Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.

9514 1404 393

Answer:

  a) k = -19

  b) P(x) = (5x +1)(3x -1)(2x -1)

  c) x = {-1/5, 1/3, 1/2}

  d) see attached

  e) no; P(-1) = -48

  f) see attached

Step-by-step explanation:

a) The second attachment shows synthetic division of P(x) by the factor (x -1/3). The remainder is 0 when the final expression is zero:

  1 + (10 +k)/9 = 0

  (10 +k)/9 = -1 . . . . . subtract 1

  10 +k = -9 . . . . . . . .multiply by 9

  k = -19 . . . . . . . . . . subtract 10

For (3x -1) to be a factor, the value of k is -19.

__

b) The graph (see part C) shows the zeros of the function to be -0.2, 0.333..., and 0.5. This means the linear factors are ...

  P(x) = (5x +1)(3x -1)(2x -1)

The linear factors can also be obtained by finishing the factoring of ...

  P(x) = (3x -1)(10x^2 -3x -1)

The quadratic factor is the synthetic division result, divided by 3. It can be factored by grouping: 10x^2 -3x -1 = (10x^2 -5x) +(2x -1) = 5x(2x -1) +1(2x -1).

So P(x) = (3x -1)(5x +1)(2x -1).

__

c) The graph shows the zeros to be x ∈ {-1/5, 1/3, 1/2}.

__

d) See the attachment for a graph

__

e) The point (-1, -40) is not on the graph. Evaluating P(-1) gives -48. The point that would be on the graph for x=-1 is (-1, -48).

__

f) See the attachment.

Answer:

right

Step-by-step explanation:

s

a

k

+

1

=

a

k

+

2

and

a

1

=

6

a

2

=

a

1

+

2

=

6

+

2

=

8

a

3

=

a

2

+

2

=

8

+

2

=

10

a

4

=

a

3

+

2

=

10

+

2

=

12

and

a

5

=

a

4

+

2

=

12

+

2

=

14

and hence first five terms are

{

6

,

8

,

10

,

12

,

14

}

As

a

k

+

1

=

a

k

+

2

, each term is

2

more than previous term

it is an arithmetic sequence with first term as

a

1

and common difference

d

and hence

n

t

h

term is

a

n

=

a

1

+

(

n

−

1

)

d

and hence

n

t

h

term of the sequence is

a

n

=

6

+

(

n

−

1

)

×

2

=

6

+

2

n

−

2

=

2

n

+

4

Answer:

y=2x+3

x=(-1)

y=-5x+6

x=1

Step-by-step explanation:

Just find x in the equation

Answer:

12 people can fit so the van had enough sests

Answer:

5

Step-by-step explanation:

thanks for the points

Answer:

A

Step-by-step explanation:

3 + (-7) + 2/5 + (-1/5)

Answer:

answer in the file

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

y=7x

21=7(2)

21=14

It is not since the values are not equal.

Brainliest? :o

No, the pair of coordinates (2,21) is not a solution for the equation; y=7x

According to the question;

Hence, by testing the coordinates in the equation; y=7x, we have;

Hence, since the equation above is not true, the pair of coordinates is not a solution of the equation.

Read more on solution of an equation;

https://brainly.com/question/1397278

Answer:

1/3

Step-by-step explanation:

The distance from -6 to -3 is 3. The distance from -2 to -1 is 1.

3/3 => 1

1/3 difference

Answer:

Step-by-step explanation:

Answer:

The expected payoff for Ann is that she loses the game

Step-by-step explanation:

The expected payoff for Ann is that she loses the game, this is because only 5 out of the 20 sections allow Ann to win money, this is only 25% of the spinner. Meaning that 75% of the spinner will cause Ann to lose the game. Rolling two times increases the odds that she will lose the game. Since the greatest probability is that Ann will land on a section that causes her to lose the game, then this is the expected payoff.

Answer:

I think it its

Step-by-step explanation:

C if its wrong sorry

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

Direction: Opens Up

Vertex:  

(

5

,

1

)

Focus:  

(

5

,

9

8

)

Axis of Symmetry:  

x

=

5

Directrix:  

y

=

7

8

x

y

3

9

4

3

5

1

6

3

7

9  

Answer:

D

Step-by-step explanation:

Answer: D) 86 - 18x - 8 = 12x + 18

Answer:

− 1 ( 5 − 2 3 + 1 7)

Step-by-step explanation:

Answer:

y = 5/3x - 4

Step-by-step explanation:

(6, 6)

m = 5/3

Slope-intercept:

y - y1 = m(x - x1)

y - 6 = 5/3(x - 6)

y - 6 = 5/3x - 10

y = 5/3x - 10 + 6

y = 5/3x - 4

hope the answer can help you.

Answer:

x is -2, -1, 0, 1, 2 and y is 0, 0.5, 1, 1.5, 2

Answer:

$356

Step-by-step explanation:

To solve this problem, use this: (200 * 3.78) - (200 * 2)

(200 * 3.78) - (200 * 2)

200 * 3.78 is the same as 2 * 378, which is 756.

756 - (200 * 2)

200 * 2 is the same as 4 * 100, which is 400.

756 - 400

Subtract 400 from 756 to get 356.

356

If they brought the pizza last week, the school could have saved $356.

Answer:

(x−2)^2=16(y+1)

Step-by-step explanation:

The equation for the parabola is (x - 2)² = 16(y + 1) if the vertex of the parabola is (2, -1) and focus of the parabola is (2, 3) option (D) is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have:

The vertex of the parabola = (2, -1)

The focus of the parabola = (2, 3)

As we know, the vertex form of the parabola is given by:

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

(x - 2)² = 4a(y - (-1))

(x - 2)² = 4a(y + 1)

The value of a can be found using the formula:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

(c, d) = (2, 3)

a = √[(2-2)² + (3-(-1))²]

a = √ (3+1)²]

a = 4

(x - 2)² = 4(4)(y + 1)

(x - 2)² = 16(y + 1)

Thus, the equation for the parabola is (x - 2)² = 16(y + 1) if the vertex of the parabola is (2, -1) and focus of the parabola is (2, 3) option (D) is correct.

Learn more about the parabola here:

brainly.com/question/8708520

#SPJ2

Answer: 70.884

Step-by-step explanation:

Answer:

1.

centre(h,k)=(-13,9)

radius (r)=6

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x+13)²+(y-9)²=6²

(x+13)²+(y-9)²=36you can write this equation too

x²+26x+169+y²-18y+81=36

x²+y²+26x-18y+169+81-36=0

x²+y²+26x-18y +214=0

is a required equation of the circle.

2.

centre(h,k)=(1,-1)

radius (r)=11

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-1)²+(y+1)²=11²

(x-1)²+(y+1)²=121

you can write this equation too

x²-2x+1+y²+2y+1=121

x²+y²-2x+2y=121-2

x²+y²-2x+2y=119

is a required equation of the circle.

3.

centre (h,k)=(3,1)

radius (r)=4units.

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-3)²+(y-1)²=4²

(x-3)²+(y-1)²=16 is a required equation.

4.

centre(h,k)=(4,-2)

radius (r)=3

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-4)²+(y+2)²=3²

(x-4)²+(y+2)²=9

you can write this equation too

Answer:

Whatever he just answered

Step-by-step explanation:

1.

centre(h,k)=(-13,9)

radius (r)=6

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x+13)²+(y-9)²=6²

(x+13)²+(y-9)²=36you can write this equation too

x²+26x+169+y²-18y+81=36

x²+y²+26x-18y+169+81-36=0

x²+y²+26x-18y +214=0

is a required equation of the circle.

2.

centre(h,k)=(1,-1)

radius (r)=11

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-1)²+(y+1)²=11²

(x-1)²+(y+1)²=121

you can write this equation too

x²-2x+1+y²+2y+1=121

x²+y²-2x+2y=121-2

x²+y²-2x+2y=119

is a required equation of the circle.

3.

centre (h,k)=(3,1)

radius (r)=4units.

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-3)²+(y-1)²=4²

(x-3)²+(y-1)²=16 is a required equation.

4.

centre(h,k)=(4,-2)

radius (r)=3

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-4)²+(y+2)²=3²

(x-4)²+(y+2)²=9

you can write this equation too

Answer:

83

Step-by-step explanation:

a = 25

The biggest angle is (3a+8) = 83

Answer:

83

Step-by-step explanation:

(3a+8)+(60-a)+(4a-38)=180

combine like terms, 6a+30=180

inverse operation to isolate the variable, 6a=150

divide six on both sides, a=25

replace a in every expression, 3(25)+8=83

60-25=35

4(25)-38=62

83 is biggest out of the three, therefore 83 is the answer.

Answer:

Surface Area: 1320

Volume: 2160

Step-by-step explanation:

Before calculating Volume and Surface Area, we need to calculate the missing side of the right triangle using the Pythagoreon theorem: [tex]a^2+b^2=c^2[/tex]

where c is the hypotenuse, 26.

Substituting the values into the equation you get:

10^2 + b^2 = 26^2

100 +b^2 = 676

Subtract 100 from both sides.

b^2 = 576

b = 24

Now that we have the missing side, we can calculate the rest of the question.

Surface Area =  2([tex]\frac{1}2[/tex] × 24 × 10) + (18 × 26) + (18 × 24)  +(18 × 10)

240 + 468 + 432 + 180 = 1320 unit^2

Volume = [tex]\frac{1}2[/tex] × base × height × length

[tex]\frac{1}2[/tex] × 24 × 10 × 18 = 2160 unit^2

Brainliest if you don't mind ;)

Answer:

Someone is bound to copy paste the links lol

Step-by-step explanation:

Answer:

adjacent

you can search it up it's one of the first pictures

Answer:

1. X- Intercepts(s) : (4,0)

X- Intercepts(s) : (4,0)

X- Intercepts(s) : (4,0) Y- Intercepts(s) : (0, -4)

X- Intercepts(s) : (4,0) Y- Intercepts(s) : (0, -4)2. . X- Intercepts(s) : (15/2, 0 in fraction form.)

X- Intercepts(s) : (4,0) Y- Intercepts(s) : (0, -4)2. . X- Intercepts(s) : (15/2, 0 in fraction form.) Y- Intercepts(s) :( 0, -5)

Step-by-step explanation:

To Find the X- Intercept Subsitute in 0 For Y solve for x. To find the y-intercept Substitute in 0 for x and solve for y.

Answer:

its 44

Step-by-step explanation:

because IRS 444 j utf d funk nhc ddh

Answer:

16units

Step-by-step explanation:

Given data

The expression for the volume of a cone is given as

v=1/3πr^2h

v= 3π

r= 12

h=???

Substitute

3π= 1/3*π*12^2*h

3= 1/3*144*h

3= 144h/3

cross multiply

3*3= 144h

9= 144h

h= 144/9

h=16 units

Hence the heeight is 16units