If 2i is a zero of f(x)=x^4+x^2+a, find the value of a. Then find the other 3 solutions.

Answers

Answer 1

i^4 = 1

i^2 = -1

If 2i is a zero:

[tex](2i)^4+(2i)^2+a=0[/tex][tex]2^4\times i^4+2^2\times i^2+a=0[/tex][tex]16\text{ - 4 = a}[/tex][tex]a=12[/tex]

So the equation is going to be:

[tex]f(x)=x^4+x^2+12[/tex]


Related Questions

Order the intervals based on the average rates of change of the function below over theintervals. Place the interval corresponding to the greatest average rate of change on top.f(x) = x2[0, 8][2, 7][4, 6]

Answers

for a function f defined on an interval, the average rate of change is

[0,8]

[tex]AV=\frac{8^2-0^2}{8-0}=\frac{64}{8}=8[/tex]

[2,7]

[tex]AV=\frac{7^2-2^2}{7-2}=\frac{49-4}{5}=\frac{45}{5}=9[/tex]

[4,6]

[tex]AV=\frac{6^2-4^2}{6-4}=\frac{36-16}{2}=\frac{20}{2}=10[/tex]

order interval:

[4,6] [2,7] and [0,8]

I need help understanding how to convert the expressions so they can cancel out in order to achieve the answer

Answers

Recall the equivalent expression of each term.

[tex]cos\beta=\frac{x}{r}[/tex][tex]tan\beta=\frac{y}{x}[/tex][tex]csc\beta=\frac{r}{y}[/tex][tex]cot\beta=\frac{x}{y}[/tex]

Using their equivalents, we can rewrite the expression as:

[tex](\frac{x}{r})(\frac{y}{x})(\frac{r}{y})(\frac{x}{y})[/tex]

Then, multiply the variables.

[tex]\frac{x^2yr}{xy^2r}[/tex]

Then, simplify by subtracting the exponents of each respective variable. The result is:

[tex]\frac{x}{y}[/tex]

Since x/y is equivalent to cot β, then the given trigonometric expression is just equal to cot (β).

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (suchas printing). The one-time fixed costs will total $39.160. The variable costs will be $11 per book. The publisher will sell the finished product to bookstores at aprice of $24.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answers

Given:

The one-time fixed costs = $39.160.

The variable costs = $11 per book.

The price of the book = $24.75 per book.

Let x be the number of books.

The production cost of the x number of books is

[tex]=39.160+11x[/tex]

The sales price of the x number of books is

[tex]=24.75x[/tex]

Given that the production cost = the sales cost.

[tex]=39.160+11x[/tex]

Write fractions for points A and B on the number line

Answers

Given: The line from 0 to 1 is divided in 6 parts and has two points. A and B marked on it.

To find:The fraction for point A and B.

Explanation: The length from 0 to 1 is divided into 6 parts.

Therefore, the length of one part will be 1/6.

The point A is markes at the second division.

Since, 1 division= 1/6

therefore, 2 divisions will be = 2x(1/6)

Therefore, the point A will correspond to the fraction

[tex]\begin{gathered} A=2\times\frac{1}{6} \\ =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}[/tex]

Now the next pint B lets count its division.

It is marked at the fifth division.

Therefore, the fraction representing B can be written as:

[tex]\begin{gathered} B=5\times(1\text{ division\rparen} \\ =5\times\frac{1}{6} \\ =\frac{5}{6} \end{gathered}[/tex]

Therefore, the point B can be represented as 5/6.

Final answer : Point A = 1/3

and point B = 5/6.

x is an acute angle. Find the value of x in degrees. cos (x)= 0.8

Answers

So, given:

The answer is 36.87°.

Runner #1's distance (in miles) with time (in minutes) is d= 1/15t.What is the Pace of the runner?Runner 1 is going 1 mile per ____ min.

Answers

The given equation is

[tex]d=\frac{1}{15}t[/tex]

Remember that the coefficient of the variable represents the range of change.

hence, the pace of the runner is 1 miler per 15 minutes.

Rosanne has $9,716 in a savings account. The interest rate is 4%, compounded annually.To the nearest cent, how much will she have in 2 years?

Answers

To answer this question, we will use the following formula for annually compounded interest:

[tex]F=A(1+r)^t,[/tex]

where A is the initial amount, r is the interest rate in decimal form, and t is the time in years.

Substituting A=9716, r=0.04, and t=2, we get:

[tex]F=9716(1+0.04)^2.[/tex]

Simplifying the above result, we get:

[tex]F=9716(1.04)^2=10508.83[/tex]

dollars.

Answer: $10508.83

The area of Seth's bedroom is 1/2 of the area of his mom's living room. Seth also has a closet with an area of 12 square feet. If the total area Seth has at his disposal is 132 square feet, what is the area of the living room?

Answers

Let S be the area of Seth's bedroom and let M be the area of his mom's living room.

Let's first set-up the e

From the question, "The area of Seth's bedroom is 1/2 of the area of his mom's living room" can be written mathematically as;

S = 1/2 M ---------------------------------------------(1)

Also, "the total area Seth has at his disposal is 132 square feet" implies;

S + 12 = 132 -----------------------------------------------------(2)

Find an ordered pair(X, Y) that is a solution to the equationX minus 5Y equals five

Answers

To solve this problem, the first step is to find the slope intercept form of the equation:

[tex]\begin{gathered} x-5y=5 \\ 5y+5=x \\ 5y=x-5 \\ y=\frac{1}{5}x-1 \end{gathered}[/tex]

Now, use a random value of x and find y, for example in this case we can use x=5 :

[tex]\begin{gathered} y=\frac{1}{5}(5)-1 \\ y=1-1 \\ y=0 \end{gathered}[/tex]

The ordered pair that is a solution for the given equation is (5,0).

list the sides in order from largest to shortest JKL

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

∠ J = 71

∠ K = 41

∠ L = 68

sides from largest to shortest = ?

Step 02:

We must apply relationship between sides and angles.

The sides from largest to shortest :

1 . ∠ J = 71 ===> side KL

2. ∠ L = 68 ===> side JK

3. ∠ K = 41 ===> side JL

This is the solution.

KL , JK , JL

Question 7-8 Work doesn’t have to be shown just an short explanation.

Answers

Step 1

Given;

[tex]\begin{gathered} \text{Two points;} \\ (1,2) \\ (-3,-4) \\ \text{where } \\ x_1=1 \\ x_2=-3 \\ y_1=2 \\ y_2=-4 \end{gathered}[/tex]

Required; To find the slope

Step 2

State the formula for the slope of a line and find the slope on the line in question 7

[tex]\begin{gathered} m=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-4-2}{-3-1}=\frac{-6}{-4}=\frac{3}{2} \end{gathered}[/tex]

Hence, the slope of the line = 3/2

|In8Word problem on unit rates associated with ratios of fractions1days, a construction crew built miles of road.4What is the unit rate in miles per day?Write your answer in simplest form.miles per dayI need help solving this problem

Answers

ANSWER :

2 miles per day

EXPLANATION :

In 1/8 day, they finished 1/4 miles of the road.

We just need to divide the work done by the time to get the rate :

[tex]\frac{1}{4}\div\frac{1}{8}[/tex]

Division can be expressed as multiplication by taking the reciprocal of the divisor.

That will be :

[tex]\frac{1}{4}\times\frac{8}{1}=2[/tex]

write the first four terms of a decreasing arithmetic sequence. use this to describe, in your own words, how to write the formula for the sequence. then use the formula to calculate the 20th term. show all work

Answers

Answer:

The 20th term = -34

Explanation:

An arithmetic sequence is one which has a common difference.

For example, the sequence below has a common difference of -2, and first term of 4

4, 2, 0, -2........

The first term, a = 4

The common difference, d = 2 - 4 = -2

The formula for nth term of an arithmetic sequence

[tex]\begin{gathered} a_n=a+(n-1)d \\ \\ a_n=4+(n-1)(-2) \\ \\ a_n=4-2n+2 \\ \\ a_n=6-2n \end{gathered}[/tex]

The 20th term is:

[tex]\begin{gathered} a_{20}=6-2(20) \\ \\ a_{20}=6-40 \\ \\ a_{20}=-34 \end{gathered}[/tex]

The 20th term = -34

Determine the exact value of cos 135 degrees and explain how you knew to use the side lengths you used

Answers

Explanation

We are required to determine the exact value of cos 135°.

Since the angle lies in the second quadrant, we have:

[tex]\begin{gathered} \cos135\degree=\cos(180\degree-45\degree) \\ \cos135\degree=-\cos45\degree \end{gathered}[/tex]

To determine the value of x, we have:

[tex]\begin{gathered} \text{ Using the Pythagorean theorem,} \\ x^2=1^2+1^2 \\ x=\sqrt{1^2+1^2} \\ x=\sqrt{1+1} \\ x=\sqrt{2} \end{gathered}[/tex]

Therefore, the value of cos 135° is:

[tex]\begin{gathered} \text{ We know that }cos\theta=\frac{adj}{hyp} \\ \therefore\cos135\degree=-\cos45\degree=-\frac{1}{\sqrt{2}} \\ \cos135\degree=-\frac{1}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}} \\ \cos135\degree=-\frac{\sqrt{2}}{2} \end{gathered}[/tex]

Hence, the answer is:

[tex]\cos(135)\operatorname{\degree}=-\frac{\sqrt{2}}{2}[/tex]

The lengths used is the lowest length of sides that can be used.

Linda goes for a run every day after school, but she likes to make some workouts easier than others. On Monday, Linda ran 3.5 miles in 35 minutes. On Tuesday, she ran 3 miles in 40 minutes. On which day did Linda run at a faster pace? Monday Tuesday Submit

Answers

1) Gathering the data

Monday 3.5 miles in 35 minutes

Tuesday 3 miles in 40 minutes

Faster pace?

2) To find out the pace let's calculate the average speed.

And we can find it by a formula:

Average Speed on Monday = 3.5 / 35 =0.1 miles per minute

Average speed on Tuesday = 3 / 40 = 0.075 miles per minute

So, Linda runs on Monday at a faster pace.

---------

Spencer Fuel Stop (cheaper) Gas World

Saturday

Sunday

Since at Fuel Stop the gasoline is cheaper than at Gas World, then Spencer will be able to buy more gas at Fuel Stop with his $20 than at the Gas world

The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 132° arc?Give the exact answer in simplest form. ____ square kilometers. (pi, fraction,)

Answers

To find the area of the sector we will use

[tex]A=\frac{L\cdot r}{2}[/tex]

Where L is

[tex]\begin{gathered} L=\frac{2\cdot\pi\cdot6\text{ km}}{360^{\circ}}\cdot132^{\circ} \\ L=\frac{132\pi\text{ km}}{30}=\frac{66\pi\text{ km}}{15}=\frac{22\pi\text{ km}}{5} \end{gathered}[/tex]

Finally, we must replace L and r in the intial equation

[tex]A=\frac{\frac{22\pi\text{ km}}{5}\cdot6\operatorname{km}}{2}=\frac{\frac{132\pi\text{ km2}}{5}}{2}=\frac{132\pi\text{ km2}}{10}=\frac{66\pi}{5}km^2[/tex]

Find the equation that represents the proportional relationship in this graph, for y in terms of x.

Answers

Answer:

2x=y

Step-by-step explanation:

0.2/0.1 using rise over run method

2x=y

Please mark brainliest and comment if you need more explanation

Find the real or imaginary solutions solutions of the following equation by factoring. y^3-512=0Choose the correct answer below.

Answers

B

1) The best way to tackle this question is to think of the difference between two cubes:

[tex]x^3-y^3=(x-y)(x^2+xy+y^2)[/tex]

2) So now, let's apply to the binomial we have:

[tex]\begin{gathered} \sqrt[3]{512}=8 \\ y^3-512=(y-8)(y^2+8y+64) \end{gathered}[/tex]

So now, let's make use of the factor zero property for the first factor and solve the quadratic using the quadratic formula:

[tex]\begin{gathered} y-8=0,y=8 \\ \\ y_=\frac{-8\pm\sqrt{8^2-4\cdot\:1\cdot\:64}}{2} \\ y_1=\frac{-8+8\sqrt{3}i}{2}=\quad4+4\sqrt{3}i \\ y_2=\frac{-8-8\sqrt{3}i}{2}=\quad-4-4\sqrt{3}i \end{gathered}[/tex]

3) Thus, the answer is:

B

The length of a photograph of Mr. Lemley playing golf is 1 4/5 inches. If the area of the photo is 33/20 square inches, what is the width of the photograph? * Your answer

Answers

Take into account that the area of a rectangular shape, is given by the following formula:

A = l·w

w: width = ?

l: length = 1 4/5 in

A: area = 33/20 in²

In order to determine the width of the photo, solve the previous formula for w:

w = A/l

convert 1 4/5 to a normal fraction:

1 4/5 = (5 + 4)/5 = 9/5

replace the values of A and l into the expression for w:

w = (33/20)/(9/5)

w = 165/180

simplify the previos fraction:

w = 165/180 = 33/36 = 11/12

Hence, the width of the photograp is 11/12 in

How do I find the zeros using synthetic division when the highest degree is 4

Answers

Answer:

Explanation:

Given f(x) defined below:

[tex]f\mleft(x\mright)=x^4-11x^3+40x^2-48x[/tex]

To find the zeros, set f(x) equal to 0.

[tex]x^4-11x^3+40x^2-48x=0[/tex]

First, observe that we can factor out x.

[tex]\begin{gathered} x(x^3-11x^2+40x-48)=0 \\ \implies x=0\text{ or }x^3-11x^2+40x-48=0 \end{gathered}[/tex]

Given that x=3 is a zero of the function, we divide using synthetic division to find the other factors.

If ABCD is dilated by a factor of 3, thecoordinate of B' would be:5С43B.21-5 4 3-2 -1 012345-1-2DB' = ([?],[])-3

Answers

First, find coordinate B.

B= ( -2,2 )

Multiply each coordinate by the dilation factor 1/2

B'= ( -2 * 1/2 , 2 * 1/2 )

B'= ( -1, 1 )

A figure is shownselect all the statements that are true

Answers

Vertical angles are the opposite angles when a "X" (cross) is formed.

They are equal.

Adjacent angles are angles next to one another. They add to 180 degrees.

Complementary angles are angles that add to 90 degrees.

From the figure, we can say the following:

• B and C are vertical angles

,

• A and D are vertical angles

,

• A and B are adjacent angles

,

• B and D are adjacent angles

,

• D and C are adjacent angles

,

• C and A are adjacent angles

The first statement is false. Since C is vertical angles to B, it should be equal to B, 50 degrees.

The second statement is true. Since B and D are adjacent angles, 50 + D = 180, So, D = 130.

Third statement is true. B and C are vertical angles.

Fourth statement is false. B and C are not adjacent angles, they are vertical.

Fifth statement is true. B and D are adjacent angles.

Sixth statement is false. B and A aren't complementary. They are rather supplementary (two angles that add to 180 degrees).

Thus,

The true statements are:

2nd

3rd

5th

Describe the effect of the transformation on (x,y) and describe the transformation in words: (x, y) → ( )

Answers

The effect of the transformation on (x,y) , it will make a similar images but at different coordinates of x and y , as shown in the image, two similar figures but at different places

To describe the given transformation, at first, we need to find the rule of transformation

Take the point as a reference and find its image

Let the point is the vertex of the image which is (1 , 2 )

the image of the point is ( 3 , 1 )

So, x coordinates changed from 1 to 3, which mean the image moved 2 units to the right

And, y- coordinates changed from 2 to 1, which mean the image moved 1 units down

So, the desciption of the transformation is:

The total image moved 2 units right and 1 unit down

graph the equation y equals 4x - 5 by plotting points

Answers

Given the equation:

y = 4x - 5

Use the slope intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

To plot the points, first make a point on the y-intercept, y = -5

At y-intercept, x = 0.

Thus, we have the point (0, -5)

Let's find the value of y, when x = 1.

y = 4(-1) -5

y = 4 - 5 =

y = -1

When x = 1, y = -1

We have the point (1, -1)

When x = 2

y = 4(2) - 5

y = 8 - 5

y = 3

When x = 2, y = 3

We have the point (2, 3)

Thus, mark the following points:

(0, -5)

(1, -1)

(2, 3)

Then connect the plotted points with a straight line.

We have the graph attached below:

what's the domain of [tex] \frac{5x}{6 - 4x} [/tex]

Answers

SOLUTION

A fraction will be undefined when its denominator is zero.

The given function will be undefined when

[tex]\begin{gathered} 6-4x=0 \\ 4x=6 \\ x=\frac{6}{4} \\ x=\frac{3}{2} \end{gathered}[/tex]

The function will be defined at all point except when x=3/2

The domain of a function refers to all possible values of x on which the function is defined.

This is given as ;

1) Find perimeter and area of a rectangle with width 7 in and length 12 in. P = A found the decimeter of a square wi with area 64 cm?

Answers

To solve the exercise, let us first draw the rectangle:

The formula to find the area of ​​a rectangle is

[tex]\begin{gathered} A=l\cdot w \\ \text{ Where } \\ A\text{ is the area,} \\ l\text{ is the length and} \\ w\text{ is the width of the rectangle} \end{gathered}[/tex]

So, in this case, you have

[tex]\begin{gathered} l=12\text{ in} \\ w=7\text{ in} \\ A=l\cdot w \\ A=12\text{ in}\cdot7\text{ in} \\ A=84in^2 \end{gathered}[/tex]

On the other hand, the perimeter is the sum of all the sides of a geometric figure. Then, in this case, you have

[tex]\begin{gathered} P=12\text{ in }+7\text{ in }+12\text{ in }+7\text{ in} \\ P=38\text{ in} \end{gathered}[/tex]

Therefore, the perimeter and area of this rectangle are:

[tex]\begin{gathered} A=84in^2 \\ P=38\text{ in} \end{gathered}[/tex]

What are the factors after you do yhr 4th step?

Answers

Here given that

[tex](x-\frac{2}{3})(x+\frac{9}{3})[/tex]

Further simplification we have to take lcm first

[tex](\frac{3x}{3}-\frac{2}{3})(\frac{3x}{3}+\frac{9}{3})=\frac{(3x-2)}{3}\times\frac{(3x+9)}{3}=\frac{(3x-2)(3x+9)}{9}[/tex]

Also

So finally we get the factors are

[tex](3x-2)(3x+9)[/tex]

Refer to the figure below. Then find the indicated values:A) f(7)B) g(0) + f(3)C) f(g(7))D) g(f(8))E) x if f(x) =2

Answers

Given the graph in the image question, it can be seen that:

[tex]\begin{gathered} y=f(x) \\ y=g(x) \end{gathered}[/tex]

To answer the questions, we have:

a. f(7)

[tex]f(7)=1[/tex]

b. g(0)+f(3)

[tex]\begin{gathered} g(0)=6 \\ f(3)=-1 \\ g(0)+f(3)=6+(-1)_{} \\ =6-1 \\ =5 \end{gathered}[/tex]

c. f(g(7))

[tex]\begin{gathered} We\text{ do }g(7)\text{ first and then do the f(x) of the result:} \\ g(7)=6 \\ f(g(7))=f(6) \\ =1 \end{gathered}[/tex]

d. g(f(8))

[tex]\begin{gathered} We\text{ do f}(8)\text{ first and then do the f(x) of the result:} \\ f(8)=1 \\ g(f(8))=g(1) \\ =6 \end{gathered}[/tex]

e. x if f(x)=2

[tex]\begin{gathered} f(x)=2 \\ \text{ To get }f(x),\text{ we look at the point 2 on the y axis and trace it to x} \\ f(x)=2\text{ at point }-7\text{ on the x axis} \\ \text{Hence, x=-7} \end{gathered}[/tex]

Find a translation that has the same effect as the composition of translations below. T(5.1) (x,y) followed by T-3,7) (x,y) T Choose the correct answer below. O A. (x,y) → (X + 8.y-6) O B. (x,y)(x+2.y-6) O C. (x,y)-(x + 2.y + 8) O D. (x,y)--(X + 8.y + 8)

Answers

Answer

Option C is correct.

Explanation

The translation T (a, b) changes the coordinates A (x, y) into A (x + a, y + b).

So, a translation of T (5, 1) followed by T (-3, 7) becomes a single translation of

T (5 - 3, 1 + 7) = T (2, 8)

And this would turn A (x, y) into A' (x + 2, y + 8).

Hope this Helps!!!

lake Question Find the value of x to the nearest degree. 8 4 Not drawn to scale 59 b. 63 54 d. 27 A

Answers

We can relate the sides and the angle of right triangles with trigonometric ratios.

In this case, we can write:

[tex]\begin{gathered} \tan (x)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{8}{4}=2 \\ x=\arctan (2)\approx63\degree \end{gathered}[/tex]

Answer: x = 63°

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