according to the rational root theorem which of the following are possible roots of the polynomial function below? F(x)=6x^3-7x^2+2x+8

Answer:

j' = (1,-2)   k'=(3,-1) L' = (3,-3)

Step-by-step explanation:

I think that you just multiply all the x,y values for the three points by 1/5?

5 1

-10 -2

j' = (1,-2)

~~~~~~~~~~~~~~~~~~  

15 3

-5 -1

k'=(3,-1)

~~~~~~~~~~~~~~~

15 3

-15 -3

l' = (3,-3)

x ³ = 1

x ³ - 1 = 0

x ³ - 1³ = 0

Factorize the right side as a difference of cubes:

(x - 1) (x ² + x + 1) = 0

Then

x - 1 = 0   or   x ² + x + 1 = 0

The first equation yields x = 1 as a root.

For the other equation, rearrange and complete the square to get the other two roots,

x ² + x + 1/4 = -3/4

(x + 1/2)² = -3/4

x + 1/2 = ±√(-3/4) = ± i √3/2

x = -1/2 ± i √3/2

x = (-1 ± i √3)/2

Since complex roots occurs in conjugate pairs, taking the sum of these two roots eliminates the imaginary part:

(-1 + i √3)/2 + (-1 - i √3)/2 = (-1 - 1)/2 = -2/2 = -1

and adding to 1 indeed shows that the sum of roots is zero.

Step-by-step explanation:

Disclaimer: When writing this on the paper use the theta symbol, I'm using x since I'm on mobile.

2.

i).

[tex] \sin(x) \tan(x) \sec(x) = \tan {}^{2} (x) [/tex]

[tex] \sin(x) \sec(x) \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \sin(x) \frac{1}{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \frac{ \sin(x) }{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \tan( x) ) \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \tan {}^{2} (x) = \tan {}^{2} (x) [/tex]

iii).

[tex] \sec {}^{2} (x) (1 - \sin {}^{2} ( x ) ) = 1[/tex]

[tex] \sec {}^{2} (x) ( \cos {}^{2} (x) ) = 1[/tex]

[tex] \frac{1}{ \cos {}^{2} (x) } \cos {}^{2} (x) = 1[/tex]

[tex]1 = 1[/tex]

v).

[tex] \cot {}^{2} (a) - \cos {}^{2} (a) = \cot {}^{2} (a) \cos {}^{2} (a) [/tex]

[tex] \frac{ \cos{}^{2} (x) }{ \sin {}^{2} (x) ) } - \cos {}^{2} (x) [/tex]

Factor out cosine

[tex] \cos {}^{2} (x) ( \frac{1}{ \sin {}^{2} (x) } - 1) [/tex]

Simplify

[tex] \cos {}^{2} (x) ( \frac{1 - \sin {}^{2} (x) }{ \sin(x) } [/tex]

[tex] \cos {}^{2} (x( \frac{ \cos {}^{2} (x) }{ \sin {}^{2} (x) } ) = [/tex]

[tex]( \cos {}^{2} ( x ) ( \cot {}^{2} (x) )[/tex]

Answer:

y = -10

Step-by-step explanation:

When x = 17, the equation be -17 + y = -27 when you plug in 17 for x

Then, add 17 to both sides to get y = -10

Answer:  " y =  -10 . "

___________________

Step-by-step explanation:

___________________

The question:

Find the  value of  "y" when "x" equals 17.

Given the equation:

 - x + y = -27 ;

___________________

We plug in the given value: "17" ; for "x" ; and solve for "y" :

- 17 + y = -27 ;

_____________________

↔ y + (-17) = -27 ;

Rewrite as:

   y − 17  = -27 ;   {since:  "adding a negative value" is the same

                                           as "subtracting a positive value."}.

_____________________

Now, we add "17" to each side of the equation;

to isolate "y" on one side of the equation; and to solve for "y" :

  y − 17 + 17  = -27 + 17 ;

to get:

  y  =  - 10 .

_____________________

Hope this is helpful to you.

Best wishes to you in your academic pursuits—

    and within the "Brainly" community!

_____________________

Answer:

Step 1: 12-2a=3a-18

Step 2: 12-5a=-18

Step 3: -5a=-30

Step 4: a=6

I hope this helps!

pls ❤ and give brainliest pls

Answer:

SOH-CAH-TOA

[tex]\sin \left(x\right)=\frac{6}{\sqrt{49+36}}[/tex] = 40.60°

SOH = SIN = OPP/HYP

SIN(Θ) = 6/[tex]\sqrt{49+36 }[/tex]

Step-by-step explanation:

There are 30 possible combinations of teachers.

Given that at Tubman Middle School, there are 6 English teachers and 5 science teachers, to determine, if each student takes one English class and one science class, how many possible combinations of teachers are there, the following calculation must be performed:

To calculate possible combinations, the number of options A must be multiplied by the number of options B. Thus, the calculation would be as follows.

Therefore, there are 30 possible combinations of teachers.

Learn more about combinations in https://brainly.com/question/24180105.

Answer:

A

$2.50

Step-by-step explanation:

b = cost of bracelet

n = cost of necklace

2b+3n = 15.50

4b+1n = 13.50

Multiply the first equation by -2

-4b -6n = -31

4b +n = 13.50

---------------------------

-5n = -17.50

Divide each side by -5

-5n/-5 = -17.5/-5

n = 3.50

Now we can find b

4b+n = 13.50

4b+3.50 = 13.50

4b+3.50-3.50 = 13.50 -3.50

4b = 10

Divide by 4

4b/4 = 10/4

b = 2.50

Step-by-step explanation:

5.

[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]

Simplify both radicals.

[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]

Apply Quadratic Formula

First. find the discramnint.

[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]

Now find the divisor 2a.

[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]

Then,take the square root of the discrimant.

[tex] \sqrt{64} = 8[/tex]

Finally, add -b.

[tex] - (4 + 2 \sqrt{7} )[/tex]

So our possible root is

[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]

Which simplified gives us

[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]

Rationalize the denominator.

[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]

Which simplified gives us

[tex] \frac{6 + \sqrt{7} }{29} [/tex].

6. The answer is 2.

9514 1404 393

Answer:

  5. x = (6 +√7)/29; a=6, b=1, c=29

  6. x = 2

Step-by-step explanation:

The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.

  [tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]

__

Use the substitution z=3^x to put the equation in the form ...

  z² -3z -54 = 0

  (z -9)(z +6) = 0 . . . . . factor

  z = 9 or -6 . . . . . . . . value of z that make the factors zero

Only the positive solution is useful, since 3^x cannot be negative.

  z = 9 = 3^2 = 3^x . . . . use the value of z to find x

  x = 2

Answer:

a

Step-by-step explanation:

Answer:

baba booey

Step-by-step explanation:

444

Answer:

(x-3)(5x+4)

x=3 x=-4/5

Answer:

(5x + 4)(x - 3)

Step-by-step explanation:

Hello!

Factor:

Think: What two numbers add up to -11 but multiply to (5)(-12)?

Answer: -15 and 4

Continue:

The factored expression is (5x + 4)(x - 3)

Answer:

Here is the detailed answer below

Step-by-step explanation:

Answer:

1.2 = 12/10 = 6/5

2.25 = 225/100 = 9/4

3.5 = 35/10 = 7/2

4.06 = 406/100 = 203/50

Answer:

is whole number

Step-by-step explanation:

plz mrk me brainliest

Answer:

0 is larger than all negative numbers.

Step-by-step explanation:

When dealing with negative numbers, the number closer to zero is the bigger number. Zero (0) has the unique distinction of being neither positive nor negative.

Answer:

y + 4 = (x - 2)^2

Step-by-step explanation:

The vertex form of the equation of a vertical parabola is

y - k = a(x - h)^2, where (h, k) represents the vertex and a is a scaling factor which stretches or compresses the parabola vertically.  If all we know is the vertex (2, -4), then the desired equation is:

y + 4 = a(x - 2)^2

If there is no vertical stretching or compression, then the equation becomes:

y + 4 = (x - 2)^2

Answer:

y = x² - 4x

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (2, - 4) , with a = 1 , the equation is

y = (x - 2)² - 4 ← expand using FOIL

 = x² - 4x + 4 - 4

y = x² - 4x ← equation of parabola

Answer:

8r+8pg-pq

Step-by-step explanation:

The subtractable pg cancels out one of the 9 pg's. So 9 pg-1 pg= 8 pg

Hope this helps!

Answer:

x=4sqrt3 a=4 b=3  ,y=8sqrt3 c=8 d=3

Step-by-step explanation:

because this is a 30-60-90 triangle, it is easy to find the side lengths. the longer leg is sqrt(3) times the shorter leg so x= 12/sqrt(3) or 4sqrt(3). the hypotenuse is 2 times the shorter leg so y= 8sqrt(3)

Answer:

A)60°

Step-by-step explanation:

a straight line is 180° then

if a line bisect it in to a half it become 90°

then

the exterior angle of a triangle is equal to the sum of two interior angles

this means 150°-90°=60°

Answer: A) 60

Step-by-step explanation:

The line at the top signifies 180 degrees, as does any straight line. The 150° that intersects with P tells you that P must be 30 degrees, as 180 - 150 = 30.

The three angles of a triangle must always equal 180°. Angle R tells you that it’s 90°, shown by the square instead of a curve. If you subtract the value of P we found before, and the value of R we just found, you get your answer.

180 - 30 - 90 = 60.

Answer:

Just agree on having ice cream

Step-by-step explanation:

Answer:

D is right option

Step-by-step explanation:

Similarities:

Both the biomes experience less precipitation due to this they have a less diversity of flora and fauna as compared to other biomes like savanna, grasslands, chaparral etc. Let us see how they differ from each other!

Low rain fall _ annual rainfal of lessthan 20cm in deserts, 15-20cm in tundra

Minimal life_ only small shurbs can survive in both kind of environments

Poor drainage.. In deserts, though sandy soil may seem much porous, these are most flood prone areas of world. The tundra is characterised by permafrost soils ie, under the thin layer of soil, a thick ice sheet is present and hence is no seepage.

High range of temperatures: In tundra, the maximum temperatures are recorded in summer (abt 10^C) and minimum during winter(-20 to -30^C). While, in desert too, the temperature range is high but diurnally ie, nights are too cold and day time is scorching.

Answer:

Area of parallelogram = 21

Step-by-step explanation:

A = BH

Plug in

A = 7×3

Solve

A = 21

The answer will be 21.

Step-by-step explanatio

Step-by-step explanation:

<TOS=122° [being vertically opposite angle]

Answer:

angleTOS =122°

EXPLANATION:

[ If two straight lines intersect at point O, vertically opposite angles are equal]As vertically opposite angles are equal; Hence AngleTOS=QOR=122°

Answer:

Step-by-step explanation:

Answer:

18.8

Step-by-step explanation:

Surface area=2*pi*r*(r+h)=2*pi*1*(3)=18.8

Answer:

d) 16, 19, 14 + x

e) x + 20, 30, 33, 15, y - 20, x+x+20=60 and James would be 20.

f) 13

g) 120

Step-by-step explanation:

D.

(1) 14 + 2 = 16

(2) 14 + 5 = 19

(3) 14 + x

E.

(1) x + 20

(2) 10 + 20 = 30

(3) 13 + 20 = 33

(4) 35 - 20 = 15

(5) y - 20

(6) x + (x + 20) = 60 | 2x + 20 = 60 | 2x = 40 | x = 20

F.

200 - 148 = 52

52 / 4 = 13 each

G.

500 + 100 = 600

600 / 5 = 120 without the discount

Hope this helps!

Answer:

I am not sure on the answer but i think its $9,000

Step-by-step explanation:

11,000x0.20=2,200

2,200+11,000=13,200

22,200-13,200=9,000

which would mean she got $9,000 from commissions.

if you did 100,000x0.03=3,000

9,000/3,000= 3

so she would have had 3 commissions worth over 100,000

You can use the distributive property to multiply:

( y )( y² - 2y + 4 ) + ( 2 )( y² - 2y + 4) =

y³ - 2y² + 4y + 2y² - 4y + 8 =

y³ + 8

The -2y² and the 2y² cancel each other, and the 4y and -4y cancel each other out!