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natima [27]
3 years ago
10

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x4 – 2x2 – 3x + 4?

Mathematics
2 answers:
iogann1982 [59]3 years ago
6 0
The answer is the first choice - see picture for solution:

kolezko [41]3 years ago
4 0

Answer:

Option 1.

Step-by-step explanation:

According to rational root theorem, all the potential rational roots of a function f(x) is defined as

roots=\dfrac{p}{q}

where, p is a factor of constant term and q is the factor of leading coefficient.

The given function is

f(x)=9x^4-2x^2-3x+4

Here, leading coefficient is 9 and factors of 9 are ±1, ±3, ±9.

Constant term is 4 and factors of 4 are ±1, ±2, ±4.

All the potential rational roots of f(x) are

\pm \dfrac{1}{9},\pm \dfrac{2}{9},\pm \dfrac{4}{9},\pm \dfrac{1}{3},\pm \dfrac{2}{3},\pm \dfrac{4}{3},\pm 1,\pm 2,\pm 4

Therefore, option 1 is correct.

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Answer:

y=15

Step-by-step explanation:

3y+27=5y-3

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30=2y

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Thats assuming A and B are equal ^

Hope this helps :)

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(x3+3x2-12x-18)÷(x-3)
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Step-by-step explanation:

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Find the equations of the tangents to the curve y = x²-x-12 at each of the points where the curve crosses the x-axis.​
poizon [28]

Step-by-step explanation:

First, find the zeroes of the parabola

{x}^{2}  - x - 12

{x}^{2}  - 4x + 3x - 12

x(x  - 4) + 3(x - 4)

(x +  3)(x  - 4) = 0

x =  - 3

x - 4 = 0

x = 4

So the zeroes or where the curve crosses the x axis is at 4 and -3.

Now, we take the derivative of the function.

\frac{d}{dx} ( {x}^{2}  - x - 12) = 2x - 1

Plug in -3, and 4 into the derivative function

2( - 3) =  - 7

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So at x=-3, our slope of the tangent line is -7 and must pass through (-3,0). So we use point slope formula.

y - y _{1} = m(x - x _{1})

y - 0 =  - 7(x - (  - 3)

y =  - 7x - 21

At x=4, our slope of tangent line is 7, and pass through (4,0) so

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y = 7x - 28

So the equations of tangent is

y =  - 7x - 21

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6 0
2 years ago
Ned, the owner of neds shop, sells peanuts for $10 per pound and cashews for $9 per pound. Ned wants to create a 20 pound barrel
Ymorist [56]
We will use a system of equation for this one. 
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This represents the pounds.
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We can make the first equation equal C.
C=20-P
10P+9(20-P)=191
10P+180-9P
P+180=191
P=11
There are 11 pounds of peanuts, which means there's 9 pounds of cashews.

4 0
3 years ago
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