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sergij07 [2.7K]
4 years ago
9

Use the definition of the logarithmic function to find x. log4 0.25=x x=?

Mathematics
1 answer:
GREYUIT [131]4 years ago
5 0
The answer is -1.

log_4(0.25)  =log_4( \frac{1}{4})= log_4(4^{-1} ) \\  \\ 
log(x^{a} ) = a*log(x) \\  \\ 
log_4(4^{-1} )= -1 *log_4(4) \\  \\ 
log_y(x) =  \frac{log(x)}{log(y)}  \\  \\ 
-1 *log_4(4) = -1* \frac{log(4)}{log(4)} = -1
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The midpoints of a regular hexagon are connected to form a smaller hexagon. The small hexagon has perimeter 2sqrt3. What is the
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Answer:

4

Step-by-step explanation:

x - length of side of larger hexagon

y - length of side of smaller hexagon

We know that,

x/y = \sqrt{3} /2

y = 2x/\sqrt{3}

Hence,

perimeter of             = (2/\sqrt{3}) * perimeter of smaller hexagon

larger hexagon

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4 years ago
Which graph represents the function h(x)=x+0.5
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Answer:

The correct graph of h(x) will be number 3 (c).

Step-by-step explanation:

We have the function h(x) = |x| + 0.5

On putting x=0, in the function h(x), we get,  

h(0) = |0| + 0.5

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h(0)=0.5

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3 years ago
Find an for the arithmetic series with s16 = -288 And a1 =-21
Maru [420]
If d is the common difference between terms in the sequence \{a_n\}, then

a_1=-21
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a_3=a_2+d=-21+2d
...
a_n=a_{n-1}+d=\cdots=-21+(n-1)d

You're told that S_{16}=-288 (the sum of the first 16 terms in the sequence, presumably). Well, we know that

S_{16}=\displaystyle\sum_{n=1}^{16}a_n=\sum_{n=1}^{16}(-21+(n-1)d)
S_{16}=\displaystyle(-21-d)\sum_{n=1}^{16}1+d\sum_{n=1}^{16}n

Recall that

\displaystyle\sum_{n=1}^kn=\frac{k(k+1)}2

so that we have

-288=16(-21-d)+\dfrac{16(16+1)}2d\implies d=\dfrac25

So we get

\begin{cases}a_1=-21\\\\a_n=-21+\dfrac25(n-1)\end{cases}
8 0
3 years ago
Complete the synthetic division problem below.
miskamm [114]

Step-by-step explanation:

c

6 0
3 years ago
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If a pack of ramen noodles cost $3.48 what is the unit rate (in cents)?
tresset_1 [31]

Answer:

348 cents per pack

Step-by-step explanation:

$3.48         348 cents

----------- or ----------------- = 348 cents per pack

1 pack          1 pack

3 0
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