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3 years ago

5 to the power of 5 divided by 5 to the power of 3

Mathematics

1 answer:

Lemur [1.5K]3 years ago

6 0

Answer:

Step-by-step explanation:

5 to the power of 5 is 3125.

because you do 5x5x5x5

then you do 5x5x5 which is 125

3125/125 = 25

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Which graph represents the following piecewise defined function?

kenny6666 [7]

The correct answer is shown in attached figure
To find the correct graph, we should study the continuity of the function

Check the continuity at x = -2
from the left ⇒⇒ f(-2) = 1/2 * -2 + 3 = 2
from the right ⇒⇒ f(-2) = 2
∴ The function is continuous at x = -2

Check the continuity at x = 3
from the left ⇒⇒ f(3) = 2
from the right ⇒⇒ f(3) = 2*3 - 3 = 3
∴ The function is jump discontinuous at x = 3

From the previous results the correct graph is the last as shown in attached graph.

5 0

3 years ago

Read 2 more answers

At an interest rate of 8% compounded annually, how long will it take to double the following investments?

Paladinen [302]

Let's see, if the first one has a Principal of $50, when it doubles the accumulated amount will then be $100,

recall your logarithm rules for an exponential,

$\bf \textit{Logarithm of exponentials}\\\\
log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\
-------------------------------\\\\
\qquad \textit{Compound Interest Earned Amount}
\\\\
$

$\bf A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$100\\
P=\textit{original amount deposited}\to &\$50\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annnually, thus once}
\end{array}\to &1\\
t=years
\end{cases}
\\\\\\
100=50\left(1+\frac{0.08}{1}\right)^{1\cdot t}\implies 100=50(1.08)^t
\\\\\\
\cfrac{100}{50}=1.08^t\implies 2=1.08^t\implies log(2)=log(1.08^t)
\\\\\\
$

$\bf log(2)=t\cdot log(1.08)\implies \cfrac{log(2)}{log(1.08)}=t\implies 9.0065\approx t\\\\
-------------------------------\\\\
$

now, for the second amount, if the Principal is 500, the accumulated amount is 1000 when doubled,

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$1000\\
P=\textit{original amount deposited}\to &\$500\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annnually, thus once}
\end{array}\to &1\\
t=years
\end{cases}
\\\\\\
1000=500\left(1+\frac{0.08}{1}\right)^{1\cdot t}\implies 1000=500(1.08)^t
\\\\\\
$

$\bf \cfrac{1000}{500}=1.08^t\implies 2=1.08^t\implies log(2)=log(1.08^t)
\\\\\\
log(2)=t\cdot log(1.08)\implies \cfrac{log(2)}{log(1.08)}=t\implies 9.0065\approx t\\\\
-------------------------------$

now, for the last, Principal is 1700, amount is then 3400,

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$3400\\
P=\textit{original amount deposited}\to &\$1700\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annnually, thus once}
\end{array}\to &1\\
t=years
\end{cases}$

$\bf 3400=1700\left(1+\frac{0.08}{1}\right)^{1\cdot t}\implies 3400=1700(1.08)^t
\\\\\\
\cfrac{3400}{1700}=1.08^t\implies 2=1.08^t\implies log(2)=log(1.08^t)
\\\\\\
log(2)=t\cdot log(1.08)\implies \cfrac{log(2)}{log(1.08)}=t\implies 9.0065\approx t$

8 0

4 years ago

What is the equation of the line that is perpendicular to y = one-fifth x + 4 and that passes through (5,–4)?

zysi [14]

Answer:

y= -5x + 21

Step-by-step explanation:

The equation of the line that passes through (5, -4) and is perpendicular to line y = 1/5x + 4 is y= -5x + 21

The slope that is perpendicular to the slope 1/5x is -5x.

To find a perpendicular slope, you take the negative reciprocal. (so you change the signs (1/5x is positive so now it would be negative) and -5/1 is basically -5)

However, y = -5x + 4 does NOT pass through (5, -4)

But we still have to write the equation in slope intercept form or the equation of the line

The formula for slope- intercept form is : y= mx + b

So we must plug in (m) which is our -5x and for y we look at the coordinates they gave us ----- (5, -4). -4 is our y. In the coordinates we also have x listed which is 5, so we all plug that in.

y = -5x + b (as you can see -5x is plugged in here)

-4 = -5x + b (as you can see -4 is plugged in here)

4 = -5(5) + b (as you can see 5 is plugged in here)

NOW WE MUST SOLVE!

<h3>Isolate B</h3>

-4 = -25 + b

Add 25 from both sides.

-4 = -25 + b

+25 25

----------------

21 = b

We can now plug this into our slope intercept formula---y= mx+ b---to find the equation of the line.

<h2>Therefore, y = -5 x +21</h2>

4 0

3 years ago

Just number 8! please answer asap. it’s due tmr!!

Furkat [3]

3 1/4 divided by 8 convert mixed number to an improper fraction

13/4 divided by 8

Dividing is a equivalent to multiplying with the reciprocal
13/4x1/8

Multiply the fractions

13/32

Answer

13/32

8 0

3 years ago

Please someone help me

jarptica [38.1K]

x is always +3 ahead (30-27=3)

and y is always trailing behind x by -3

8 0

3 years ago

Read 2 more answers