Answer:
You can use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if you know the length of the triangle's other two sides, called the legs. You can use the Pythagorean Theorem to find a value for the length of c, the hypotenuse.
For this case we must find an expression equivalent to:

So:
We expanded
by moving 2 out of the logarithm:

By definition of logarithm properties we have to:
The logarithm of a product is equal to the sum of the logarithms of each factor:

The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.

Then, rewriting the expression:

We apply distributive property:

Answer:
An equivalent expression is:

Alex bought all the string needed for $125.
It costs $18 for the remaining materials to make each puppet.
So if we closely observe then we see that here $125 is the fixed cost because its not going to change with number of puppets.
And the variable cost is $18.
In this case we can model a Total cost function C(x) for for x number of puppets as below

The total cost to make 50 puppets=$1025
1 Cancel <span>33</span>
<span>x+\frac{6}{x}+4+x-1<span>x+<span><span>x</span><span>6</span><span></span></span>+4+x−1</span></span>
2 Collect like terms
<span>(x+x)+\frac{6}{x}+(4-1)<span>(x+x)+<span><span>x</span><span>6</span><span></span></span>+(4−1)</span></span>
3 Simplify
<span><span>2x+\frac{6}{x}+3<span>2x+<span><span>x</span><span>6</span><span></span></span>+3</span></span><span>
</span></span>
Answer:
Jim reached a greater depth by one foot, as he started 12 feet below the surface.
Step-by-step explanation:
Jim
12 feet+17 feet = 29
29-3 feet (rose 3 feet) = 26
26+8= 34 feet
Carla
0 feet (surface)+ 19 feet= 19
19-3 feet= 16
16+17= 33 feet