Answer
The equation of line x = 2.
Step by step explanation
First we have to find the slope from the given two points.
(2, 1) and (2, -2)
Here x1 =2, y1 = 1, x2 =2 and y2 = -2
Slope formula =
= (-2 - 1) /(2 - 2)
= -3/0
Slope(m) = 0
Here the value of x coordinates are the same and slope = 0, therefore, it is vertical line.
Hence the equation x = 2.
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Answer:
The amount needed to pay off the loan after 4 years is $70,192
Step-by-step explanation:
When interest is compounded annually, total amount A after t years is given by:
where P is the initial amount (principal), r is the rate and t is time in years.
From the question:
P = $60,000
r = 4% = 0.04
t = 4
The amount needed to pay off the loan after 4 years is $70,192
If we divide the amount by four, we will get the amount that is paid yearly (70192/4 = 17548). $17,548 is paid yearly.
Answer:
Part 1) The domain of the quadratic function is the interval (-∞,∞)
Part 2) The range is the interval (-∞,1]
Step-by-step explanation:
we have
This is a quadratic equation (vertical parabola) open downward (the leading coefficient is negative)
step 1
Find the domain
The domain of a function is the set of all possible values of x
The domain of the quadratic function is the interval
(-∞,∞)
All real numbers
step 2
Find the range
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
we have a vertical parabola open downward
The vertex is a maximum
Let
(h,k) the vertex of the parabola
so
The range is the interval
(-∞,k]
Find the vertex
Factor -1 the leading coefficient
Complete the square
Rewrite as perfect squares
The vertex is the point (7,1)
therefore
The range is the interval
(-∞,1]