58,511 divieded by 21 the qoutient is 2,786 r?

F(x) = x2 – 3x – 2 is shifted 4 units left. The result is g(x). What is g(x)?

Ray Of Light [21]

$\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... your expression is not in vertex form, that's ok... to do a horizontal shift to the left by 4 units, we can simply, add the C and B component to the "x" variable, C=4, B =1, that way the horizontal shift of C/B or 4/1 is just +4, giving us a horizontal shift to the left

$\bf f(x)=x^2-3x-2\impliedby \textit{let's change that for }f(1x+4)
\\\\\\
f(1x+4)=(1x+4)^2-3(1x+4)-2
\\\\\\
f(x+4)=x^2+8x+16-3x-12-2
\\\\\\
f(x+4)=x^2-5x+2\impliedby g(x)$

8 0

3 years ago

Read 2 more answers

Write the expression using only positive exponents. Assume no denominator equals zero.

ipn [44]

Answer:

The answer is

$\frac{4}{ {y}^{2} }$

6 0

3 years ago

8 < -3x + 10<br><br>greater than sign meaning greater than or equal to!

goldfiish [28.3K]

Answer:

2/3 >=x

Step-by-step explanation:

8 =< -3x + 10

subtract 10 from each side

8-10 <= -3x+10-10

-2 <=-3x

divide by -3 (remember to flip the inequality)

-2/-3 >= -3x/-3

2/3 >=x

4 0

3 years ago

Read 2 more answers

Which answer is in slope-intercept form for the given equation? 4x - 9y = -36<br><br> Thanks

jek_recluse [69]

Answer:

y = 4/9 x + 4

Step-by-step explanation:

Slope intercept form: y = mx = b

So 4x - 9y = -36

9y = 4x+ 36

y = 4/9 x + 4

4 0

3 years ago

g: Consider the following game. A coin is flipped. If it lands tails we stop playing and winnothing. If it lands heads we spin a

galben [10]

Answer:

E[W] = $25 (assuming the currency is in dollars)

Var(W) = 1041.67

Step-by-step explanation:

Probability of winning first starts with the coin toss.

For a win, the coin needs to land on heads.

Probability of that = 1/2 = 0.5

Then probability of winning any amount = 1/100 = 0.01

Total probability of winning any amount = 0.5 × 0.01 = 0.005

But expected value is given by

E(X) = Σ xᵢpᵢ

where xᵢ is each amount that could be won

pᵢ is the probability of each amount to be won and it is the same for all the possible winnings = 0.005

So,

E(W) = Σ 0.005 xᵢ

Summing from 0 to 100 (0 indicating getting a tail from the coin toss). This could be done with dome faster with an integral sign

E(W) = ∫ 0.005 x dx

Integrating from 0 to 100

E(W) = [0.005 x²/2]¹⁰⁰₀

E(W) = [0.0025 x²]¹⁰⁰₀ = 0.0025(100² - 0²) = 0.0025 × 10000 = $25

Variance is given by

Variance = Var(X) = Σxᵢ²pᵢ − μ²

μ = expected value

We calculate the expression, Σxᵢ²pᵢ which is another sum from 0 to 100

Σxᵢ²pᵢ = Σ 0.005xᵢ²

Σ 0.005 xᵢ² = ∫ 0.005 x² dx

Integrating from 0 to 100

∫ 0.005 x² dx = [0.005 x³/3]¹⁰⁰₀ = [0.1667x³]¹⁰⁰₀ = 0.1667(100³ - 0³) = 1666.67

Var(W) = 1666.67 - 25² = 1666.67 - 625 = 1041.67.

5 0

3 years ago