1 A polynomial expression of degree three is shown below.
8x3 + 125
Which expression represents the correct factorization of the polynomial?
A (2x + 5)(4x2 + 10x + 25)
B (2x + 5)(4x2 + 10x - 25)
C (2x + 5)(4x2 - 10x + 25)
D (4x + 25)(2x2 - 10x + 5)

Answers

Answer 1

Answer:

D şıkkı iyi dersler hadi

Answer 2

Answer:

C: [tex](2x+5)(4x^2-10x+25)[/tex]

Step-by-step explanation:

First of all, you need to be able to recognize the two terms as cubes, and what they are cubes of. In this case, [tex]8x^3 = (2x)^3[/tex] and [tex]125=5^3[/tex].

Then you have to find a way you like to remember the formula for how to factorize. The way I do it is by saying "the binomial has the same zero as the original, so [tex]x^3+a^3=(x+a)(...)[/tex] and [tex]x^3-a^3 = (x-a)(...)[/tex] and the whole expression has one minus sign attached to the second term of either factor. In the sum of cubes first parenthesis has a plus, so the second term of the other parentesis has to take that minus: [tex]x^3+a^3=(x+a)(x^2-ax+a^2)[/tex] while in the difference of cubes you already used a minus, so everything else goes plus: [tex]x^3-a^3=(x-a)(x^2+ax+a^2)[/tex]

Or you commit the two formulas to memory.


Related Questions

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region y=4x^2, y=x^2 + 3

Answers

Answer:

Step-by-step explanation:

integrate with respect to x

Area is symmetric so will be twice the integral from zero to 1

( I cannot seem to figure out how to make the lower limit negative in this editor)

[tex]A = 2\int\limits^1_0 {(x^2 + 3) - 4x^2} \, dx[/tex])

[tex]A = 2\int\limits^1_0 {-3x^2 + 3} \, dx[/tex]

[tex]A = 6\int\limits^1_0 {-x^2 + 1} \, dx[/tex]

A = 6(-⅓x³ + x)[tex]\left \| {{x=1} \atop {x=0}} \right.[/tex]

A = 6((-⅓(1)³ + (1)) - (-⅓(0)³ + (0)))

A = 6(⅔)

A = 4 units²

Multiply and write in standard form:
(2x)(x^2 - 6x + 3)
Show all work for full credit.

Answers

2x(x2-6x+3)

4x^3-12x^2+6x

The dean of a business college in the Midwest claims that he can correctly identify whether a student is a finance major or a music industry management major by the way the student dresses. Suppose in actuality that he can correctly identify finance majors 84% of the time, while 16% of the time he mistakenly identifies a music industry management major as a finance major. Presented with one student and asked to identify the major of this student (who is either a finance or music industry management major), the dean considers this to be a hypothesis test with the null hypothesis being that the student is a finance major and the alternative that the student is a music industry management major. Which of the following statements illustrates a Type I error?

a. Saying that the student is a finance major when in fact the student is a music industry management major.
b. Saying that the student is a music industry management major when in fact the student is a music industry management major.
c. Saying that the student is a finance major when in fact the student is a finance major.
d. Saying that the student is a music industry management major when in fact the student is a finance major.

Answers

Using error concepts, it is found that the option that represents a Type I error is:

d. Saying that the student is a music industry management major when in fact the student is a finance major.

The definitions of each type of error are as follows:

A Type I error happens when a true null hypothesis is rejected. A Type II error happens when a false null hypothesis is not-rejected.

In this problem, the Hypothesis are:

Null: Student is a finance major.Alternative: Student is a music industry management major.

By the definition of a Type I error, in this problem, it would consist in saying that a finance major student is a music industry management major student, hence option d is correct.

You can learn more about Type I and II errors at https://brainly.com/question/25225353

A salesperson rent a car for a work trip. The rental car company charges the salesperson $25 each day and a flat fee of $100 for insurance.
If the salesperson is charged a total of $225 to rent the car for 2 days, which statement is true?
The equation 25% + 100 = 225 can be used to find 2, and the salesperson rents the car for exactly 2 days.
The equation 252 + 100 = 225 can be used to find z, and the salesperson rents the car for exactly 5 days.
The equation 100:1 + 25 = 225 can be used to find 2, and the salesperson rents the car for exactly 2 days.
O The equation 100.0 + 25
225 can be used to find, and the salesperson rents the car for exactly 5 days.

Answers

The true statement will be "the equation 25z + 100 = 225 can be used to find z, and the salesperson rents the car for exactly 5 days.

Let the number of days used to rent the car be z

If the rental car company charges the salesperson $25 each day, the total charges for "z" days will be $25z

If a flat fee of $100 for insurance is added and the salesperson is charged a total of $225 for "z" days, hence the required equation that represents this statement is expressed as:

Rental charges for "z" days  + $100 = total charge25z + 100 = 225

The true statement will be "the equation 25z + 100 = 225 can be used to find z, and the salesperson rents the car for exactly 5 days.

Learn more on functions here: https://brainly.com/question/17431959

what’s is the surface area of the tent if the length is 2 meters, the width is 2 meters, and the height is 3 meters?

Answers

Answer:

45 is the right answer

Step-by-step explanation:

Fill in the blanks so the left side of each is a perfect square trinomial. That it complete the square

x^ 2 -2x+?=(x-?)^ 2

the question mark are the empty boxes for the numbers

Answers

Answer:

1

Step-by-step explanation:

Look at the LHS: you have the square of x, then you have 2 times x, times -1. to complete a square you just need to add the square of -1, that is 1. That becomes

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

Given f(x) = x + 2, describe how setting k = 4 affects the slope and y-intercept of the graph of g compared to the graph of f.
g(x) = (4x) + 2
g(x)=4(x+2)

Answers

Answer:

g(2)=(4x) +2=7y

g(3)=4(x+2)

Please help me solve

Answers

Answer:

i think t = 24

Step-by-step explanation:

68°+(5t-8)° = 180°

5t-8 = 180-68

5t-8 = 112

5t = 120

t = 120/5

t = 24

answer is t i hope this helps.

how many more seconds does it take to drive 1 mile at 40 miles per hour than 60 miles per hour​

Answers

Answer:

165 seconds

Step-by-step explanation:

If you were going steadily 60 miles per hour, you would go one mile in one minute. So, if you were going steadily 40 miles per hour, without your speed going up or down, you would get through one mile in 3 3/4 minutes (which is 165 seconds more than 1 minute).

Hope this helps. Pls give brainliest! Also, pls sub to kgirl633 on yt!

What is the value of x

Answers

Answer:

5"

root4square+3square=root25

=5

Plz I need help

























......................

Answers

Answer:

B. (0, -4) and (4, -4)

Step-by-step explanation:

The solutions are the points of intersection of the circle and the parabola.

(0, -4) and (4, -4)

a box contains 4 red balls and 6 purple balls. Ezra takes out a ball, puts it back and then takes out another ball. what is the probability that both balls were red

Answers

Answer:

16/100 = 4/25

Step-by-step explanation:

4/10 * 4/10 = 16/100

Help help help help math math

Answers

Answer:

umm i think its A/B

Step-by-step explanation:

Answer:

√49 < √56 < √64

Step-by-step explanation:

√56 = 7.4833....

7x7 = 49

8x8 = 64

√49 < √56 < √64

A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 90 yards, what are its dimensions?

Answers

Answer:

L=30 W=15

Step-by-step explanation:

90 divided by 6 is 15. 15 is the Width. Multiply 15 by 2 and you get 30 which is the Length.

mom left $5.00 for his 7 children. how much did each child receive
a.0.17
b.0.70
c.17
d.71

please answer it correctly.​

Answers

Answer:

.71

Step-by-step explanation:

Answer:

B. 0.70

Step-by-step explanation:

Just divide the total amount of money by the total amount of people.

5/7=0.71428...

if you round up correctly, you get 0.70; thus, it is B.

Also, his is for he, mom is a she, so use her instead of his...

Mary charges $5.60 per square foot of carpet, plus a $150 installation fee. How much should Mary charge the customer to the nearest cent?

Answers

Answer:

Step-by-step explanation:

Total = t

Square feet = f

t = 5.6f + 150

you didnt say how many square feet the customer wanted, but just plug it in for f and t is the answer

Answer:

375.30

Step-by-step explanation:

it's 375.302 but simplified to 375.30

Loquan has 2 pieces of fabric, each measuring 3 & 1/4 feet long. How many feet of fabric does Loquan have in total?

Answers

Answer:

3+1/4= 3 1/4

Hope This Helps!!!

The total fabric which Loquan has is equal to 6.5 feet.

It is given that Loquan has 2 pieces of fabric . Each of the fabric is [tex]3\frac{1}{4}[/tex] feet long.

We have to find out the total fabric in feet which Loquan does have.

What will be the total length if there are two ropes of 1 meter each ?

The total length of the rope can be calculated by multiplying no. of ropes with length of one rope and that will be equal to 2 × 1 or 2 meter.

As per the question ;

Loquan has 2 pieces of fabric , each having length of  [tex]3\frac{1}{4}[/tex] feet

The total length of fabric can be calculated by multiplying 2 with

[tex]3\frac{1}{4}[/tex] feet.

i.e.,

2 ×  [tex]3\frac{1}{4}[/tex]

= 2 × [tex]\frac{13}{4}[/tex]

= [tex]\frac{13}{2}[/tex]

= 6.5 feet

Thus , the total fabric which Loquan has is equal to 6.5 feet.

To learn more about unitary methods click here ;

https://brainly.com/question/26700669

#SPJ2

Help help help math math

Answers

Answer:

Function

Step-by-step explanation:

Hope it help !!

4. Calculate Karl Pearson's Coefficient of Correlation X 43 44 46 40 44 42 45 42 38 40 42 57. Y 29 31 19 18 19 27 27 29 41 30 26 10​

Answers

Answer:

Enter the following transactions into richard’s checkbook register and state his ending balance: date type description amount 03/01 check #204 blue sky apartments $455. 00 03/05 dep payroll automatic deposit $390. 36 03/08 debit benny’s hamburgers and fries $9. 20 03/15 check #205 car payment $251. 59 03/19 dep payroll automatic deposit $390. 36 a. $715. 79 b. $1,009. 81 c. $780. 72 d. $880. 24.

What is an equation of the line that passes through the points (-4, -5) and (-2, -6)?

Answers

Answer: [tex]y=-\frac{1}{2}x-7[/tex]

Ok done. Thank to me :>

Which is equivalent to vg*
Og
O 78%
12784
8 4x

Answers

Answer:

  (c)  (12th root of 8)^x

Step-by-step explanation:

The applicable rules of exponents are ...

  [tex](a^b)^c=a^{bc}\\\\\sqrt[n]{a}=a^{1 \! /n}[/tex]

In this case, we have ...

  [tex](\sqrt[3]{8})^{x/4}=8^{1/3\cdot x/4}=8^{x/12}=\boxed{\left(\!\sqrt[12]{8}\right)^x}[/tex]

Graph the following features: Y-intercept = 1 Slope 3/2 ​

Answers

Y=Mx+b, so y=3/2x+1. Put in desmos graphing calculator.

Triangle DNO has vertices at D(5, 8), N(– 3, 10), and O(– 3, 6). If vertex D is translated 4 units to the right, the best name for Triangle DNO is:

Answer Choices:
a. Scalene
b. Isosceles
c. Equilateral
d. Right
e. none of these

Answers

Using distance between two points to find the lengths of the edges of the triangle, the correct option is:

b. Isosceles

The distance between two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], is given by:

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

Vertex D is translated 4 units to the right is (9,8).

The lengths of the edges are:

[tex]DN = \sqrt{(9 - (-3))^2 + (8 - 10)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}[/tex]

[tex]DO = \sqrt{(9 - (-3))^2 + (8 - 6)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}[/tex]

[tex]NO = \sqrt{(-3 - (-3))^2 + (10 - 6)^2} = \sqrt{0^2 + 4^2} = 4[/tex]

Two edges of the same length, hence, it is an isosceles triangle, given by option b.

You can learn more about distance between two points at https://brainly.com/question/18345417

If sin ∅ = a/b then prove that (sec ∅ + tan ∅) = √b+a/b-a​

Answers

Given that

Sin θ = a/b

LHS = Sec θ + Tan θ

⇛(1/Cos θ) + (Sin θ/ Cos θ)

⇛(1+Sin θ)/Cos θ

We know that

Sin² A + Cos² A = 1

⇛Cos² A = 1-Sin² A

⇛Cos A =√(1-Sin² A)

LHS = (1+Sin θ)/√(1- Sin² θ)

⇛ LHS = {1+(a/b)}/√{1-(a/b)²}

= {(b+a)/b}/√(1-(a²/b²))

= {(b+a)/b}/√{(b²-a²)/b²}

= {(b+a)/b}/√{(b²-a²)/b}

= (b+a)/√(b²-a²)

= √{(b+a)(b+a)/(b²-a²)}

⇛ LHS = √{(b+a)(b+a)/(b+a)(b-a)}

Now, (x+y)(x-y) = x²-y²

Where ,

x = b and y = a

On cancelling (b+a) then

⇛LHS = √{(b+a)/(b-a)}

⇛RHS

⇛ LHS = RHS

Sec θ + Tan θ = √{(b+a)/(b-a)}

Hence, Proved.

Answer: If Sinθ=a/b then Secθ+Tanθ=√{(b+a)/(b-a)}.

also read similar questions:- i) sin^2 A sec^2 B + tan^2 B cos^2 A = sin^2A + tan²B..

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Sec x -tan x sin x =1/secx Help me prove it..

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Which relationships have the same constant of proportionality between y and x as the following table?
y
4
32
7
56
8 64
Choose 3 answers:

Answers

Answer:

A,C and D are the answers.

Step-by-step explanation:

I did it on Khan Academy and got it right.

Solve the following compound inequality: 4 less-than-or-equal-to x + 4 less-than-or-equal-to 12. a. 0 less-than-or-equal-to x less-than-or-equal-to 8 c. 8 less-than-or-equal-to x less-than-or-equal-to 16 b. x less-than-or-equal-to 8 d. no solution Please select the best answer from the choices provided A B C D

Answers

Answer:

A. 0 <= x <= 8

Step-by-step explanation:

4 <= x + 4 <= 12

Remove 4 from all sides

4 - 4 <= x + 4 -4 <= 12 - 4

0 <= x <= 8

What is the 18th term to the sequence 14,18,22

Answers

the 18th term is 82

Simplify 5(2x−1)+(−4x+8) . Write your answer in factored form.

please make it simple :)

Answers

Answer:

6x+3

Step-by-step explanation:

I hope this is what you where looking for

hellooo merry christmas !
can someone please help mee? ik its a lot but even just a little help would be very mich appreciated :))

Answers

Answer:

.....

Step-by-step explanation:

merry Christmas to you too

#10) Mrs. Sommer states that angle I is 65 degrees. Is she correct? why or why not​

Answers

Answer: Mrs. Somner is correct.

Step-by-step explanation: In a triangle, the angles add up to 180 degrees. Since we know that Triangle ABC is equal to Triangle RST, we can assume that their angle values are equal as well. Angle A is 41 degrees, and Angle B is 74 degrees. This adds up to 115 degrees. If we subtract 115 from 180, we get 65. Therefore, Mrs. Somner is correct.

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