Natalie tried to evaluate the expression \left( 4^{-3} \cdot 2^{-3} \right)^{0}(4 −3
⋅2
−3
)
0
left parenthesis, 4, start superscript, minus, 3, end superscript, dot, 2, start superscript, minus, 3, end superscript, right parenthesis, start superscript, 0, end superscript.
\begin{aligned} &\phantom{=}\left( 4^{-3} \cdot 2^{-3} \right)^{0} &=\left( 8^{-3}\right)^{0} &\text{Step } 1 &= 8^{0} &\text{Step } 2 &=0&\text{Step } 3 \end{aligned}
​

=(4
−3
⋅2
−3
)
0

=(8
−3
)
0

=8
0

=0
​

Step 1
Step 2
Step 3
​

Did Natalie make a mistake? If so, in which step?

no oblique asymptote

step-by-step explanation:

to find the oblique asymptote of f(x)

here numerator has degree 1 and denomintor degree 2

degree of numerator < degree of denominator

hence there is no oblique asymptote

when the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly,   giving us a horizontal asymptote of the x-axis. or we can write

f(x) = a polynomial of x + a proper fraction.

in this case only we have oblique asymptotes but not when numerator has less degree.

statement #3: proof- ang is congruent to ang ecd : angles are congruent.  

step-by-step explanation:

1: the missing angles in statement #3  

a.) acb  

reason- the reason why the answer is acb is because angle ecd and angle acb are both the same size *that's what the word congruent means this is really simple.  

2: the missing word in reason #3  

c.) vertical  

reason- the reason why the answer is vertical is because the angles in that diagram on figure 2 is slanted, which is vertical, and the e and a both lay on vertical lines. along with the other's, but e and a are the 2 main points you want to focus on. and c is kind of like your starting point, because c is for both angles, not just one.  

i hope that was and understanding.