Hey there!
<u>Solve </u><u>for </u><u>x </u><u>:</u>
x = 6 ✅
3x - 2 = 16
<em>></em><em>></em><em> </em><em>Add </em><em>2</em><em> </em><em>to </em><em>both </em><em>sides </em><em>:</em>
3x - 2 + 2 = 16 + 2
3x = 18
<em>></em><em>></em><em> </em><em>Divide </em><em>e</em><em>ach </em><em>side </em><em>by </em><em>3</em><em> </em><em>:</em>
3x / 3 = 18 / 3
x = 6
▪️Let's verify :
3(6) - 2 ⇔18 - 2 ⇔ 16
Therefore, your answer is x = 6
Learn more about first-degree equations :
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Find 1/9 :
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Find 9/9 :
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Answer: The total amount is $324.-----------------------------------------------
Let's try plugging in some negative numbers. Let's do x=-1. 5+-1=4. So we know that if we put in a negative number for x, then n will be positive. But what if we do a number greater than -5, because 5+-5=0. So let's try x=-6. So 5+(-6)=-1. Hmm. So here it is. We know that any number under -5 will be positive and any number above -5 will be negative.
Answer:
F(x) and g(x) are not inverse functions.
Step-by-step explanation:
In order to calculate the inverse function of a function, we have to isolate X and after that, we change the variables.
As our function f(x) is a exponentian function, we can apply logarithm with base 10 (log) in both sides in order to isolate X. Remember that log10=1.
![[tex]y=10^{(x+\frac{2}{3}) }\\\\log y=log 10^{(x+\frac{2}{3}) }\\log y = (x+\frac{2}{3}) . log10\\\frac{log Y}{log10} = (x+\frac{2}{3})\\\frac{log Y}{1} = (x+\frac{2}{3})\\log Y-\frac{2}{3}=x](https://tex.z-dn.net/?f=%5Btex%5Dy%3D10%5E%7B%28x%2B%5Cfrac%7B2%7D%7B3%7D%29%20%7D%5C%5C%5C%5Clog%20y%3Dlog%2010%5E%7B%28x%2B%5Cfrac%7B2%7D%7B3%7D%29%20%7D%5C%5Clog%20y%20%3D%20%28x%2B%5Cfrac%7B2%7D%7B3%7D%29%20.%20log10%5C%5C%5Cfrac%7Blog%20Y%7D%7Blog10%7D%20%3D%20%28x%2B%5Cfrac%7B2%7D%7B3%7D%29%5C%5C%5Cfrac%7Blog%20Y%7D%7B1%7D%20%3D%20%28x%2B%5Cfrac%7B2%7D%7B3%7D%29%5C%5Clog%20Y-%5Cfrac%7B2%7D%7B3%7D%3Dx)
[/tex]
Now we change the variables.
F(x) and g(x) are not inverse functions.
The following formula is applicable;
A=P(1+r)^n
Where,
A = Total amount accrued after 10 years (this is the amount from which the yearly withdrawals will be made from for the 30 years after retirement)
P=Amount invested today
r= Annual compound interest for the 10 years before retirement
n= Number of years the investments will be made.
Therefore,
A= Yearly withdrawals*30 years = $25,000*30 = $750,000
r= 9% = 0.09
n= 10 years
P= A/{(1+r)^n} = 750,000/{(1+0.09)^10} = $316,808.11
Therefore, he should invest $316,808.11 today.
