What is the following number rounded to the nearest hundred of 327,659

Explain how to solve 5^(x − 2) = 8 using the change of base formula log base b of y equals log y over log b.

Ray Of Light [21]

Answer:

x = 3.3

Step-by-step explanation:

A equation is given to us and we need to solve out for x. The given equation is ,

Take log on both sides with base as " 10" . We have ,

Simplify using the property of log , , we have ,

Simplify ,

Again simplify using the property of log ,

We know that log 5 = 0.69 and log 2 = 0.301 , on substituting this , we have ,

Simplify the RHS ,

Add 2 both sides ,

Hence the Value of x is 3.30 .

3 0

2 years ago

What value of b will cause the system to have an infinite number of solutions?

irga5000 [103]

b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

<u>Solution: </u>

Need to calculate value of b so that given system of equations have an infinite number of solutions

$\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}$

Let us bring the equations in same form for sake of simplicity in comparison

$\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}$

Now we have two equations

$\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}$

Let us first see what is requirement for system of equations have an infinite number of solutions

If $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ are two equation

$\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ then the given system of equation has no infinitely many solutions.

In our case,

$\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}$

As for infinitely many solutions $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}$

Hence b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

8 0

3 years ago

Can somebody plz help answer this word problem using equations thx :3 (only if u done this before) lol :)

ycow [4]

Answer:

one num = 6

another = 24

Step-by-step explanation:

One number = x

Another = 4x

Difference = 18

4x - x = 18

3x = 18 ; x = 18/3 = 6

8 0

3 years ago

The value of x is 1. Find the value of each expression and type

krek1111 [17]

Answer:

can I get a hiaaa

How was the government able to make children go to residential school?

6 0

3 years ago

Find the domain of the function. <br><br> y = <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%2B%201" id="TexFormula1" title

Step2247 [10]

Answer:

[0, infinity)

Step-by-step explanation:

A square root can only use positive numbers, otherwise it becomes imaginary. A function needs to be real to output real values. Therefore, the domain is everything from 0 onwards.

5 0

3 years ago