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ale4655 [162]
3 years ago
9

What is the remainder when x^{6}-4x^4+4x^2-10 is divided by x+3?

Mathematics
1 answer:
vovangra [49]3 years ago
3 0

Answer:

431

Step-by-step explanation:

Let

p(x) =  {x}^{6}  - 4 {x}^{4}  + 4 {x}^{2}  - 10

We want to find the remainder when this polynomial is divided by x+3.

We use the remainder theorem.

Which says that, when p(x) is divided by x-a, the remainder is p(a)=R.

Therefore the remainder when p(x) is divided by x+3 is p(-3).

p( - 3) =  {( - 3)}^{6}  - 4 { (- 3)}^{4}  + 4 {( - 3)}^{2}  - 10

We evaluate:

p( - 3) = 729 - 4 (81)+ 4 {( 9)} - 10

We multiply to get;

p( - 3) = 729 - 324+ 36- 10

We simplify to get:

p( - 3) =431

Therefore the remainder is 431

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Express the radical using the imaginary unit, i
Kipish [7]

Answer:

7i.

Step-by-step explanation:

Note : The given expression must be \sqrt{-49}.

We have to write this radical value in the imaginary value.

The given value can be rewritten as

\sqrt{-49}=\sqrt{49\times (-1)}

\sqrt{-49}=\sqrt{49}\times \sqrt{-1}    [\because \sqrt{ab}=\sqrt{a}\sqrt{b}]

\sqrt{-49}=7\times i    [\because \sqrt{-1}=i]

\sqrt{-49}=7i

Therefore, the required expression is 7i.

8 0
3 years ago
6.
Otrada [13]

Answer:

C. y= -2x^2 + 4

Step-by-step explanation:

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12

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(

0

,

4

)

Focus:  

(

0

,

33

8

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

31

8

x

y

−

2

12

−

1

6

0

4

1

6

2

12

______________

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:  

(

0

,

4

)

Focus:  

(

0

,

31

8

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

33

8

x

y

−

2

−

4

−

1

2

0

4

1

2

2

−

4

_______________

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

(

0

,

−

4

)

Focus:  

(

0

,

−

31

8

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

−

33

8

x

y

−

2

4

−

1

−

2

0

−

4

1

−

2

2

4

6 0
3 years ago
Write the standard equation of the circle with center (5, -4) and radius 3.
Leya [2.2K]

Answer:

( x - 5 )^2 + ( y +4 )^2 = 9

Step-by-step explanation:

( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius

Brainliest maybe?

8 0
3 years ago
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!
IgorC [24]

Answer:

x^2+6x+9

Step-by-step explanation:

x^2 +6x

Take the coefficient of x

6

Divide by 2

6/2 = 3

Square it

3^2 = 9

Add 9 to each side

x^2+6x+9

4 0
4 years ago
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Nina [5.8K]
21x -15 + 5 = 10x - 5
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5 0
3 years ago
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