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ANEK [815]
3 years ago
12

The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x).

Mathematics
1 answer:
Kay [80]3 years ago
8 0

Answer:

  g(x) = |x| -9

Step-by-step explanation:

In the form ...

  g(x) = a|x -h| +k

the parameters are ...

  • a: the vertical scale factor (1)
  • h: the right shift of the vertex (0)
  • k: the upward shift of the vertex (-9)

The vertex of |x| is (0, 0). The vertex of g(x) is (0, -9), so there has been a vertical shift of -9 and no horizontal shift. The slopes of the lines on the graph of g(x) have a magnitude of 1, so the vertical scale is not changed from the original function (a=1).

Then the translated function is ...

  g(x) = |x| -9

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The Expression 4x^2-p(x)+7 leaves a remainder of -2 when divided by (x-3) find the value of p
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Answer:

(c)  For p = 15,  4x^2-p(x)+7 leaves a remainder of -2 when divided by (x-3).

Step-by-step explanation:

Here,  The dividend expression is  4x^2-p(x)+7 = E(x)

The Divisor = (x-3)

Remainder  = -2

Now, by <u>REMAINDER THEOREM</u>:

Dividend  = (Divisor x Quotient)  + Remainder

If ( x -3 ) divides the given polynomial with a remainder -2.

⇒  x = 3  is a  solution of given polynomial E(x)  - (-2) =  

E(x)  - (-2)  = 4x^2-p(x)+7 -(-2)  = 4x^2-p(x)+9 =  S(x)

Now, S(3) = 0

⇒4x^2-p(x)+9 = 4(3)^2 - p(3) + 9 = 0\\\implies 36 - 3p + 9 = 0\\\implies 45= 3p , \\or p  =15

or, p =1 5

Hence, for p = 15,  4x^2-p(x)+7 leaves a remainder of -2 when divided by (x-3).

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3 years ago
F(x) = -3x – 2<br> g(x) = 2x + 5<br> Find (f*g)(5)
antiseptic1488 [7]

Answer:

hope it will help u in understanding

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Math help, please? <br> 20 points ! <br><br> Find the indicated limit, if it exists.
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I think this the correct solution. but please correct me if I'm wrong

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Veronika [31]
Abd is a right angled triangle so by pythagoras we know
{g}^{2}  =  {11}^{2}  +  {13}^{2}  \\  {g}^{2}  = 290 \\ g =  \sqrt{290}  \: or \: g = 17.03cm
and to calculate h we need to use the sine rule
\frac{h}{ \sin(22) }  =  \frac{g}{ \sin(32) }  \\  \frac{h}{ \sin(22) }  =  \frac{17.03}{ \sin(32) }  \\ h =  \frac{17.03}{ \sin(32) } \times  \sin(22)   \\ h = 12.04cm
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3 years ago
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