If f(x)=x^2+2x−5 and g(x)=2x+4, what is (f⋅g)(x)

Answers

Answer 1

Answer:

Step-by-step explanation:

f(x)=x²+2x−5 and g(x)=2x+4

(f⋅g)(x) = (x²+2x−5)(2x+4) = 2x^3 +4x² -10x +4x²+8x-20

(f⋅g)(x) = 2x^3+8x² -2x -20

Answer 2

For this case we have the following functions:

[tex]f (x) = x ^ 2 + 2x-5\\g (x) = 2x + 4[/tex]

We must find [tex](f * g) (x)[/tex]. By definition we have to:

[tex](f * g) (x) = f (x) * g (x)[/tex]

So:

[tex](f * g) (x) = (x ^ 2 + 2x-5) (2x + 4)[/tex]

Applying distributive property we have:

[tex](f * g) (x) = 2x ^ 3 + 4x ^ 2 + 4x ^ 2 + 8x-10x-20[/tex]

We add similar terms:

[tex](f * g) (x) = 2x ^ 3 + 8x ^ 2-2x-20[/tex]

Answer:

[tex](f * g) (x) = 2x ^ 3 + 8x ^ 2-2x-20[/tex]


Related Questions

finding whole number equal to fraction 8/1

Answers

Answer: 8

Step-by-step explanation: 8 divided by 1 is 8

8 is the whole number equal to fraction 8/1.

What is Number system?

A number system is defined as a system of writing to express numbers.

The given fraction is 8/1

Eight divided by one.

A fraction represents a part of a whole or, more generally, any number of equal parts.

8 is the numerator and 1 is the denominator.

The complete set of natural numbers along with '0' are called whole numbers.

If a number is divided by another number then the result will be the numerator which is whole number.

8/1=8

Hence, 8 is the  whole number equal to fraction 8/1.

To learn more on Number system click:

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EXPLAIN!!!!!!!!!!!!!!

Answers

Answer:

111

Step-by-step explanation:

because the lines are parallel and they are on opposite sides its like having two angles on the same line but on different sides so they are supplementary meaning they add up to 180 and 180-69 = 111

please mark brainliest :)

3) Find the length of a rectangular lot with a perimeter of 92 m if the length is 8 m more than
the width.​

Answers

Answer:

26 m

Step-by-step explanation:

Perimeter = 92 m

Length = 8 m more than width

Width: 20 m

Therefore,

length=26 m
Final answer:

The width of the rectangular lot is 19 m and the length is 27 m.

Explanation:

The subject of this question is the calculation of the length of a rectangular lot. The perimeter of a rectangle is the sum of all its sides, given by the formula 2*(length + width). From the question, we know that the perimeter is 92 m, and the length is 8 m more than the width. Suppose 'w' is the width. Thus the length is 'w + 8' m.

So, we can set up the equation 2*(w + w + 8) = 92. Solving this equation will give us the value for the width (w) and consequently, the length by adding 8 to it.

Step-by-step solution:Combine like terms on the left side to get 2*(2w + 8) = 92.Then, distribute 2 to get 4w + 16 = 92.Subtract 16 from both sides to have 4w = 76.Finally, divide by 4 to find w = 19 m.The length (w+8) will then be 19m + 8m = 27m.

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How do u factor this?

Answers

Answer:(a+b)^2+(ab+a+b)2

Step-by-step explanation:

You break it up into two part, based on the exponents.

(a^2+b^2)+(2ab+2a+2b)

Now you can factor out from each...

(a+b)^2+(ab+a+b)2

Answer: (x+y+2)(x+y)

Step-by-step explanation:

Using square roots and factorising

Everyday there are 4 times more like on an internet video of a horse which is modeled by the function c(n)=(4)^n-1 where n is the number of day since the video posted on the first day there were 100 likes what is the function that shows the number of likes each day

Answers

Answer:

Step-by-step explanation:

A better way to write the first function would be:

c(n) = 4*c(n-1), meaning that the number of likes is equal to four times the number of likes from the previous day. 

On the first day, c(n)=c(0) = 100

Therefore:

C(n) = 100 * 4^n 

Let's plug in a view values to test our function: 

When n= 0 (first day)

C(0) = 100 * 4 ^0 = 100*1 = 100 likes

C(1) = 100 * 4^1 = 100 * 4 = 400 likes, four times the previous day

C(2) = 100 * 4^2 = 100 * 16 = 1600 likes, four times the previous day

And so on. Our function is an accurate descriptor of the model. 

Solve the system of equation and choose the correct ordered pair.!2x-6y=8 5x-4y=31

Answers

Answer:

The correct ordered pair is (7,1)

Step-by-step explanation:

The given system has equations:

[tex]2x - 6y = 8....(1)[/tex]

[tex]5x- 4y = 31....(2)[/tex]

We make x the subject in the first equation to get:

[tex]x = 4 + 3y...(3)[/tex]

Put equation 3 into equation 2 to get:

[tex]5(4 + 3y) - 4y = 31[/tex]

Expand:

[tex]20 + 15y - 4y = 31[/tex]

[tex]15y - 4y = 31 - 20[/tex]

[tex]11y = 11[/tex]

[tex]y = 1[/tex]

Put y=1 into equation 3 and solve for x.

[tex]x = 4 + 3( 1) = 7[/tex]

The correct ordered pair is (7,1)

PLEASE HELP PLEASE
Which number is not divisible by either of the numbers 3 and 5?

A. 5000
B. 2374
C. 1203
D. 2505

Answers

Answer:

The answer is B. 2374

Answer:

B. 2374

Step-by-step explanation:

Division by 5: If a number ends in 0 or 5 it is divisible by 5.

A. 5000 is divisible by 5.

D. 2505 is divisible by 5.

Division by 3: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

B. 2374

Add the digits of 2374: 2 + 3 + 7 + 4 = 16. 16 is not divisible by 3, so 2374 is not divisible by 3. It is also not divisible by 5 since it does not end in 0 or 5.

C. 1203

Add the digits of 1203: 1 + 2 + 0 + 3 = 6. Since 6 is divisible by 3, 1203 is divisible by 3.

Answer: B. 2374

25. Tom and Jerry must stuff and mail 1000
envelopes for a new marketing campaign. Jerry
can do the job alone in 6 hours. If Tom helps,
they can get the job done in 4 hours. How long
would it take Tom to do the job by himself?
A. 4 hours
B. 5 hours
C. 8 hours
D. 12 hours​

Answers

Answer:

12

Step-by-step explanation:

The general formula for this is

Formula

1/t1 + 1/t2 = 1/t_tot

givens

t1 = 6 hours

t2 = x

t_tot = 4 hours

Solution

1/6 + 1/x = 1/4                 Subtract 1/6 from both sides.

1/6-1/6 + 1/x = 1/4 - 1/6   Change to 12 as your common denominator

1/x = 3/12 - 2/12              subtract

1/x = 1/12                         Cross multiply

x = 12

Tom would need 12 hours to do the job alone.

Answer:

Option D. 12 hours

Step-by-step explanation:

Let the work done by Tom to do the job alone = x hours

So per hour work done by Tom = [tex]\frac{1}{x}[/tex]

Jerry can do the job alone in the time = 6 hours

Per hour work done by Jerry = [tex]\frac{1}{6}[/tex]

Similarly job done by both together in the time = 4 hours

Per hour work done by both together = [tex]\frac{1}{4}[/tex]

Now we know,

Per hour work done by both together = per hour work done by Tom + Per hour work don by Jerry

[tex]\frac{1}{4}=\frac{1}{x}+\frac{1}{6}[/tex]

[tex]\frac{1}{x}=\frac{1}{4}-\frac{1}{6}[/tex]

[tex]\frac{1}{x}=\frac{3-2}{12}[/tex]

[tex]\frac{1}{x}=\frac{1}{12}[/tex]

x = 12 hours

Option D. will be the answer.

please Answer fast .......​

Answers

Answer:

Option 3 [tex]\frac{67}{441}[/tex]

Step-by-step explanation:

step 1

Find the roots of the quadratic equation

we have

[tex]3x^{2}+5x-7=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]3x^{2}+5x-7=0[/tex]

so

[tex]a=3\\b=5\\c=-7[/tex]

substitute in the formula

[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(3)(-7)}} {2(3)}[/tex]

[tex]x=\frac{-5(+/-)\sqrt{109}} {6}[/tex]

[tex]x=\frac{-5+\sqrt{109}} {6}[/tex]

[tex]x=\frac{-5-\sqrt{109}} {6}[/tex]

step 2

Let

[tex]\alpha=\frac{-5+\sqrt{109}} {6}[/tex]

[tex]\beta=\frac{-5-\sqrt{109}} {6}[/tex]

we need to calculate

[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]

step 3

Calculate   [tex](3\alpha+5)^{2}[/tex]

[tex](3\alpha+5)^{2}=[3(\frac{-5+\sqrt{109}} {6})+5]^{2}[/tex]

[tex]=[(\frac{-5+\sqrt{109}} {2})+5]^{2}[/tex]

[tex]=[(\frac{-5+\sqrt{109}+10} {2})]^{2}[/tex]

[tex]=[(\frac{5+\sqrt{109}} {2})]^{2}[/tex]

[tex]=[(\frac{25+10\sqrt{109}+109} {4})][/tex]

[tex]=[(\frac{134+10\sqrt{109}} {4})][/tex]

[tex]=[(\frac{67+5\sqrt{109}} {2})][/tex]

step 4

Calculate   [tex](3\beta+5)^{2}[/tex]

[tex](3\beta+5)^{2}=[3(\frac{-5-\sqrt{109}} {6})+5]^{2}[/tex]

[tex]=[(\frac{-5-\sqrt{109}} {2})+5]^{2}[/tex]

[tex]=[(\frac{-5-\sqrt{109}+10} {2})]^{2}[/tex]

[tex]=[(\frac{5-\sqrt{109}} {2})]^{2}[/tex]

[tex]=[(\frac{25-10\sqrt{109}+109} {4})][/tex]

[tex]=[(\frac{134-10\sqrt{109}} {4})][/tex]

[tex]=[(\frac{67-5\sqrt{109}} {2})][/tex]

step 5

substitute

[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]

[tex]\frac{1}{[(\frac{67+5\sqrt{109}} {2})]}+ \frac{1}{[(\frac{67-5\sqrt{109}} {2})]}[/tex]

[tex]\frac{2}{67+5\sqrt{109}} +\frac{2}{67-5\sqrt{109}}\\ \\\frac{2(67-5\sqrt{109})+2(67+5\sqrt{109})}{(67+5\sqrt{109})(67-5\sqrt{109})} \\ \\\frac{268}{1764}[/tex]

Simplify

Divide by 4 both numerator and denominator

[tex]\frac{268}{1764}=\frac{67}{441}[/tex]

Answer:

  3)  67/441

Step-by-step explanation:

Comparing the given equation to the expressions you need to evaluate, you find there might be a simplification.

  3x² +5x -7 = 0 . . . . . given equation

  3x² +5x = 7 . . . . . . . add 7

  x(3x +5) = 7 . . . . . . . factor

  3x +5 = 7/x . . . . . . . . divide by x

Now, we can substitute into the expression you are evaluating to get ...

  1/(3α +5)² +1/(3β +5)² = 1/(7/α)² +1/(7/β)² = (α² +β²)/49

__

We know that when we divide the original quadratic by 3, we get

  x² +(5/3)x -7/3 = 0

and that (α+β) = -5/3, the opposite of the x coefficient, and that α·β = -7/3, the constant term. The sum of squares is ...

  α² +β² = (α+β)² -2αβ = (-5/3)² -2(-7/3) = 25/9 +14/3 = 67/9

Then the value of the desired expression is ...

  (67/9)/49 = 67/441

4,792÷8 show your work​

Answers

Answer:

4,792 ÷ 8 = 599

Step-by-step explanation:

Look at the picture.

Use the long division.

Solve for x.
A. 2
B. 4
C. 6
D. 8

Answers

The full length of one line times the length of the line outside the circle is equal the the other line.

(x-1) +5 x 5 = (2+x)+4 x 4

Simplify:

(x+4) x 5 = (x +6) x 4

5x +20 = 4x +24

Subtract 20 from each side:

5x = 4x +4

Subtract 4x from each side:

x = 4

The answer is B. 4



Select the equation of the line parallel to the equation 2x + 4y = -5 that passes through the point (-4, -8).

a). x + 2y = 16

b). 2x + y = -16

c). 2x + 4y = -9

d). x + 2y = -20

Answers

Answer:

D.

Step-by-step explanation:

First, put your original equation in slope-intercept form to find your slope.

[tex]y=mx+b\\2x+4y=-5\\4y=-2x-5\\y=-\frac{1}{2} x-\frac{5}{4}[/tex]

Now that you have your slope ([tex]-\frac{1}{2}[/tex]) and a point, you can use point-slope form to find your y-intercept.

[tex]y-y1=m(x-x1)\\y-(-8)=-\frac{1}{2} (x-(-4))\\y+8=-\frac{1}{2} (x+4)\\y+8=-\frac{1}{2} x-2\\y=-\frac{1}{2} x-10[/tex]

Your answer choices are all in [tex]Ax+By=C[/tex] form, so lets convert our equation into that form.

[tex]y=-\frac{1}{2} x-10\\1/2x+y=-10\\x+2y=-20[/tex]

If we multiply all of our terms by 2, we can get answer choice D.

When you multiply a function by -1, what is the effect on its graph?

Answers

Step-by-step explanation:

[tex]\dfrac{a}{b}\cdot(-1)=-\dfrac{a}{b}[/tex]

On the number line, fractions a/b and -a/b lie on the opposite sides of the number 0, at the same distance (look at the picture).

raph the equation with a diameter that has endpoints at (-3, 4) and (5, -2). Label the center and at least four points on the circle. Write the equation of the circle.

Answers

Answer:

Equation:

[tex]{x}^{2} + {y}^{2} + 2x - 2y - 35= 0[/tex]

The point (0,-5), (0,7), (5,0) and (-7,0)also lie on this circle.

Step-by-step explanation:

We want to find the equation of a circle with a diamterhat hs endpoints at (-3, 4) and (5, -2).

The center of this circle is the midpoint of (-3, 4) and (5, -2).

We use the midpoint formula:

[tex]( \frac{x_1+x_2}{2}, \frac{y_1+y_2,}{2} )[/tex]

Plug in the points to get:

[tex]( \frac{ - 3+5}{2}, \frac{ - 2+4}{2} )[/tex]

[tex]( \frac{ -2}{2}, \frac{ 2}{2} )[/tex]

[tex]( - 1, 1)[/tex]

We find the radius of the circle using the center (-1,1) and the point (5,-2) on the circle using the distance formula:

[tex]r = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]

[tex]r = \sqrt{ {(5 - - 1)}^{2} + {( - 2- - 1)}^{2} } [/tex]

[tex]r = \sqrt{ {(6)}^{2} + {( - 1)}^{2} } [/tex]

[tex]r = \sqrt{ 36+ 1 } = \sqrt{37} [/tex]

The equation of the circle is given by:

[tex](x-h)^2 + (y-k)^2 = {r}^{2} [/tex]

Where (h,k)=(-1,1) and r=√37 is the radius

We plug in the values to get:

[tex](x- - 1)^2 + (y-1)^2 = {( \sqrt{37}) }^{2} [/tex]

[tex](x + 1)^2 + (y - 1)^2 = 37[/tex]

We expand to get:

[tex] {x}^{2} + 2x + 1 + {y}^{2} - 2y + 1 = 37[/tex]

[tex]{x}^{2} + {y}^{2} + 2x - 2y +2 - 37= 0[/tex]

[tex]{x}^{2} + {y}^{2} + 2x - 2y - 35= 0[/tex]

We want to find at least four points on this circle.

We can choose any point for x and solve for y or vice-versa

When y=0,

[tex]{x}^{2} + {0}^{2} + 2x - 2(0) - 35= 0[/tex]

[tex]{x}^{2} +2x - 35= 0[/tex]

[tex](x - 5)(x + 7) = 0[/tex]

[tex]x = 5 \: or \: x = - 7[/tex]

The point (5,0) and (-7,0) lies on the circle.

When x=0

[tex]{0}^{2} + {y}^{2} + 2(0) - 2y - 35= 0[/tex]

[tex] {y}^{2} - 2y - 35= 0[/tex]

[tex](y - 7)(y + 5) = 0[/tex]

[tex]y = 7 \: or \: y = - 5[/tex]

The point (0,-5) and (0,7) lie on this circle.

Type the correct answer in the box. For this item, any non-integer answer should be entered as a decimal rounded to the hundredths place. Statistics show that a certain soccer player has a 63% chance of missing the goal each time he shoots. If this player shoots twice, the probability that he scores a goal both times is_____ %.

Answers

Answer:

13.69%.

Step-by-step explanation:

The probability he scores in 1 shot = 1 - 0.63 = 0.37.

The probability that he scores twice in 2 shots = 0.37 * 0.37

= 0.1369

= 13.69%.

The probabilities are multiplied because the 2 events are independent.

Answer:

For plato user the answer is 13.69 %.

Step-by-step explanation:

If this player shoots twice, the probability that he scores a goal both times is  

13.69 %.

HELP ME WITH THIS QUESTION THANKS!✔✔

Answers

Answer:

-1 9/18 and then -32/40 and then 1 8/20

Step-by-step explanation:

The largest negatives is the least , then the second to least and then non-negative should be the greatest or the last

-1 9/18, -32/40, 1 8/20

PLEASE HELP!!!!!!!!!!!!

How does the graph of g(x) = −(x + 3)^4 compare to the parent function of f(x) = x^4
A) g(x) is shifted 3 units to the right and 1 unit up
B) g(x) is shifted 3 units to the right and 1 unit down
C) g(x) is shifted 3 units to the right and reflected over the x-axis
D)g(x) is shifted 3 units to the left and reflected over the x-axis
I would rlly appreciate it!!! :)

Answers

Answer: Option D

Step-by-step explanation:

If we have a main function [tex]f (x) = x ^ 4[/tex]

And we perform the transformation:

[tex]g (x) = f (x + h) = (x + h) ^ 4[/tex]

Then it is fulfilled that:

If [tex]h> 0[/tex] the graph of [tex]f(x)[/tex] moves horizontally h units to the left

If [tex]h <0[/tex] the graph of [tex]f(x)[/tex] moves horizontally h units to the right

If we have a main function [tex]f (x) = x ^ 4[/tex]

And we perform the transformation:

[tex]g (x) = -f(x) = -x ^ 4[/tex]

Then it is fulfilled that:

The graph of [tex]g(x)[/tex] is equal to the graph of [tex]f(x)[/tex] reflected on the x axis

In this case we have to:

[tex]g(x) = -(x + 3)^4[/tex] and [tex]f(x) = x^4[/tex]

Therefore [tex]h=3>0[/tex] and [tex]g(x) = -f(x)[/tex]

This mean that: g(x) is shifted 3 units to the left and reflected over the x-axis.

In 46 years Christopher will be three times as old as he is right now. How old is he right now

Answers

Answer:

23

Step-by-step explanation:

Let his current age = x

Now if you add 46 to that, you will get x + 46.

x + 46

At which point he will be 3 times as old as he is now

x + 46 = 3x            Subtract x from both sides.

x-x + 46 = 3x-x      Combine

46 = 2x                  Divide by 2

46/2=2x/2             Do the division

23 = x

He is 23 right now

===============

It might be a little easier to see if you represent the situation a little more literally.

3x - 46 = x            The answer comes to the same thing. You might think about which way you want to do it.

You are choosing 3 of your 7 trophies and arranging them in a row on a shelf.
In how many different ways can you choose and arrange the trophies?

Answers

Answer:

21

Step-by-step explanation:

you can arrange 7×3 ways

Answer with explanation:

Number of trophies possessed by me= 7

Number of trophies that is to be selected from 7 trophies =3

⇒⇒So, Chosing 3 out of 7 trophies and arranging them on a shelf requires Concept of Permutation, as order of arrangement is also taken into consideration

    [tex]=_{3}^{7}\textrm{P}\\\\=\frac{7!}{(7-3)!}\\\\=\frac{7!}{4!}\\\\=\frac{4!*5*6*7}{4!}\\\\=5*6*7\\\\=210\text{Ways}[/tex]

Or

⇒First place can be filled in 7 ways,second place can be filled in 6 ways and third place can be filled in 5 ways.

So total number of ways of selecting 3 trophies from 7 trophies

                             =7 *6 *5

                             =210 ways

Now, 3 trophies can be arranged in a shelf in 3! =3 *2*1=6 ways.

 

There are 22 participants in a spelling bee. In how many ways can the top 5 participants finish? Use the formula for permutations to find your answer

Answers

Answer:

3,160,080

Explanation:

The formula for permuations is nPk:

[tex]_nP_k=\frac{n!}{(n-k)!}=(n)(n-1)(n-2)...(n-k+1)[/tex]

Where n is the total number of elements from which you must choose combinations of k number of elements, and where the order of selection is relevant.

In this case n = 22 (the number of participants), k = 5 (the number of top participants). Since, the order in which the participants finish is relevant, then you have to use the formula of permutations, such as the question states.

Calculations:

[tex]_{22}P_5=\frac{22!}{(22-5)!}=22.21.20.19.18=3,160,080[/tex]

PLEASE ANSWER 9 and 10
GEOMETRY SOLVING FOR MISSING ANGLE

Answers

Answer:

9. 75°

10. 60°

Step-by-step explanation:

Note the angle-intercept theorem. If you create an angle in the opposite side of a circle from 2 points on other side, the arc will have a measure TWICE that of the intercepted angle created on other side.

Question 9

Arc WX has a measure 76, thus the angle created is Angle V, which should be HALF of that. So angle V is  76/2 = 38

Now looking at the triangle inside the circle, we know three angles of a triangle add up to 180, thus we can write and solve for "?" angle:

X + W + V = 180

? + 67 + 38 = 180

? + 105 = 180

? = 180 - 105 = 75°

Question 10

Using the theorem we can say that Angle B is HALF of ARC XYZ.

So,

2*Angle B = Arc XY + Arc YZ

2*102 = Arc XY + 124

204 = Arc XY + 124

Arc XY = 204 - 124 = 80°

Also, Arc BX + Arc XY is twice that of Angle Z (which is 70), thus

Arc BX + Arc XY = 70 *2

Arc BX + Arc XY = 140

Arc BX + 80 = 140

Arc BX = 140 - 80 = 60°

WILL GIVE BRAINLEST SUPER EASY A coyote can run up to 43 miles per hour while a rabbit can run up to 35 per hour. Write two equivalent expressions and then find how many more miles a coyote can run in six hours than a rabbit at these rates.

Answers

48 more miles

Coyote= 43h

Rabbit= 35h

Coyote= 43(6)= 258

Rabbit= 35(6)= 210

Now subtract 258 by 210

258-210= 48

Determine the area and perimeter of figure described:
square with sides of length 9mm​

Answers

Answer:

Perimeter= 36mm

Area= 81mm

Step-by-step explanation:

Solve the equation 25x^2+121=0

Answers

Subtract 121 from both sides:

[tex]25x^2=-121[/tex]

Divide both sides by 25:

[tex]x^2 = -\dfrac{121}{25}[/tex]

The solutions would be

[tex]x = \pm\sqrt{-\dfrac{121}{25}}[/tex]

This expression cannot be evaluated using real numbers, because the square root of negative numbers are not allowed. If we're using complex numbers, the solutions are

[tex]x = \pm\sqrt{-\dfrac{121}{25}} = \pm\dfrac{11i}{5}[/tex]

4.4.45
For the following polynomial, one zero
is given. Find the remaining zeros.
The
(Sim
to se!
P(x) = x4 + 27x^2 - 324, 6i is a zero.

Answers

Answer:

[tex](x-6i)(x+6i)(x-3)(x+3)[/tex]

Step-by-step explanation:

If 6i is a zero then -6i is a zero.

In general, if a+bi is a zero then a-bi is a zero (if the polynomial has real coefficients which this one does: 1,27,-324).

Let's test it to see:

Check [tex]x=6i[/tex]

[tex]P(6i)=(6i)^4+27(6i)^2-324\\

P(6i)=6^4(i^4)+27(6)^2(i^2)-324\\

P(6i)=1296(1)+27(6^2)(-1)-324\\

P(6i)=1296-27(36)-324\\

P(6i)=1296-972-324\\

P(6i)=1296-1296\\

P(6i)=0\\[/tex]

Check [tex]x=-6i[/tex]

[tex]P(-6i)=(-6i)^4+27(-6i)^2-324\\

P(-6i)=(6i)^4+27(6i)^2-324\\

P(-6i)=P(6i)\\

P(-6i)=0\\[/tex]

So yep they both give us 0 when we plug it in.

If x=6i is a zero then x-6i is a factor by factor theorem.

If x=-6i is a zero then x+6i is a factor by factor theorem.

What is (x-6i)(x+6i)?

Let's use the multiply conjugates formula: [tex](u-v)(u+v)=u^2-v^2[/tex].

[tex](x-6i)(x+6i)=x^2-36i^2=x^2-36(-1)=x^2+36[/tex]

Now we know [tex](x^2+36)[/tex] is a factor of [tex]x^4+27x^2-324[/tex].

We can use long division or we could try to find two numbers that multiply to be -324 and add up to be 27 since this is a quadratic in terms of [tex]x^2[/tex] with leading coefficient of 1.

Well we already know we are looking for number times 36 that would give us -324.

So -324=-9(36) and 27=-9+36

So the factored form in terms of real numbers is:

[tex](x^2+36)(x^2-9)[/tex]

We already know the first factor can be factored as (x+6i)(x-6i).

The other can factored as (x-3)(x+3) since (-3)(3)=-9 and -3+3=0.

So the complete factored form is

[tex](x-6i)(x+6i)(x-3)(x+3)[/tex].

Final answer:

To find the remaining zeros of the polynomial, we use synthetic division and find a quadratic factor. The remaining zeros are the solutions to the quadratic equation x^2 + 9 = 0, which are 3i and -3i.

Explanation:

To find the remaining zeros of the polynomial, we can use polynomial long division or synthetic division. Let's use synthetic division:



Since 6i is a zero of P(x), the conjugate -6i is also a zero. We can divide P(x) by (x - 6i)(x + 6i) to find the remaining quadratic factor.



Performing the synthetic division, we get a quadratic factor of x^2 + 9. Therefore, the remaining zeros of the polynomial are the solutions to the equation x^2 + 9 = 0.



Solving the quadratic equation x^2 + 9 = 0, we find that the remaining zeros are x = 3i and x = -3i.

Learn more about Polynomial zeros here:

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Which statement is true about lines a and b?

They are parallel lines.
They are perpendicular lines.
They are skew lines.
They will intersect.

Answers

It would be C. they are skew on ED :)

Answer: C

Step-by-step explanation: your welcome

Give the equation for a circle with the given center and radius.
Center at (4, 1), radius = 6

Answers

Answer:

(x-4)^2 + (y-1)^2 = 6^2

or

(x-4)^2 + (y-1)^2 = 36

Step-by-step explanation:

The equation for a circle is given by

(x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-4)^2 + (y-1)^2 = 6^2

or

(x-4)^2 + (y-1)^2 = 36

Answer:

(x - 4)^2 + (y - 1)^2 = 6^2

Step-by-step explanation:

Adapt the standard equation of a circle with center at (h, k) and radius r:

(x-h)^2 + (y-k)^2 = r^2

Here we have:

(x - 4)^2 + (y - 1)^2 = 6^2

Identify an equation in point-slope form for the line parallel to y = x-7 that
passes through (-3,-2).

Answers

Answer:

B. y + 2 = ½(x + 3)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, which is the reason why you see two "+" in the equation. The ordered pair of [-3, -2] has two negative numbers, therefore you need to make them both positive in the equation [see above answer].

I am joyous to assist you anytime.

what is the equation of a line that contains the point (2,-5) and is parallel to the line y=3x-4

Answers

Answer:

y = 3x - 11

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (2, - 5) into the partial equation

- 5 = 6 + c ⇒ c = - 5 - 6 = - 11

y = 3x - 11 ← equation of parallel line

the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:

y = 3x - 11

To find the equation of a line that is parallel to a given line and passes through a certain point, we need to use the concept that parallel lines have the same slope. The slope-intercept form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. Given that the line is parallel to y = 3x - 4, it will have the same slope, which is 3. Thus the slope of our new line is also 3.

We want our line to pass through the point (2, -5). Plugging these values into the slope-intercept form, we get:

-5 = 3(2) + b

which simplifies to:

-5 = 6 + b

Thus, the y-intercept b of our new line is:

-5 - 6 = b
b = -11

Therefore, the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:

y = 3x - 11

Identify the explicit function for the sequence in the table.
1 9
2 14
3 19
4 24
5 29
,
O A. a[n) = 9+ (n - 1)•5
O B. a(n) = 5 + (n - 1)•9
O.C. a[n) = 9 (n-1)
O D. a(n) = 5(n-1)

Answers

Answer:

A.

[tex]a_n=9+(n-1)\cdot 5[/tex].

Step-by-step explanation:

The common difference is 5. The y values are going up by 5. So this is an arithmetic sequence since we have a common difference.

The explicit form for arithmetic sequence is:

[tex]a_n=a_1+(n-1) \cdot d[/tex] where d represents the commom difference and [tex]a_1[/tex] is the first term.

Here the first term is [tex]a_1=9[/tex] and we already determined the value for d which is 5.

Inputing these values for first term and common difference give:

[tex]a_n=9+(n-1)\cdot 5[/tex].

Answer:

the answer is A

Step-by-step explanation:

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