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4 years ago

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

1 answer:

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

Ahat [919]

Answer:

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

= $(2/\sqrt{3})*2\sqrt{3} \\= 4$

6 0

4 years ago

Which graph represents the function h(x)=x+0.5

Fynjy0 [20]

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

h(0)=0 + 0.5

h(0)=0.5

Thus, the point (0,0.5) lie on the graph of h(x).

3 0

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

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

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:

6 0

3 years ago

Read 2 more answers

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

4 years ago