Which of the following matches the graph of f (x) = 2(x – 1)2(x + 1)(x + 2)?

Answer:

As this is a quartic equation, we should expect four roots (although some may end being repeated). Notice also that the equation is symmetrical, which suggests that there might be an element of symmetry in the answer.

First, as this equation is a quadratic in terms of z2 , we can use our formula for finding the roots of a quadratic equation to give the value(s) of z2 . [If you have a problem seeing this, use the substitution y=z2 , and you get a quadratic in y .]

z2=−4±42−4×1×16√2×1=−4±16−64√2

=−4±−48√2=−2±12−−√i=−2±23–√i

=4(−12±3√2)i

=4(cos(2kπ3)+isin(2kπ3)) , where k∈1,2

=4e2kiπ3

As this is the value of z2 , whereas we want z , we need to take the square roots of both sides

z=4–√ekiπ3+nπ , where n∈0,1

=2e(k+3n)iπ3

=2cis((k+3n)iπ3)

As we have two values of k and two values of n , this gives us four solutions.

Writing these angles in terms of degrees, we have: 60, 120, 240 and 300

Evaluating, we end up with the four solutions

z=1±3–√i∪z=−1±3–√i

You can substitute z^2 = x,

Then you get x^2+4x+16=0

Step-by-step explanation:

z=1±3–√i∪z=−1±3–√i

You can substitute z^2 = x,

Then you get x^2+4x+16=0

Then you can use classical x1,2 = (-b +- √[b^2–4ac])/2a

X1,2=(-4+-√[16–16*4])/2

After you solve that you substitute back z^2 = x

Answer:

[tex]x=\frac{5±\sqrt{33} }{4}[/tex]

Step-by-step explanation:

Answer:

Hi, there!

Option A. 3.2 x 10²

Step-by-step explanation:

320 written in scientific notation is 3.2 × 102.

Answer:

He would weigh 218.5 pounds on Jupiter

Step-by-step explanation:

If objects weigh 2.3 times as much on Jupiter then you multiply Joey's weight by 2.3.

Answer: 218.5 pounds

Step-by-step explanation: If objects on Jupiter weigh 2.3 times their weight on Earth and if Joey weighs 95 pounds on Earth, he would weigh 2.3 times of his weight on Earth on Jupiter. 2.3 times 95 pounds would be 218.5 pounds. Joey would weigh 218.5 pounds on Jupiter.

Answer:

0.0081031308

Step-by-step explanation:

Answer:

x = 6, RS = 30

Step-by-step explanation:

5x + 3x = 48

8x = 48

8x/8 = 48/8

x = 6

RS = 5x

RS = 5(6)

RS = 30

Answer:

Simple Division. See explanation.

Step-by-step explanation:

Simply put, 5 1/3 divided by 2 2/7 is  2.333333 (continues on forever)

This in fraction form however is 2 1/3.

Final answer: 2 1/3 in fraction form, and 2.333 in decimal.

Answer:

13x -9

Step-by-step explanation:

4x-1 + 9x-8

Combine like terms

4x +9x  -1-8

13x -9

Answer:

9x+−8+4x+−1

(9x+4x)+(−8+−1)

13x+−9

Step-by-step explanation:

so sorry if wrong

Answer:

y = 18

Step-by-step explanation:

y/3 - 4 = 2

y/3 = 6

y = 18

Answer:

16

Step-by-step explanation:

[tex]x^{2}[/tex] = [tex]x[/tex] multiplied by [tex]x[/tex]

so [tex]4^{2}[/tex] = 16

Answer:

16

Step-by-step explanation:

4 squared should look like this:

4²

That means we just multiply 4 twice:

4 x 4

16

Here is the answer to your problem:

Answer:

I think that the answer is 19.

Step-by-step explanation:

Writing out the problem

x²+yz

Substituting the given values of the variables

(-3)²+(5)(2)

Simplifying (-3)², which is 9

9+(5)(2)

5 times 2 equals 10

9+10

19

I hope this helped you. Enjoy your day, and take care :)

Answer:

The average annual cumulative rainfall is  [tex]1[/tex] inch per month.

During month of August average rain fall is greatest because slope in this month is maximum.

Step-by-step explanation:

The graph does not represent cumulative rainfall as a function of day.

Because they have average all values for month Total cumulative rainfall is [tex]12[/tex] inches.

Total period is [tex]12[/tex] month

So average annual cumulative rainfall is

[tex]$12 / 12=1$[/tex] inch per month

Average rain fall in month of December= (average cumulative rainfall in December[tex])-([/tex]average  cumulative rainfall in November)

[tex]=12-11[/tex]

[tex]$=1$[/tex] inch

During month of August average rain fall is greatest because slope in this month is maximum.

Learn more about average, refer :

https://brainly.com/question/22390452

Answer:

G

Step-by-step explanation:

three line segments : HI, EF, and JG,

intersect in one point => G

Three axis given

[tex]\\ \sf\longmapsto \overleftrightarrow{HI}[/tex]

[tex]\\ \sf\longmapsto \overleftrightarrow{EF}[/tex]

[tex]\\ \sf\longmapsto \overleftrightarrow{GJ}[/tex]

Now

All are intersected at one point G

Answer:

13

Step-by-step explanation:

To find g f(2) , evaluate f(2) and substitute the value obtained into g(x)

f(2) = 2(2) + 1 = 4 + 1 = 5 , then

g(5) = 3(5) - 2 = 15 - 2 = 13

Answer:

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

If there are  n  students, then the number of pairs is [tex]\frac{n(n-1)}{2}[/tex].

With 12 students, [tex]\frac{12(12-1)}{2} = \frac{132}{2}=66[/tex] pairs can be formed.

The reason the formula works is this:  Each of the 12 students can be paired with 11 other students (no student is paired with him/her self).  But counting 12 x 11 = 132  counts each pair twice.  Example: student A can be paired with student B,..., student B can be paired with student A.  The pair was counted two times.

See the attached image that shows pairings of 5 students.  There are

5(5 - 1)/2 = 5(4)/2 = 10 pairs.

Answer:

52

Step-by-step explanation:

15+7+19+11+0=52

may help.

Convert into numbers

[tex]\\ \sf\longmapsto 15+7+19+13+11+0[/tex]

[tex]\\ \sf\longmapsto 22+32+11[/tex]

[tex]\\ \sf\longmapsto 55+11[/tex]

[tex]\\ \sf\longmapsto 66[/tex]

Answer:

lusia was studing weather doesnnot she

Step-by-step explanation:

1 & 2 are on the attachment

3 --------------

4)4x+5=17

 5x+5=20

5)2x+15+85+x+20=180

   3x+120              =180-120

                        3x=60

                          x=20 degrees

6)son's age=x

  3x+x=48

   4x=48

    x=12            

Therefore; son's age=12 years old

                  Mr.Robert age=12*3

                                           =36 years old

Hope this helps you

If you have any question just ask me

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Answer:

Step-by-step explanation:

Answer: 0.86

Step-by-step explanation:

Answer:

It represents the total amount that Erin is going to spend at the store.

Step-by-step explanation:

Answer:

Hello the answer is (10,−3)

Midpoint of a line with end points (x1,x2) and (y1,y2) is given by ((x1+x2)/2,(y1+y2)/2, coordinates for point C is (10, -3)

Midpoint=((x1+x2)/2,(y1+y2)/2)

B(6,0) is the midpoint

A(2, 3) and C(?,?)

we need to find coordinates of C

Use formula of midpoint

Midpoint=((x1+x2)/2,(y1+y2)/2)

(6,0)=(2+x)/2,(3+y)/2

(2+x)/2=6

2+x=12

x=10

3+y/2=0

3+y=0

y=-3

Therefore coordinates of C are (10,-3)

To learn more on midpoint of  a line click here:https://brainly.com/question/27810617

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Answer:

94

Step-by-step explanation:

When a player reaches 101 points, they win. So that means that Mack reached 101 points. Since his opponent was seven points behind, we can subtract 7 from 101 to find Mark's, that is Mack's opponent's, score:

[tex]101-7=94[/tex]

Therefore, we can safely conjecture that Mark scored 94 points.

Answer:

{72, 79.5, 86.5, 91.5, 99}

Step-by-step explanation:

I took the quiz and got it correct.

Minimum is 72

Maximum is 99

Q1 is 79.5

Q3 is 91.5

Median is 86.5

So the 5-number summary is {72, 79.5, 86.5, 91.5, 99}

Dividing the segments, it is found that:

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

[tex]K - J = \frac{1}{n}(J - L)[/tex]

And this is the answer to option b.

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

Option a:

If [tex]\mathbf{n = 4}[/tex], it has that:

[tex]K - J = \frac{1}{4}(J - L)[/tex]

This is applied to find both the x-coordinate and the y-coordinate of K.

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

Thus:

[tex]K - J = \frac{1}{4}(J - L)[/tex]

[tex]x - 4 = \frac{1}{4}(4 - 0)[/tex]

[tex]x - 4 = 1[/tex]

[tex]x = 5[/tex]

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

Thus:

[tex]K - J = \frac{1}{4}(J - L)[/tex]

[tex]y - (-5) = \frac{1}{4}(-5 - (-7))[/tex]

[tex]y + 5 = \frac{2}{4}[/tex]

[tex]y = \frac{1}{2} - 5[/tex]

[tex]y = \frac{1}{2} - \frac{10}[2}[/tex]

[tex]y = -\frac{9}{2}[/tex]

The coordinates of K if n = 4 are [tex](5,-frac{9}{2})[/tex]

A similar problem is given at https://brainly.com/question/20847604

Step-by-step explanation:

I hope it will help you so .