Answer:
The new price of the couch is $960
Step-by-step explanation:
The number -3 written as a logarithm with a base of 2 is log₂(0.125) or log₂(1/8)
<h3>What are logarithms?</h3>
As a general rule, logarithms are mathematical expressions that are written in the form log(x) or ln(x), for natural logarithms
<h3>How to rewrite the number as a logarithm?</h3>
The number is given as:
x = -3
The base of the logarithm is given as:
Base = 2
To rewrite the given number as a base of 2, we take the exponent of the number where the base is 2
This is represented as:
Number =2^-3
Apply the power rule of indices
Number =1/2^3
Evaluate the exponent
Number = 1/8
Evaluate the quotient
Number = 0.125
Hence, when the number -3 is rewritten as a logarithm with base 2, the equivalent logarithm expression is log₂(0.125) or log₂(1/8)
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Answer:
We have the equation,
i.e.
i.e.
It is required to find a system of equations having infinite solutions.
We know that,
'When the equations are dependent or their graphs are same, the system of equations has infinite number of solutions'.
So, we can take any equation having same graph as that of .
Let, us take
So, from the graph of these equations below, we get the system of equations having infinite solutions as,
and .
We have the equation for company 1: y = 3x + 5. That means it costs $3 to rent a movie with a $5 fee no matter how many movies you rent. It would benefit us to have the equation for company 2, so we need to find it using 2 points on the line. I picked the points (2,14) and (0,12). Find the slope of this by using the slope formula:
which gives us a slope of 1. Now we can use that slope and the slope-intercept form of a line to find the y-intercept, which serves as the fee for renting from company 2. 14=1(2)+b and 14 = 2 + b and b = 12. The equation then for company 2 is y=1x+12. This means it costs $1 to rent movies, but your fee to rent, no matter how many movies you pick, is $12. The "rate of change" in the choices refers to the slope. The slope in company 1's equation is 3 and the slope in company 2's equation is 1. The best description is the first choice that says "There is a higher rate of change at Company 1".