One way to solve this is to use Pythagorean theorem: the square of one leg of triangle plus square of other leg of the triangle equals c the hypotenuse (longest side of triangle). You might see this as the formula a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.
In this case, the legs are 3√2 and the hypotenuse is h.
Using the formula:
(3√2)² + (3√2)² = h²
18 + 18 = h²
h = 6
The other way to do this is with trigonometric angles.
Remember cosine is adjacent over hypotenuse.
cos(45°) = (3√2) / h
h = (3√2) / cos(45°)
h = 6
200-3w = 300-5w
Where w is the number of weeks
Rearrange and reduce:
-3w + 5w = 300-200
2 w = 100
w = 100/2 = 50 weeks
Answer:

Step-by-step explanation:
First, you have to substitute both functions into the equation to get:

Then, you distribute the negative sign in front of g(x) to get:

And finally, you add/subtract the x's that have the same power to get:

Answer:
y+1 = -1(x+10)
Step-by-step explanation:
The point slope equation of a line is
y-y1 = m(x-x1) where m is the slope and (x1, y1) is a point on the line
y - -1 = -1 (x --10)
y+1 = -1(x+10)
First of all, we need all logarithms to have the same base. So, we use the formula

To change the second term as follows:

Finally, using the property

we have

So, the equation becomes

We can now use the formula

to write the equation as

Now consider both sides as exponents of 2:

This equation has no "nice" solution, so I guess the problem is as simplifies as it can be