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Over [174]
3 years ago
7

X

Mathematics
1 answer:
ziro4ka [17]3 years ago
7 0

Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!

tinyurl.com/wpazsebu

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I need help with #11
Troyanec [42]
\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
y=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
f(x)=&{{  A}}\sqrt{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}}(\mathbb{R})^{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}} sin\left({{ B }}x+{{  C}}  \right)+{{  D}}
\end{array}

\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\
\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\
\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\
\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\
\end{array}

\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{  D}}\\
\qquad if\ {{  D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{  D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{  B}}}
\end{array}

now, with that template in mind, let's take a peek at this function

\bf \begin{array}{lllcclll}
y=&2(&1x&-2)^2&-4\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}\\\\
-----------------------------\\\\
A\cdot B=2\impliedby \textit{shrunk by a factor of 2, of half-size}\\\\
\cfrac{C}{B}= \cfrac{-2}{1}\implies -2\impliedby \textit{horizontal right shift of 2 units}\\\\
D=-4\impliedby \textit{vertical down shift of 4 units}

so, the graph of y=2(x-2)²-4, is really the same graph of y=x², BUT, narrower, and moved about horizontally and vertically
8 0
3 years ago
Read 2 more answers
e is 150% more than d . what is the ratio d:e in its simplest form? what is the ratio e:d in the form 1::n​
Bad White [126]

Answer:

d:e is 2:3

Step-by-step explanation:

if 'e' is 150% more than 'd' we can say that 'e' is 1.5 and 'd' is 1

ratio of 1/1.5 or 1÷3/2 is 2/3

3 0
3 years ago
Simplify and factor if necessary​
Dima020 [189]

Answer:

\frac{1}{x}

Step-by-step explanation:

\frac{3x - 12}{3x^{2}  - 12x}

\frac{3x - 12}{x(3x-12)}          Factor out x.

\frac{1}{x}                    Simplify.

4 0
2 years ago
the sum of three times a number and 2 less than 4 times the same number is 15. which of the following equations could be used to
Ulleksa [173]
To solve for a number x,

3x+4x-2=15
7x-2=15
7x=17
x=2 3/7
or x=~2.43

was one of your answer choices either of the first two equations?
4 0
2 years ago
Solve 3(5x-4) < 15x
ollegr [7]

Answer:

All real numbers

Step-by-step explanation:

3(5x - 4) < 15x

~Distribute left side

15x - 12 < 15x

~Subtract 15x to both sides

-12 < 0

Best of Luck!

5 0
3 years ago
Read 2 more answers
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