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loris [4]
4 years ago
6

What is the quotient of the polynomials shown below?

Mathematics
1 answer:
Zolol [24]4 years ago
5 0

Answer:

Option A is correct.

Step-by-step explanation:

We need to find the quotient of the polynomials

(6x^3+8x^2+16)\div(2x+4)

The quotient is: 3x^2-2x+4

The remainder is: 0

The division is shown in the figure attached.

Option A is correct.

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Well, some integers can be irrational, but not all! :) 
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Please help Need help
Anettt [7]
This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where 
m=slope of line
(x0,y0) is a point through which the line passes.

We know that the line passes through A(3,-6), B(1,2)

All options have a slope of -4, so that should not be a problem.  In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.

So we can check which line passes through which point:

a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3)  means that line passes through A(3,-6) => ok

b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
   ****** this equation is not the line passing through A & B *****

c. y=-4x+6  subtract 2 from both sides (to make the y-coordinate 2)
   y-2 = -4x+4, rearrange
   y-2 = -4(x-1)  
   which means that it passes through B(1,2), so ok

d. y-2=-4(x-1)
   this is the same as the previous equation, so it passes through B(1,2), 
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Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
   
8 0
3 years ago
The graphs below have the same shape. What is the equation of the red graph?
Sveta_85 [38]

we have

g(x)=4-x^{2}

the vertex of the function g(x) is the point (0,4)

the vertex of the function f(x) is the point (0,0)

so

the rule of the translation of g(x) to f(x) is

(x,y)------> (x,y-4)

that means

the translation is 4 units down

therefore

the equation of the function f(x) is

f(x)=g(x)-4\\f(x)=(4- x^{2})-4 \\f(x)=- x^{2}

therefore

<u>the answer is</u>

f(x)=- x^{2}

8 0
3 years ago
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