4x =64 find x in exponential equations

Write the following decimal number in its equivalent fraction form. Show all work for full credit.

Zigmanuir [339]

Let x=0.8888...

x=0.8888 Start with the given equation

10x=8.8888 Multiply both sides by 10. The goal is to move the decimal point to the next repeating portion (which is just one spot to the right)

Now subtract the equation x=0.8888 from 10x=8.8888 to get
10x-x=8.8888-0.8888

9x=8 Combine like terms. Notice how the decimal portions cancel out.

x=8/9 Divide both sides by 9 to isolate x

So the answer is x=8/9 which means that 8/9=0.8888 (where the 8's repeat)

8 0

3 years ago

Josie has $47 left on her checking account. If she writes a check for $55, what ill josie's balance be?

Sidana [21]

Well technically the check will not go through because she does not have a balance greater than or equal to $55, but if you need an answer it would be $47-$55= $-8.

8 0

3 years ago

Read 2 more answers

Use the principle of inclusion and exclusion to find the number of positive integers less than 1,000,000 that are not divisable

wel

This is a simple problem based on combinatorics which can be easily tackled by using inclusion-exclusion principle.
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
let n be the number of positive integers.
∴ 1≤n≤999,999
Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.

∴N(c₁) = $\frac{999,999}{6} = 166666$
N(c₂) = $\frac{999,999}{4} = 250000$
∴N(c₁c₂) = $\frac{999,999}{24} = 41667$
∴ Number of positive integers that are not divisible by 4 or 6,

N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4

8 0

3 years ago

Whats the value of 8:3 ?

umka2103 [35]

Answer:

As a mixed number, 8/3 is equal to 2-2/3.

Step-by-step explanation:

6 0

2 years ago

Please help me with precalculus?? linear and angular speed

Anit [1.1K]

13)

there are 2π radians in 1 revolution, and there are 60 seconds in 1 minute, so keeping that in mind, then,

$\bf \cfrac{4\underline{\pi} }{5~\underline{s}}\cdot \cfrac{rev}{2\underline{\pi} }\cdot \cfrac{60~\underline{s}}{min}\implies \cfrac{4\cdot 60~rev}{5\cdot 2~min}\implies \cfrac{240~rev}{10~min}\implies 24\frac{rev}{min}$

14)

$\bf \textit{linear velocity}\\\\
v=rw\quad 
\begin{cases}
r=radius\\
w=angular~speed\\
----------\\
v=32\frac{m}{sec}\\
w=100\frac{rev}{min}
\end{cases}\\\\
-------------------------------\\\\
\textit{let's convert \underline{w} to }\frac{radians}{sec}$

$\bf \cfrac{100~\underline{rev}}{\underline{min}}\cdot \cfrac{2\pi }{\underline{rev}}\cdot \cfrac{\underline{min}}{60~sec}\implies \cfrac{100\cdot 2\pi }{60~sec}\implies \cfrac{10\pi }{3~sec}\implies \cfrac{10\pi }{3}\frac{radians}{sec}\\\\
-------------------------------\\\\
v=rw\implies \cfrac{v}{w}=r\implies \cfrac{\frac{30~m}{sec}}{\frac{10\pi }{3~sec}}\implies r=\cfrac{30~m}{\underline{sec}}\cdot \cfrac{3~\underline{sec}}{10\pi }
\\\\\\
r=\cfrac{90}{10\pi }m$

15)

what is the radians per seconds "w" in revolutions per minute? just another conversion like in 13)

$\bf \cfrac{\underline{\pi} }{3~\underline{sec}}\cdot \cfrac{rev}{2\underline{\pi }}\cdot \cfrac{60~\underline{sec}}{min}\implies \cfrac{60 ~rev}{3\cdot 2 ~min}\implies \cfrac{60 ~rev}{6 ~min}\implies 10\frac{rev}{min}$

4 0

3 years ago

4x =64 find x in exponential equations ​

4x =64 find x in exponential equations