Factor the expression completely.
x^4-17x^2+72

Answers

Answer 1

Answer:

It's neither:

x =√ 9.000 = 3.00000 or :

x =√ 9.000 = -3.00000 or :

x =√ 8.000 = 2.82843 or :

x =√ 8.000 = -2.82843

Four solutions

Answer 2

Answer:

x^4 - 17x^2 + 72 = (x^2 - 9)(x^2 - 8)

Step-by-step explanation:

First, we need to find two numbers that multiply to give us 72 and whose sum is -17. We can see that 8 and 9 multiply to give us 72, and their sum is 8 + 9 = 17. Since we want the sum to be negative, we need to change one of the signs. So we write -(8 + 9) = -17.

Next, we write the expression as the product of two binomials. We factor out the common factor x^2 from the first two terms: x^4 - 17x^2 + 72 = x^2(x^2 - 17) + 72

Now, we complete the square in the first binomial. To do this, we need to add and subtract (17/2)^2 = (8.5)^2 = 72.25 inside the bracket:

x^2(x^2 - 17) + 72 = x^2(x^2 - 17 + 72.25 - 72.25) + 72 = x^2(x^2 - 17 + 72.25) - 72.25 + 72

Now we can rewrite the square of a binomial :

x^2(x^2 - 17 + 72.25) = x^2((x-8.5)^2)

Finally, we can combine the two binomials

x^2((x-8.5)^2) + 72 = (x^2(x-8.5)^2) + 8(9)

So the expression x^4 - 17x^2 + 72 factors completely as (x^2 - 9)(x^2 - 8)

Hope this helps!


Related Questions

Given a prime $p$ and an integer $a$, we say that $a$ is a primitive root $\pmod p$ if the set $\{a,a^2,a^3,\ldots,a^{p-1}\}$ contains exactly one element congruent to each of $1,2,3,\ldots,p-1\pmod p$.For example, $2$ is a primitive root $\pmod 5$ because $\{2,2^2,2^3,2^4\}\equiv \{2,4,3,1\}\pmod 5$, and this list contains every residue from $1$ to $4$ exactly once.However, $4$ is not a primitive root $\pmod 5$ because $\{4,4^2,4^3,4^4\}\equiv\{4,1,4,1\}\pmod 5$, and this list does not contain every residue from $1$ to $4$ exactly once.What is the sum of all integers in the set $\{1,2,3,4,5,6\}$ that are primitive roots $\pmod 7$

Answers

Only 3 & 5 from the set {1,2,3,4,5,6} are primitive root (mod7), therefore, sum of integers is 3 + 5 = 8.

What is primitive root?

A number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n in modular arithmetic. That is, g is a primitive root modulo n if for every integer a coprime to n, some integer k for which gk ≡ a (mod n).

The index or discrete logarithm of a to the base g modulo n is a value k like this. So, if and only if g is a generator of the multiplicative group of integers modulo n, g is a primitive root modulo n.

In Article 57 of his Disquisitiones Arithmeticae (1801), Gauss defined primitive roots and credited Euler with coining the term.

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Bru.h I suck at doing this and mostly like DECIMALS I don’t like that- someone pl help me

Answers

Answer:

D

Step-by-step explanation:

Answer:

5,006.04

Step-by-step explanation:

Hope it Helps!

:)

During the grand opening of an electronics store, any customer has a 17% chance of winning a free laptop. What is the chance that a customer does not win a free laptop?\

Answers

23/100 of a chance I’m pretty sure

state if the function is a growth or decay and the factor

y=2x

Answers

Answer:

the function shows growth of a factor of 2

Step-by-step explanation:

Answer:

The function is a growth, the factor 2

Manchu has drawn a
rectangle with a base of
24 cm and an area of
336 cm². He cuts the
rectangle as shown to make two triangles.
What are the height and area of each
triangle?

Answers

Answer:

Height of each triangle: 14cm

Area of each triangle: 168cm²

Step-by-step explanation:

So we know that the base of the area is 24. Lets find the height.

336 ÷ 24 = 14

If he makes two triangles out of the rectangle that just means he cuts it in half.

To find the area of one triangle lets do:

336 ÷ 2 = 168

Let's double check our answer:

(14 × 24) ÷ 2 = 168

Seems great!

Convert the improper fractions to mixed numbers

Answers

Answer:

28.1 7/8

29.3

30.18/8=9/4=2 1/4

Step-by-step explanation:

Answer:

28. 1 [tex]\frac{7}{8}[/tex]

29. 3

30. 2[tex]\frac{2}{8}[/tex]

4. Find the probability that a randomly chosen point lies inside the shaded region. 4.
Express your answer as a decimal rounded to the nearest hundredth.

Answers

0.167 or 0.17 rounded to the nearest hundredth.

How do you round off decimal to the nearest hundredth?

When rounding to the nearest hundredth, you want to look at the third decimal place, the one to the right of the hundredth place. If the value in the third decimal place is less than 5, you truncate everything to the right of the hundredth place, leaving the number unchanged.

If the value in the third decimal place is greater than or equal to 5, you add one to the number in the hundredth place.

The total area of the rectangle is 15*5 = 75 square feet.

The area of the triangle inside the rectangle is (1/2)25 = 12.5 square feet.

The shaded region is the area of the triangle, so the probability that a randomly chosen point lies inside the shaded region is

12.5/75 = 0.167 or 0.17 rounded to the nearest hundredth.

Hence, 0.167 or 0.17 is rounded to the nearest hundredth.

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A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. Which box has the greater lateral surface area and by how much

Answers

On solving the provided question, we can say that So, the total surface area of cuboid is larger by (610 — 600 = IO) cm2

what is cuboid?

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

(Lateral surface area of cube = 4edge2

lateral surface area of cuboid =2h (l + b)

[tex]2 x 8(12.5+ 10)\\= 16 x 22.5\\= 360\\[/tex]

lateral surface area of the cube is larger by (400

- 360

= 40)cm2

Total surface area of cube = 6edge2

= 600

lateral surface area of cuboid

[tex]=2 (lb + bh + hl)\\2(12.5 x 10+ x 8+8 x 12.5)\\= 2 (125 + 80 + 100)\\= 610[/tex]

So, the total surface area of cuboid is larger by (610 — 600 = IO) cm2

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what is the distance between (-3,5) and (4,5)

Answers

Answer: 7

Step-by-step explanation:

Distance (d) = √(4 - -3)2 + (5 - 5)2

= √(7)2 + (0)2

= √49

= 7

ΔX = 4 – -3 = 7

ΔY = 5 – 5 = 0

y = 0x + 5

When x=0, y = 5

Answer:

Step-by-step explanation:

D = SQRT(x 2 - x 1) 2 + (y 2 - y 1) 2

X2 Y2

(-3,5)

X1 Y1

(4,5)

D= SQRT (-3-4)^2 + (5-5)^2

D= SQRT 49

D=7

In the diagram below, transversal t intersects parallel lines I and m.

What is the value of x?

Answers

Step-by-step explanation:

x+10=116

x=116-110

=106

x=106

Need help answering this question!!!!

Answers

For this case we use the following formula
Area of Sector = Area * radians of sector / 2 * pi radians
Where,
Area: it is the area of the complete circle.
We have then:
Area = pi * r ^ 2
Area = pi * (6) ^ 2
Area = 36pi
Substituting values:
5pi = 36pi * radians of sector / 2 * pi
Clearing:
radians of sector = ((5pi) * (2pi)) / (36pi)
radians of sector = (10pi ^ 2) / (36pi)
radians of sector = (10pi) / (36)
radians of sector = (10/36) pi
radians of sector = (5/18) pi
in degrees:
(5/18) pi * (180 / pi) = 50 degrees
Answer:
The measure of the central angle is:
50 degrees

Please help me answer this math question !

Answers

Answer:

y=-3x+6

Step-by-step explanation:

253 x 804 =
Solve by using standard algorithms

Answers

Answer:

203412

Step-by-step explanation:

253

*804

___

16

  40

    32

      20

         12

______

 203412

This is a Vedic Math trick you can use to multiply fast, called the criss-cross method.

ILL GIVE BRAINLIEST

Answers

Answer:

I can't read the question it's too blurry

What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.

Answers

The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required to be determined is; 25.

What is the maximum possible quotient of any pair of numbers from the set?

It is evident from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Therefore, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Ultimately, it can be inferred that the greatest possible quotient as required is; 25.

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can you find the proportion pwease :)

Answers

Answer:

15 cookies, 10 brownies.

Step-by-step explanation:

I'm assuming that she is selling the same amount of cookies and brownies per hour. If that is the case...

Multiply it by 5. If 3 cookies were sold in one hour, and there's 5 hours, just multiply 3 by 5. Total number is 15 cookies.

Same goes for brownies. Multiple 2 brownies by 5. That makes 10 brownies.

What are the 3 algorithms?

Answers

Sequencing, selection, and iteration are the three fundamental building blocks that make up an algorithm.

What is algorithm?

An algorithm in mathematics is a process, a description of a series of steps that can be used to solve a mathematical computation, but they are now much more prevalent than that. The long division algorithm is perhaps the most well-known application of algorithms in science (and in daily life, for that matter).

Algorithms are all about figuring out the most effective ways to perform the math, despite the fact that the above explanation might sound a little fussy and detailed. Mathematicians are known for being lazy, so they frequently seek out shortcuts, as the anonymous mathematician puts it. For locating these short cuts, algorithms are used.

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which fraction is greater? a)3/18,2/6​

Answers

Answer:

2/6

Step-by-step explanation:

The LCD of 18 and 6, so when you multiply 2/6, it will be 5/18. So 5/18 is greater than 3/18

Answer:

3/18  is smaller than 2/6

Step-by-step explanation:

which is the best way to answer a 10 question multiple choice test in which each question has 6 choices for answers


- 1 ) flipping a coin ?

- 2 ) rolling a die ?

- 3 ) spinning a spinner with 4 equal sections ?

- 4 ) spinning a spinner with 10 equal sections

Answers

Answer:

Rolling a die.

Step-by-step explanation:

A die has 6 sides for every answer and the only choice regarding the number 6 and you can roll (questions) times.

(x - 7)2 + (y + 5)2 = 4
what’s the center and radius

Answers

Answer:

(7, - 5 ) and r = 2

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 7)² + (y + 5)² = 4 ← is in standard form

with centre = (h, k ) = (7, - 5 ) and r = [tex]\sqrt{4}[/tex] = 2

Pls help me to do this

Answers

Answer:

1. 2 more children

2. 13 centimeters

3. Can't determine without ruler

Step-by-step explanation:

1. 5-3 = 2

2. 22-9 = 13

Which is the product of [tex]\frac{7}{9\\}[/tex] and 6?
( 100 POINTS )

Answers

Answer:

[tex] \sf \: \frac{14}{3} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]

[tex] \sf \rightarrow \: \frac{(7 \times 6)}{9} [/tex]

[tex] \sf \rightarrow \: \frac{42}{9} [/tex]

[tex] \sf \rightarrow \: \frac{14}{3} [/tex]

Hence, the product is 14/3.

Need help ASAP. Question in photo. Will mark brainliest if correct

Answers

Answer:

C

Step-by-step explanation:

I did this question today, pls lmk if u get it right

I NEED HELP ASAP!!! PLEASE HELP ME!!!!!!!

Answers

I believe the answer is D. I don’t know if u already know the answer






.

A $1,200 bond earns 3% simple interest per year on its purchase price. What is the amount of interest earned after 15 MONTHS?
Select one:
$1245
$3
$36
$45​

Answers

Answer:

45$

Step-by-step explanation:

Answer:

$45

Step-by-step explanation:

$1,200 x 0.03% = $36 yearly

$36/12 = $3 per month

$3 x 15 months = $45

L) simplify

sin²x ( cot²x + 1 )

Answers

Answer: 1.

Step-by-step explanation:

[tex]\displaystyle\\sin^2x(cot^2x+1)=\\\\sin^2x(\frac{cos^2x}{sin^2x}+1)=\\\\\frac{sin^2xcos^2x}{sin^2x}+sin^2x=\\\\cos^2x+sin^2x=\\\\1.[/tex]

Amelia made a line plot of her scores on 25-point math quizzes. What is the difference between the total of her most frequent number of points per quiz and the total of her greatest number of points scored per quiz? A. 0 points B. 6 points C. 18 points D. 22 points

Answers

Answer:

I think it B.

Step-by-step explanation:

What is the volume of a cube with three 1/3 inch sides

Answers

Answer:

(1/27) in^3

Step-by-step explanation:

"sides" is inappropriate here.  You meant "a cube with three edges each 1/3 inch long."

V of cube:  V = s^3, where s:  side length

Here, V = (1/3 in)^3 = (1/27) in^3

Note:  all cubes have 6 (six) sides, including this one with 6  1/3 in sides.

Craig won first prize in Mrs. Short's class

so he gets to pick a prize from the treasure

box. He doesn't know what he wants, so

he is going to chose randomly. There are 7

different gift card prizes: fast food, ice cream,

CD's, DVD's, movies, the mall and Carowinds.

If there is an equal number of each card in

the box, what is the probability he will pull out

the gift card for Carowinds?

Group of answer choices

0/7

6/7

1/7

1/2

Answers

Answer:

[tex] \frac{1}{7}[/tex]

Answer:

1/7

Step-by-step explanation:

there is seen prizes and he pulls seven times so the odds would be 1/7

Is the area of an equilateral triangle is 9 root 3 cm square then the semi perimeter of the triangle is?

Answers

The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.

what is triangle ?

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

given

area of equilateral triangle = [tex]9\sqrt{3}cm^{2}[/tex]

formula of area of equilateral triangle = [tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex]

a = side of triangle

[tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex]  =  [tex]9\sqrt{3}cm^{2}[/tex]

[tex]a^{2} = \frac{4* 9\sqrt{3} }{\sqrt{3} }[/tex]

[tex]a^{2} = 36\\ a = 6 cm[/tex]

since equilateral triangle all sides are equal

perimeter of triangle = 6 + 6 + 6

= 18cm

the semi perimeter of the triangle = 18 /2 = 9 cm

The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.

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