If f(x) = 2x - 4 and g(x)= -5x + 6, then what is g(g(x))?

A line that passes through (-1, 6) and the origin

zmey [24]

Answer: The equation is y = -6*x

Step-by-step explanation:

I suppose that we want to find the equation for a line that passes through the point (-1, 6) and the origin (remember that the origin is the point (0,0))

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If this line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of the line is equal to:

a = (y₂ - y₁)/(x₂ - x₁)

Now we know that our line passes through the points (0, 0) and (-1, 6), then the slope is:

a = (6 - 0)/(-1 - 0) = 6/-1 = -6

Then our equation is something like:

y = -6*x + b

To find the value of b we can use the fact that this line passes through the point (0, 0).

This means that when x = 0, y is also equal to zero.

If we replace these values in the equation we get:

0 = -6*0 + b

0 = b

Then our equation is:

y = -6*x

7 0

2 years ago

An investment company pays 8% compounded semiannually. You want to have $12,000 in the future. (A) How much should you deposit

Leno4ka [110]

Before we start answering the question, let's define the compound interest formula:
$A = P(1+ \frac{r}{n}) ^{nt}$
Where:
'A' is the amount of money in dollars
'P' is the principal amount of money in dollars
'r' is the interest rate (decimal)
'n' is the number of times interest is compounded per year
't' is the time in years

(A) Find Principal Amount
Given:
A = 12,000
P = ?
r = 0.08
n = 2 (semiannually)
t = 5
Now we plug our values in and solve:
$12,000 = P(1+ \frac{0.08}{2}) ^{(2)(5)}$
$12,000 = P(1.04) ^{10}$
$P = 8106.77$
∴ You would have to deposit $8106.77 in order to have $12,000 in 5 years from now.

(B) Find Principal Amount
Same given values as above, with the exception of 't' which is now 10 instead of 5.
$12,000 = P(1+ \frac{0.08}{2}) ^{(2)(10)}$
$12,000 = P(1.04) ^{20}$
$P = 5476.64$
∴ You would have to deposit $5476.64 in order to have $12,000 in 10 years from now.

Hope this helps!

4 0

3 years ago

The change in altitude of a bird after 2 __ 1 2 seconds was –41 __ 1 4 feet. What was the average change in altitude of the bird

svlad2 [7]

Answer:

$Average\ Change = -1\frac{7}{10} ft/s$