8}{x+4}=\frac{(x+4)(x+2)}{x+4}=x+2

We we able to cancel out that factor that was giving us x=-4 is a zero.  

Therefore there is a hole at x=-4.

7 0
3 years ago
F(x) = 4x − 12 <br><br> f−1(x) =___? x +____?
natali 33 [55]

Answer:

f^{-1}(x)=\frac{1}{4}x+3

Step-by-step explanation:

We have been given the function f(x)=4x-12

Below are steps for finding the inverse of the function.

Step 1:

Replace f(x) with y

y=4x-12

Step 2:

Interchange x and y

x=4y-12

Step 3:

Solve for y

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Step 4:

Replace y with f^{-1}(x)

f^{-1}(x)=\frac{1}{4}x+3

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Answer:

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Step-by-step explanation:

So x=0, so plug in 0 for x. 5(0) + 6 - (0)^2 = 6

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