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3 years ago

Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL

1 answer:

7 0

Foil method:
FOIL stands for
first-multiply the first term in each set of parenthesis
outer-multiply the outer term in each of the perenthesis
inner- multiply the inner term in each of the parenthesis
last- multiply the last term in each of the parenthesis
(3x+8)(x+1)
(3x*x)=3x^2
(3x*1)=3x
8*x=8x
8*1=8
thus we shall have:
3x^2+3x+8x+8
=3x^2+11x+8

Distributive property:

(3x+8)(x+1)
3x(x+1)+8(x+1)
3x^2+3x+8x+8
=3x^2+11x+8

Both methods are efficient, it all depends with the users preference

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What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8?

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The common ratio in a geometric sequence is the ratio between 2 consecutive terms:

-8/2=-4,

then the sequence is 2, -8, 32, -128, -512, 2048, ...

let $a_n$ be the nth term of the sequence, then

$a_1= 2$
$a_2=2(-4)$
$a_3=2(-4)(-4)=2(-4)^{2}$
$a_4=2(-4)(-4)(-4)=2(-4)^{3}$
.
.
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so clearly $a_n=2(-4)^{n-1}$

and, clearly n are integers >0, since we have a 1st term, a second term and so on... of a sequence (we do not have a "zero'th term"!

Answer:

<span>C. an=2(-4)^n-1; all integers where n>0</span>

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3 years ago

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3 years ago

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3 years ago

How does the graph of f(x)=3lx+2l+4 relate to its parent function?

Sergeeva-Olga [200]

$\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 above in mind, let's see this one

$\bf parent\implies f(x)=|x|
\\\\\\
\begin{array}{lllcclll}
f(x)=&3|&1x&+2|&+4\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

A=3, B=1, shrunk by AB or 3 units, about 1/3
C=2, horizontal shift by C/B or 2/1 or just 2, to the left
D=4, vertical shift upwards of 4 units

check the picture below

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3 years ago