What is the completely factored form of x4 + 8x2 – 9?

Answers

Answer 1

ANSWER

[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]

EXPLANATION

The given function is

[tex] {x}^{4} + 8 {x}^{2} - 9[/tex]

Split the middle term

[tex] {x}^{4} + 9 {x}^{2} - {x}^{2} - 9[/tex]

Factor by grouping;

[tex]{x}^{2} ( {x}^{2} + 9) -1 ({x}^{2} + 9)[/tex]

Factor further to get:

[tex] ( {x}^{2} + 9)({x}^{2} - 1)[/tex]

Apply difference of two squares to get:

[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]

Answer 2

Answer:

[tex](x^2+9)(x-1)(x+1)[/tex]

Step-by-step explanation:

We would need to let u = x^2 and use middle term factorization first. let's do this:

if u = x^2, then x^4 + 8x^2 – 9 would be

u^2+8u-9

Middle term factorization of this is:

(u+9)(u-1)

now replacing back u = x^2:

(x^2+9)(x^2-1)

Using the formula a^2 - b^2 = (a+b)(a-b), we can write (x^2 - 1) as (x+1)(x-1).

So, the final factored form is:  (x^2+9)(x-1)(x+1)


Related Questions

what is 2/5 of 255???

Answers

Answer:

102

Step-by-step explanation:

Answer:

102.

Step-by-step explanation:

First, divide 255 by 5 (255÷5=51).

Then multiply the result of 255÷5 by 2 (51×2)

And 51×2=102

How does the a value affect your sine graph?

Answers

Answer:

Changing value of "a" changes the amplitude of the sine graph.

Step-by-step explanation:

Question says to find about how does the a value affect your sine graph.

General equation of sine function can be given as:

[tex]y=a\cdot\sin\left(b\left(x-h\right)\right)+k[/tex]

There value of "a" gives amplitude.

So changing value of "a" changes the amplitude of the sine graph.

What’s the distance between (-3,-22) and (-13,-23)

Answers

Answer:

d = sqrt(101)

Step-by-step explanation:

To find the distance between two points, we use the formula

d =sqrt ((x2-x1)^2 + (y2-y1)^2)  where (x1,y1) and (x2,x2) are the points

d = sqrt ((-13--3)^2 + (-23--22)^2)

d = sqrt ((-13+3)^2 + (-23+22)^2)

d = sqrt((-10)^2 + (-1)^2)

d = sqrt(100)+1)

d = sqrt(101)

Use the correct order of operations to solve the problem below. 8 × 9 + 12 ÷ 4 - (5 + 3)

Answers

8•9+12\4-(5+3)

We are gonna use the method PEMDAS (Parenthesis, Exponents, Multiplication/Division, Addition/ Subtraction) to help us solve this equation.

8•9+12/4-8

72+12/4-8

72+3-8

75-8

67

Final answer:

To solve the equation 8 × 9 + 12 ÷ 4 - (5 + 3), apply the order of operations (BIDMAS/PEMDAS): Brackets, Indices, Division/Multiplication (left to right), Addition/Subtraction (left to right). The final answer is 67.

Explanation:

The subject of this question is Mathematics and it pertains to the correct order of operations. To solve the provided equation, 8 × 9 + 12 ÷ 4 - (5 + 3), we must follow the order of operations which is popularly known as BIDMAS or PEMDAS. This acronym stands for:

Brackets(or Parentheses in the PEMDAS variant)Indices (or Exponents)Division and Multiplication(in order from left to right)Addition and Subtraction(in order from left to right).

Here, we proceed by doing the operations within the brackets. (5+3) equals 8. Now, substitute 8 in the expression and we get 8 × 9 + 12 ÷ 4 - 8. Now according to BIDMAS/PEMDAS, the next step is to do multiplication and division from left to right. The expression now becomes 72 + 3 - 8. Finally, we do addition and subtraction from left to right, so the final result is 67.

Learn more about Order of Operations here:

https://brainly.com/question/15840745

#SPJ3

I need help with solving the equation

2x - 5 = x - 7

and i need the steps to solve the problem

Answers

2x - 5 = x - 7

First, let's subtract x from both sides:

2x - x - 5 = x - x - 7

x - 5 = -7

Now, let's add 5 to both sides:

x - 5 + 5 = -7 + 5

x = -2

Answer:

x = -2

Step-by-step explanation:

2x - 5 = x - 7

2x - x - 5 = -7

2x - x = -7 + 5

Now we have isolated x

2x - x = 5 - 7

2x - x = -2

x = -2

What is the classification for this polynomial 4uv2w2

Answers

Answer:

The polynomial 4uv²w²  is a monomial, since its a single term.

Degree of polynomial: it is sum of exponent of its variables.

power of u = 1, power of v = 2, power of w = 2

Degree of polynomial: 5

A piece of machinery valued at $250,000 depreciates at 12% per year by the fixed rate method. After how many years will the value have depreciated to 100,000

Answers

Answer:

6.7 years (approx)

Step-by-step explanation:

What is the missing value in the equation shown □ x1/10=0.034

Answers

Answer:

0.34

Step-by-step explanation:

Do the inverse operation so;

0.034 / 1/10 = 0.34

Now go back and subsitute,

0.34 * 1/10 = 0.034

Final answer:

In the equation □ x 1/10 = 0.034, the missing value is 0.34 as obtained by isolating □ on one side, i.e., □ = 0.34.

Explanation:

The equation presented in the question is □ x 1/10 = 0.034. The missing value is the number that should be multiplied by 1/10 to result in 0.034. To solve for this missing value, we can rearrange the equation using the basic algebraic method. We isolate the missing value (□) on one side by dividing both sides of the equation by 1/10. This results in □ = 0.034 / (1/10), which simplifies further to □ = 0.34. Therefore, the missing value in the equation □ x 1/10 = 0.034 is 0.34.

Learn more about Equation Solving here:

https://brainly.com/question/19297665

#SPJ3

A bookshop has a sale.
A book normally costing $39.95 is priced at $23.97.
By what percentage has the price been reduced?

please show working out

Answers

Answer:

The price been reduced by a percentage of 40%

Step-by-step explanation:

we know that

$39.95 -----> represent the 100%

so

The difference of prices is equal to ($39.95-$23.97)=$15.98

Using proportion

Find the percentage of the difference

100/39.95=x/15.98

x=100*15.98/39.95

x=40%

Answer:

40% is the percentage decreased.

Hope it helped!

Thanks.

Based on the graph how many real nunber solutions does x^3+6x^2+8=0 have ?

Answers

Answer:

ONE

Step-by-step explanation:

ONE real number solution.  The graph intersects the x-axis in only one place.

PLEASE HELP DETAILS ARE BELOW I WILL RATE BRAINIEST CHORD AND ARCS FIND THE MEASURE OF ARC CD DETAILS BELOW

Answers

Wouldn’t it be 36.7 because that’s the arch am I right?

Answer:

The measure of arc CD is 114.6°.

Step-by-step explanation:

Let the center of the circle be O and OP is perpendicular to CD at point point P.

The perpendicular line from the center of circle divide each chord in two equal parts. so, CP=DP.

[tex]CP=\frac{CD}{2}=\frac{36.7}{2}=18.35[/tex]

In a right angles triangle,

[tex]\sin\theta =\frac{opposite}{hypotenuse}[/tex]

In a right angles triangle OPC,

[tex]\sin\angle POC =\frac{18.35}{21.8}[/tex]

[tex]\angle POC =\sin^{-1} (\frac{18.35}{21.8})[/tex]

[tex]\angle POC \approx 57.3[/tex]

In triangle OPC and OPD,

[tex]OC=OD[/tex]                  (Radius)

[tex]OP=OP[/tex]                  (Reflexive property)

[tex]CP=DP[/tex]                   (Altitude on chord from center)

By SSS postulate

[tex]\triangle OPC\cong \triangle OPD[/tex]

[tex]\angle POC\cong \angle POD[/tex]                      (CPCTC)

[tex]\angle POC=\angle POD[/tex]

The measure of angle COD is

[tex]\angle COD=\angle POC+\angle POD[/tex]

[tex]\angle COD=2\angle POC[/tex]

[tex]\angle COD=2(57.3)[/tex]

[tex]\angle COD=114.6[/tex]

Therefore the measure of arc CD is 114.6°.

Which expression is equivalent to (-3y-x)-(5y-8x)

A.-8y-8x
B.-8y+7x
C.2y-7x
D.8y+8x

Answers

Multiply the negative sign into the second bracket and get rid of both brackets

-3y-x-5y+8x

Collect like terms

-8y+7x

Answer:

B:  -8y + 7x

Step-by-step explanation:

Start with (-3y-x)-(5y-8x).  This is a subtraction problem.  Subtract 5y from -3y, obtaining -8y.  Next, subtract -8x from -x; this is equivalent to  -x - (-8x), or 7x.

Then the difference -x + 8x = 7x.

Combining the x and y results, we get   B:  -8y + 7x.

The truck lot has 274 eighteen wheelers and 89 regular trucks. How many wheels are in the parking lot?
Put a equation please c: thank you

Answers

Answer=5288

Step-by-step explanation: I got it know so basically (18*274) + (89*4) which equals 4932+356=5288

Answer:

5288 wheels

Step-by-step explanation:

Wheel count:  18(274) + 89(4) (since regular trucks have 4 wheels)

This comes to 4932 + 356, or 5288 wheels in the lot.

ILL GIVE BRANLIEST!!!
What value of g makes the equation true? (X+7)(x-4)=x^2+gc-28

Answers

Answer:

The left side is not equal to the right side, which means that the given statement is false.

False

Step-by-step explanation:

Answer: g= 3x/c

Not sure if this helps

Mr Johnson, the store owner, ordered 48 boxes of jawbreakers. Each box contained 392 pieces of candy. How many lawbreakers did Mr. Johnson order?​

Answers

Answer:

Mr. Johnson would have ordered 18816 jaw breakers.

Step-by-step explanation:

Multiply 392 by 48

Mr. Johnson ordered a total of 18816 jawbreakers by multiplying the number of boxes (48) by the number of pieces of candy per box (392).

The question involves calculating the total number of jawbreakers Mr. Johnson ordered. To do this, we need to multiply the number of boxes ordered by the number of pieces of candy per box.

Step-by-step calculation:

Identify the number of boxes ordered: 48 boxes.

Identify the number of candies per box: 392 pieces.

Multiply the number of boxes by the number of candies per box to find the total: 48 boxes × 392 pieces/box = 18816 jawbreakers.

Therefore, Mr. Johnson ordered a total of 18816 jawbreakers.

Marco buys a certain brand of shampoo for a supplier $7.25 per bottle he sells it to his customers at a makeup 25% what would the makeup be

Answers

Answer:

Markup= 1.81

Sale price =9.06

Step-by-step explanation:

The markup is the original prices times the markup rate

markup = 7.25 * 25%

            = 7.25 * .25

             =1.8125

We round this to the nearest cent

           =1.81

The new sale price will be the original price + the markup

7.25+1.81

9.06

Answer:

9.06, or real explanation.

Step-by-step explanation:

"Marco buys a certain brand of shampoo for a supplier $7.25 per bottle he sells it to his customers at a makeup 25% what would the makeup be"

I am going to assume makeup is supposed to be markup, but I will answer all there is.

To find how much higher he charges people for the shampoo, we can multiply the original cost by the percent of increase, so in our case 7.25*.25

7.25*.25=1.8125, or $1.81

1.8125 is the total extra he charges people for the soap.

NOW FOR THE TOTAL COST-------------------

For the total cost we take the original + the added cost

1.8125+7.25=9.0625, or 9.06

The total cost of a dress,including tax, was $121.37. If 6% tax was added to the sale price, what was the sale price before taxes?

Answers

Answer:

We have

sale price + 6% x sale price = $121.37;

Then

(106/100) x sale price = $121.37;

sale price = $121.37 x 100 / 106;

sale price = $12137 / 106;

sale price = $114.50;

Step-by-step explanation:

To find the sale price of a dress before a 6% tax added up to a total of $121.37, divide the total by 1.06. The original sale price was $114.50.

The student is asking how to calculate the sale price of a dress before tax when the total cost, including a 6% tax, was $121.37. To find the sale price before taxes, you need to divide the total cost by 1 plus the tax rate expressed as a decimal.

First, convert the percentage to a decimal, which gives us 0.06 for a 6% tax. Then, add 1 to the tax rate (1 + 0.06 = 1.06) and divide the total cost by this sum to get the original price:

Sale price = Total cost / (1 + Tax rate)
Sale price = $121.37 / 1.06
Sale price = $114.50 (rounded to the nearest penny)

Therefore, the original sale price of the dress was $114.50.

Match the expression with its
name.

9x^4-3x+4

A. Quadratic monomial
B. Not a polynomial
C. Cubic binomial
D. Fourth-degree trinomial

Answers

Answer:

D. Fourth-degree trinomial

Step-by-step explanation:

I think this would be the correct answer because the highest degree the polynomial is raised to would be 4 (hence the fourth degree). It would be a trinomial because of 9x^4, 3x, and 4

The ratio of roses to daisies is 8 roses to 6 daisies.
If there are 16 roses, how many daisies are there?

Answers

12 Roses since your multiplying by 2

Answer:12

Step-by-step explanation: there are 8 roses and 6 daisies, if 8 turns into 16, that’s multiplied by 2, so you multiply 6 by 2 and get 12,

8 * 6

_ * _

16*X, cross multiply

Which matrix is equal to... (picture added)

Answers

Answer:

D [tex]\left[\begin{array}{ccc}-6&-6.5&1.7\\-2&-8.5&19.3\end{array}\right][/tex]

Step-by-step explanation:

Two matrices are equal when they

have the same sizes (so options A and B are false)have equal corresponding elements (so option C is false, because -6≠6, -6.5≠6.5, 1.7≠-1.7 and so on)

If in option D the second row is 2  -8.5  19.3 , then these matrix is equal to the given.

Answer:

Its D on edge

Step-by-step explanation:

In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = x - 16?

Answers

Answer: Option C.

Step-by-step explanation:

The equation of the line in slope-intercept form is:

[tex]y=mx+b[/tex]

Where the slope is "m" and the intersection of the line with the y-axis is "b".

Given the function f(x) in the form [tex]f(x)=x[/tex], you can identify that:

[tex]m=1\\b=0[/tex]

This means that the line passes through the origin (0,0)

And from the function g(x) in the form [tex]g(x)=x-16[/tex], , you can identify that:

[tex]m=1\\b=-16[/tex]

This means that the line of the function g(x) and the line of the function f(x) have the same slope, but the line of g(x) passes through the point (0,-16)

Therefore, the graph of f(x) must be shifted 16 units down to produce the graph of g(x)

Find the unknown: 4:2:3 = x : 18: 27​

Answers

Final answer:

To find the unknown values in the given ratios, solve for x by setting up proportions and using cross-multiplication to calculate the missing value.

Explanation:

Find the unknown: 4:2:3 = x : 18: 27

Calculate the ratio of the known values: 4/2 = 2, and 3/2 = 1.5.Set up the proportion: 2 = x/18 and 1.5 = x/27.Solve for x by cross-multiplication: x = 36 for the first ratio and x = 40.5 for the second ratio.

Which statement is true?
is not a logarithmic function because the base is greater than 0.
is not a logarithmic function because the base is a square root.
is not a logarithmic function because the base is equal to 1.
is not a logarithmic function because the base is a fraction.

Answers

3 is correct , base is never equal to 1 cause all of solves of logarithm will be 0

Answer with explanation:

Consider a Logarithmic Function

  [tex]y=\log_{a} b\\\\y=\frac{\log b}{\log a}\\\\ \text{if, a=1,then}\\\\y=\frac{\log b}{\log 1}\\\\y=\frac{\log b}{0}[/tex]

which is not defined.

Also,⇒ a∈(0,∞)≠1.

b> 0, that is, b∈(0,∞)

Option C:

 is not a logarithmic function because the base is equal to 1.

when is a sequence geometric

Answers

I also think its A cause you find the next term when your multiply the constant (common ratio) so it makes sense for it to be A

Answer:

when each term is multipled by the same number to get the next number

Step-by-step explanation:

[tex]\text{A geometric sequence:}\\\\a_1,\ a_2,\ a_3,\ a_4,\ ....\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}=r=constant\\\\r-\text{common ratio}\\\\a_2=a_1r\\a_3=a_2r\\a_4=a_3r\\\vdots\\a_n=a_{n-1}r\\\\\text{next term is created from the previous one by multiplying it}\\\text{by the same number}[/tex]

Find the slope intercept form of the equation for the line that goes through (3, 5) and is parallel to y=5x - 1.

Answers

Answer:

y=5x-10

Step-by-step explanation:

slope intercept form is y=mx+b

since we know it is parallel to y=5x-1, we know that it has the same slope of 5.

So, we plug it in:

y=mx+b

y=5

x=3

(taken from point (3,5))

m=5

(taken from parallel line)

5=(5)(3)+b

5=15+b

b=-10

The equation would be y=5x-10

there are two cubes. the smaller cube has a surface area of 24 square units. the larger cube has a surface area that is twice that of the smaller cube. what is the volume, in cubic units, of the larger cube?​

Answers

24 times 2 which will be 48

Find the angle between u = i+sqr of 7j and v = -i+9j. Round to the nearest tenth of a degree.

Answers

[tex]\bf ~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\stackrel{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} u=i+\sqrt{7}j\implies &<1,\sqrt{7}>\\\\ v=-i+9j\implies &<-1,9> \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf u\cdot v\implies (1)(-1)~+~(\sqrt{7})(9)\implies -1+9\sqrt{7}\implies 9\sqrt{7}-1~\hfill dot~product \\\\[-0.35em] ~\dotfill\\\\ ||u||\implies \sqrt{1^2+(\sqrt{7})^2}\implies \sqrt{1+7}\implies \sqrt{8}~\hfill magnitudes \\\\\\ ||v||\implies \sqrt{(-1)^2+9^2}\implies \sqrt{1+81}\implies \sqrt{82} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{8}\cdot \sqrt{82}} \right)\implies \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{656}} \right) \\\\\\ \theta \approx cos^{-1}(0.8906496638868531)\implies \theta \approx 27.05[/tex]

make sure your calculator is in Degree mode.

If the arithmetic pattern shown continues, what will be the 8th number?

54, 48, 42, 36, ...

Answers

Each time, you are subtracting 6 to get to the next term. The 8th term would be 12.

the graph of a function never has two diferent points with the same x coordinate because ​

Answers

It is undefined, meaning it will not pass the vertical line test

The number line is a graph of the

Answers

Answer: real numbers?

Step-by-step explanation:

Answer:

The number line is graph of the or can be graph of any of the following set of numbers.

  1. Natural numbers

  2. Whole numbers

  3. Integers

  4.Rational Numbers

   5.Irrational numbers

   6. Real numbers

We can represent all this set of numbers on the graph of number line.

Other Questions
Apply A hydrate contains 0.050 mol of H,O for every0.00998 mol of ionic compound. Write a generalizedformula of the hydrate. please help me with these two history questionsan image is attached find a polynomial with zeros at x=2,x=-1 and x=0 The diameter of a circle is 6 units what is the radius of the circle Josh leans the ladder against a side of her house which is 10 feet. If the base of the latter is 3 feet away from the house, how tall is the ladder? ( use Pythagorean theorem ) Choose all the answers that apply.Condensation:1. forms clouds2. is the change from a liquid into a gas3. is the change from a gas into a liquid4. happens immediately before evaporation5. returns freshwater to the earth The scatter plot below shows the ages and heights of a varsity basketball team. Each dot represents one player. What is the total number of 17-year olds whose height is 74 inches or less?A. 0B. 1C. 2D. 3 Someone please help me out with this question fill in the blanks. spell all words correctWhich grain is a nutritious grain that has a sweet, nutty flavor when cooked, and makes a fine alternative for breakfast foods?___________is a nutritious grain that has a sweet, nutty flavor when cooked, and makes a fine alternative for breakfast foods. What is the current in a circuit with a 6.0 V battery and a 2.0 resistor? The answer to the question The palace of pizza offers small, medium, or large pizzas with 14 different toppings available. How many different one-topping pizzas do they serve? How do you determine the length ? Which letters is correct What is defined as an action involving the voluntary transfer of energy? Which example illustrates an environmental policy based on tradable emission permits? Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100.Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.4800+183x=80004800+186>(ine under the arrow)=8000 What is the definition of physical science? Plz I need help with these questions from the Alchemist.The crystal merchant serves as an example as one who has chosen to ___________ his Personal Legend.Question 1 options:CreateForgetGrowGive UpQuestion 2 (1 point) The crystal merchant lives by the philosophy maktub, it is written,__________________.Question 2 options:Pursue your dreamsLetting life happen to him instead of pursuing his dreamsFollow the path that your ancestors have followedBeing patientQuestion 3 (1 point) The boy and Fatima also say maktub in different situations. The boy says it to himself when he realizes that the histories of all people are connected and we are able to know everything.Question 3 options:TrueFalseQuestion 4 (1 point) Some examples of magical realism in the story include all of the following, except:Question 4 options:The old womans daughterThe protagonists recurring dream about finding treasureThe old man who gives him stones and who appears to have mystical powersthe dream of the hawksQuestion 5 (1 point) What kept the Englishman from transforming lead into gold?Question 5 options:FearHatredPrideIgnorance How does the animated version use the visual effects to show the first-person point of view? Steam Workshop Downloader