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miv72 [106K]
2 years ago
10

Subtract. (2p^2+q)-(p^2+q) Is the answer P^2 P^2+2q P^2-2q 3p^2

Mathematics
1 answer:
Fofino [41]2 years ago
4 0

Answer:

 -p5q2 - p3q5 + 2p3 + 2pq2 + 2q3  

 ____________________________

              p3q2              

Step-by-step explanation:

            2

Simplify   ——

           q2

Equation at the end of step  1  :

      (p+q)         2

 (((2•—————)-(q3))+——)-p2

      (p3)         q2

Step  2  :

           p + q

Simplify   —————

            p3   (p + q)             2      

 (((2 • ———————) -  q3) +  ——) -  p2

          p3               q2      

Step  3  :    2 • (p + q)            2      

 ((——————————— -  q3) +  ——) -  p2

       p3                q2               q3     q3 • p3

   q3 =  ——  =  ———————

         1        p3  

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Answer:

The graph of g(x) is wider.

Step-by-step explanation:

Parent function:

f(x)=x^2

New function:

g(x)=\left(\dfrac{1}{2}x\right)^2=\dfrac{1}{4}x^2

<u>Transformations</u>:

For a > 0

f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}

f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}

\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\  & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}

\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\  & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}

If the parent function is <u>shifted ¹/₄ unit up</u>:

\implies g(x)=x^2+\dfrac{1}{4}

If the parent function is <u>shifted ¹/₄ unit down</u>:

\implies g(x)=x^2-\dfrac{1}{4}

If the parent function is <u>compressed vertically</u> by a factor of ¹/₄:

\implies g(x)=\dfrac{1}{4}x^2

If the parent function is <u>stretched horizontally</u> by a factor of ¹/₂:

\implies g(x)=\left(\dfrac{1}{2}x\right)^2

Therefore, a vertical compression and a horizontal stretch mean that the graph of g(x) is wider.

4 0
1 year ago
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