9514 1404 393
Answer:
E. The transformation of f obtained by adding 4 to the input of f
Step-by-step explanation:
The expected graph was ...
g(x) = f(x -4) . . . . . subtracting 4 from the input.
This transformation has the effect of shifting the graph 4 units to the <em>right</em>.
__
The student's graph is of f(x) shifted 4 units to the left, equivalent to a right shift of -4, hence a graph of ...
g(x) = f(x -(-4))
g(x) = f(x +4) . . . . . . adding 4 to the input (choice E)
![\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5Ctextit%7Blogarithm%20of%20factors%7D%20%5C%5C%5C%5C%20%5Clog_a%28xy%29%5Cimplies%20%5Clog_a%28x%29%2B%5Clog_a%28y%29%20%5Cend%7Barray%7D%20~%5Chspace%7B4em%7D%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5Ctextit%7BLogarithm%20of%20rationals%7D%20%5C%5C%5C%5C%20%5Clog_a%5Cleft%28%20%5Cfrac%7Bx%7D%7By%7D%5Cright%29%5Cimplies%20%5Clog_a%28x%29-%5Clog_a%28y%29%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5Ctextit%7BLogarithm%20of%20exponentials%7D%20%5C%5C%5C%5C%20%5Clog_a%5Cleft%28%20x%5Eb%20%5Cright%29%5Cimplies%20b%5Ccdot%20%5Clog_a%28x%29%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\bf \log(0.5)\implies \log\left( \cfrac{1}{2} \right)\implies \log(1)-\log(2)\implies 0-a\implies -a \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log(0.5)\implies \log\left( \cfrac{1}{2} \right)\implies \begin{array}{llll} \log(1)&-&\log(2)\\\\ \log\left( 3\cdot \frac{1}{3} \right)&-&a\\\\ \log(3)+\log\left( \frac{1}{3} \right)\\\\ b+\log(3^{-1})\\\\ b+[-1\log(3)]\\\\ b+(-1b)\\\\ b-b\\ 0&-&a \end{array}](https://tex.z-dn.net/?f=%5Cbf%20%5Clog%280.5%29%5Cimplies%20%5Clog%5Cleft%28%20%5Ccfrac%7B1%7D%7B2%7D%20%5Cright%29%5Cimplies%20%5Clog%281%29-%5Clog%282%29%5Cimplies%200-a%5Cimplies%20-a%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Clog%280.5%29%5Cimplies%20%5Clog%5Cleft%28%20%5Ccfrac%7B1%7D%7B2%7D%20%5Cright%29%5Cimplies%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5Clog%281%29%26-%26%5Clog%282%29%5C%5C%5C%5C%20%5Clog%5Cleft%28%203%5Ccdot%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%29%26-%26a%5C%5C%5C%5C%20%5Clog%283%29%2B%5Clog%5Cleft%28%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%29%5C%5C%5C%5C%20b%2B%5Clog%283%5E%7B-1%7D%29%5C%5C%5C%5C%20b%2B%5B-1%5Clog%283%29%5D%5C%5C%5C%5C%20b%2B%28-1b%29%5C%5C%5C%5C%20b-b%5C%5C%200%26-%26a%20%5Cend%7Barray%7D)
so, we can use those two methods, and we'd end up with -a anyway.
Answer:
18.8 feet
Step-by-step explanation:
\tan M = \frac{\text{opposite}}{\text{adjacent}}=\frac{x}{5.4}
tanM=
adjacent
opposite
=
5.4
x
\tan 74=\frac{x}{5.4}
tan74=
5.4
x
5.4\tan 74=x
5.4tan74=x
Cross multiply.
x=18.832\approx \mathbf{18.8}\text{ feet}
x=18.832≈18.8 feet
Type into calculator and roundto the nearest tenth of a foot.
M
N
O
5.4
18.8
(adjacent to ∠M)
(opp. of ∠M)
(hypotenuse)
74°
-9 I believe that's the answr
Answer: -16, 81, 19
Step-by-step explanation:
f(x)=-16x^2+81x+0
19 feet