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Anit [1.1K]
3 years ago
6

A rental car company charges drivers a flat fee to rent a car plus $.25 for each mile they drive if a driver paid $100 and drive

s 160 miles which equation can he use to find his total cost y in terms of the number of miles driven x
Mathematics
1 answer:
Yakvenalex [24]3 years ago
5 0
160(.25) + 100 = y

y= 140
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Please help solve for x..
aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

x^{100}-4^x \cdot x^{98}-x^2+4^x=0

Factor out -1:

\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0

Divide both sides by -1:

\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0

Rearrange the terms:

\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0

\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:

\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0

Factor the first two terms and the last two terms separately:

\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0

Factor out the common term (x^{98}-1) :

\implies (4^x-x^2)(x^{98}-1)=0

<u>Zero Product Property</u>:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}

Therefore, the solutions to the given equation are: x = 1 or x = -1

Learn more here:

brainly.com/question/27751281

brainly.com/question/21186424

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Could you please give an explanation step by step on how to get your answer
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Jeff is 6 years older than Sam. In four years he will be twice as old as Sam was 5 years ago. Find both their ages now... can u
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