Answer:
Step-by-step explanation:
What is a complementary angle?
Answer:
First, two lines are perpendicular if one has slope m, and the other has slope -1/m (Not 1m as Alan says)
That is the first error of Alan.
Now, there is another error.
If m = 0, then -1/m tends to minus infinity (in this case we would have a vertical line).
But we can not really divide by zero, so we should state that:
m can not be zero, if a line is horizontal, the perpendicular line must be vertical.
Short Answer x = - 6
Remark
You gave the second best answer.
The trick here is not to divide both sides by 2. Solve the problem this way.
log_5(x + 1)^2 = 2 Take the antilog of both sides
(x + 1)^2 = 5^2 Expand the equation
x^2 + 2x + 1 = 25 Subtract 25 from both sides.
x^2 + 2x - 24 = 0 Factor
(x + 6)(x - 4) = 0 Find the zeros.
x + 6 = 0
x = - 6 <<<<<<<< Answer. This is the extraneous root.
The reason this is an extraneous root is that x<=0 do not have a logarithem
x - 4 = 0
x = 4 This is a legitimate result to the original equation.
Answer:
The initial height of the balloon is 2 feet.
Step-by-step explanation:
The height of the balloon in feet after t seconds is given by the following equation:

What is the initial height of the balloon?
This is h when t = 0, that is, h(0). So

The initial height of the balloon is 2 feet.
The first thing we must do for this case is to find the equation of the line.

We have then:

We choose an ordered pair:

Substituting values:
From here we conclude:
Intersection with y:
We evaluate x = 0 in the function:
Slope of the line:
Point (-2, -5):
We evaluate the value of x = -2 and the value of y = -5

The equation is satisfied.
Point (8, 0):
It is part of the table, therefore belongs to the line.
Answer:
The slope is 1/2
The y-intercept is -4.
The points (-2, -5) and (8, 0) are also on the line.