a(b^2+c^2+bc) + b(c^2+a^2+ca) + c(a^2+b^2+ab)

Answers

Answer 1

Answer:

(a-b)(b-c)(a-c)

Step-by-step explanation:

a^2(b - c) + b^2(c-a) + c^2(a - b)

= a^2b - a^2c + b^2c - b^2a + c^2a-c^2b

=a^2b - b^2a - a^2c + b^2c + c^2a -c^2b

= ab(a - b) - c(a^2 - b^2) +c^2(a - b)

=ab(a - b) -c(a - b)(a + b) +c^2(a - b)

=(a - b)(ab - c(a + b) +c^2)

=(a - b)(ab - cb -ca + c^2)

= (a - b)(b(a-c) -c(a-c))

=(a-b)(b-c)(a-c)


Related Questions

When a coin and die are tossed together find the probability of getting:
a)coin with head and die with prime number
b)coin with head and die with composite number
c)coin with tail and die with even prime number

Answers

Answer:

a) 1/4

b) 1/6

c) 1/12

Step-by-step explanation:

Let S be the sample space.

S={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

n(s) =12

Events

A: coin with head and die with prime number .

B:coin with head and die with composite number.

C:coin with tail and die with even prime number.

a) A={H2,H3,H5}

n(A) = 3

P(A) =n(A)/n(S)

=3/12

= 1/4

b) B={H4,H6}

n(B)= 2

P(B) = n(B)/n(S)

= 2/12

= 1/6

c) C ={T2}

n(C) = 1

P(C) = n(C)/n(S)

= 1/12

Can you answer this math homework? Please!

Answers

Answer:

y + 2.3 = 0.45x

y = 0.45x - 2.3

-2y = 4.2x - 7.8

-2(0.45x - 2.3) = 4.2x - 7.8

-0.90x + 4.6 = 4.2x - 7.8

-0.90x - 4.2x = -7.8 - 4.6

-5.1x = - 12.4

x = -12.4 / -5.1

x = 2.4

y + 2.3 = 0.45x

y = 0.45(2.4) - 2.3

y = 1.08 - 2.3

y = -1.2

solution is : (2.4, - 1.2)

Step-by-step explanation:

The two lines intersect at answer A. (2.4, -1.2)


Question 4(Multiple Choice Worth 4 points)
.
(08.03)Solve the system of equations and choose the correct answer from the list of options.
X + y = -3
y = 2x + 2

a- five over 3, four over 3
b-negative five over 3, negative four over 3
c- negative 3 over 5 negative 3 over 4
D- 3 over 4, 3 over 5

Answers

Answer:

Hello,

Answer B (-5/3,-4/3)

Step-by-step explanation:

I am going to use the substitution 's method.

[tex]\left\{\begin{array}{ccc}x+y&=&-3\\y&=&2x+2\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&2x+2\\x+2x+2&=&-3\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&2x+2\\3x&=&-5\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x&=&-\dfrac{5}{3} \\\\y&=&2*(-\dfrac{5}{3})+2\\\end {array} \right.\\\\\\\boxed{\left\{\begin{array}{ccc}x&=&-\dfrac{5}{3} \\\\y&=&-\dfrac{4}{3}\\\end {array} \right.\\}[/tex]

Please help me answer this question.

Answers

Answer:

total candy = 54 bags

y=17

x=37

Step-by-step explanation:

5x + 4y = 253

x-y = 20

x = 20+y

5(20+y) + 4y = 253

100 + 9y = 253

9y = 153

y=17

x=37

2. Dentre as formas de representar um número decimal, a mais comum é a que utiliza vírgula. Valor como 0,25 está presente nos comércios, nos hospitais, nas lanchonetes e em muitos outros lugares. Esse valor também pode ser representado por A. ( ) 25/10 B. ( ) 1/4 C. ( )1/25 D. ( ) 1/25

Answers

Answer:

B: 0.25 = 1/4

Step-by-step explanation:

Queremos encontrar otra representación del número 0.25

Notar que hay dos decimales luego de la coma, por lo que podemos multiplicar este número y dividir por 100.

0.25 = 0.25*1 = 0.25*(100/100) = (0.25*100)/(100) = 25/100

Ahora tenemos el número escrito como una fracción, la cual debemos simplificar.

25/100

Podemos ver que tanto el numerador como el denominador son multiplos de 5, por lo que podemos dividir ambos por 5:

25/100 = (25/5)/(100/5) = 5/20

Nuevamente, ambos son multiplos de 5, por lo que podemos dividir ambos por 5.

5/20 = (5/5)/(20/5) = 1/4

así tenemos:

0.25 = 25/100 = 5/20 = 1/4

0.25 = 1/4

La opción correcta es B.

i need help ASAP please

Answers

Answer:

reflection over Y axis

Step-by-step explanation:

Answer:

I believe it is D) a reflection over the Y-axis

Step-by-step explanation

it is going over the Y-axis as if it is a sort of mirror, if it were going over the x-axis it would be flipped upside down, if it was A the shape would be going over the original shape. I don't know how to explain C. (I hope this helped and I hope it was correct lol)

What should be done so that the expression will have a value of 28?

6 + 2 + 32 × 2

Answers

Answer:

6+2+(32×2)

6+2+(64)

8+64

72

difference between 72 and 28

72-28

=44

add 44 to make the value 28

A rectangle is 12 feet long and 5 feet wide. If the length of the rectangle is increased by 25% and the width is decreased by 20%, what is the change in the area of the rectangle? The change in the area of the rectangle is

Answers

Answer:

no change in area

Step-by-step explanation:

The original area is

A = 12*5 = 60 ft^2

The new length and width

l = 12 + .25 (12) = 12+3 =15

w = 5 - .2 (5) =5-1 = 4

The new area is

A = l*w =15*4 = 60 ft^2

The area is the same

A student survey was conducted at a major university. Data were collected from a random sample of 206 undergraduate students, and the information that was collected included physical characteristics (such as height and handedness), study habits, academic performance and attitudes, and social behaviors. In this exercise we will focus on exploring relationships between some of those variables. The variables are:

Answers

Answer:

Students Major

Cheat reporting response

Number of Alcohols taken

Student's Height

Step-by-step explanation:

The Variables are the following:

Categorical variables

1. Major – The student's majors -

Arts & Social Science or STEM

2. Cheat - Response about reporting cheating - Yes or No

Quantitative Variables

3. Alcohol - Number of alcoholic beverages consumed in a typical week

4. Height - Self-reported height (in inches)

Find out the values of x and y from the following ordered pairs.
(x + y, 2) = (13, 2x – y)

Answers

Answer:

(x, y) = (5,8)

Step-by-step explanation:

Comparing the ordered pairs we get, x+y=13 and 2=2x-y. Solving it we will get, x=5 and y=8

9. what is the measure of QSR

Answers

Answer:  C) 142 degrees

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

Explanation:

Extend segment MN such that it intersects side ST. Mark the intersection as point A. See the diagram below.

We're given that angle MNT is 72 degrees. The angle TNA is equal to 180-(angle MNT) = 180 - 72 = 108 degrees, since angles MNT and TNA add to 180.

For now, focus entirely on triangle TNA. We see from the diagram that T = 34 and we just found that N = 108. Let's find angle A

A+N+T = 180

A+108+34 = 180

A+142 = 180

A = 180-142

A = 38

So angle NAT is 38 degrees.

----------------------------

Since segment MA is an extension of MN, and because MN || SQ, this means MA is also parallel to SQ.

We found at the conclusion of the last section that angle NAT was 38 degrees. Angles QST and NAT are corresponding angles. They are congruent since MA || SQ. This makes angle QST to also be 38 degrees

----------------------------

The angles QSR and QST are a linear pair, so they are supplementary

(angle QSR) + (angle QST) = 180

angle QSR = 180 - (angle QST)

angle QSR = 180 - 38

angle QSR = 142 degrees

How to find a parallel sides of trapezium length 7.3mm and 5.3mm ,and it's height is 5mm calculate the area of a trapezium

Answers

Answer:

31.50 mm²

Step-by-step explanation:

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Characteristics of a trapezoid

It has 4 vertices and edges

If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogram

Area of a trapezoid =  1/2 x (sum of the lengths of the parallel sides) x height

1/2 x ( 7.3 + 5.3) x 5 = 31.50 mm²

6. The right triangles ABC and DEF are
similar. The hypotenuse of AABC
measures 28 cm and the hypotenuse
of A DEF measures 7 cm. If one of the
legs of AABC measures 16 cm, what
does the corresponding leg of ADEF
measure?
F 1 cm
H 12 cm
G 4 cm
J 64 cm

Answers

Answer:

G. 4 cm

Step-by-step explanation:

28 divided by 7 equals 4.

So, 16 divided by 4 equals 4, which is the answer.

4 is the multiple that relates AABC to ADEF.

use the information in the diagram, set up a proportion to solve for the height of the tree

Answers

Answer:

Step-by-step explanation:

There are a couple of ways you could solve this problem. B is one of them.

The correct answer is going to be Small hypotenuse / Large hypotenuse = tree / building height

Let the tree equal x

100/220 = x / 176           Multiply both sides by 176

100 * 176 / 220 = x

x = 80

Notice that 80 is almost 1/2 of 176 so the answer should be right since 100 is nearly 1/2 of 220

GIVE FULL STEP BY STEP OF THIS MATHS WORD PROBLEM
Sohanlal is a gardener. He is paid ₹160 daily, find how much money will he
get in the month of September?

Answers

Answer:

Step-by-step explanation:

days in september=30

salry paid per day=Rs.160

salary paid in 30 days=160×30=Rs.4800

Answer:

4800

Step-by-step explanation:

In the month of September there are only 30 days. So assuming Sohanlal works the entire month of September we will multiply how much he makes daily which is 160 times the amount of days he works which is 30. this will look like this:

160 × 30 = 4800

Complete the missing parts of the
table for the following function. (picture) please answer all asap

Answers

Answer:

x=-1  y = 1/3

x = 1  y = 3

x = 3  y = 27

Step-by-step explanation:

y = 3^x

Let x = -1

y = 3^-1 = 1/3^1 = 1/3

Let x = 1

y = 3^1 = 3

Let x = 3

y = 3^3 = 27

Question 4 of 5
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each explicit formula to its corresponding recursive formula.
(8) = 5(5)(1-1)
(n) = 3 +5(n-1)
(3) = 5+3(1-1)
7(n) = 3(5)(n-1)
$(n) = 5 +5(n-1)
f(1) = 5
(*) = 3;(n - 1), for 3
(1) = 5
(n) = f(n-1) +5, for n?
f(1) = 5
f(n) = f(n-1) + 3, for n?

Answers

Given:

The recursive formulae.

To find:

The correct explicit formulae for the given recursive formulae.

Solution:

If the recursive formula of a GP is [tex]f(n)=rf(n-1), f(1)=a, n\geq 2[/tex], then the explicit formula of that GP is:

[tex]f(n)=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

The first recursive formula is:

[tex]f(1)=5[/tex]

[tex]f(n)=3f(n-1)[/tex] for [tex]n\geq 2[/tex].

It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:

[tex]f(n)=5(3)^{n-1}[/tex]

Therefore, the required explicit formula for the first recursive formula is [tex]f(n)=5(3)^{n-1}[/tex].

If the recursive formula of an AP is [tex]f(n)=f(n-1)+d, f(1)=a, n\geq 2[/tex], then the explicit formula of that AP is:

[tex]f(n)=a+(n-1)d[/tex]

Where, a is the first term and d is the common difference.

The second recursive formula is:

[tex]f(1)=5[/tex]

[tex]f(n)=f(n-1)+5[/tex] for [tex]n\geq 2[/tex].

It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:

[tex]f(n)=5+(n-1)5[/tex]

[tex]f(n)=5+5(n-1)[/tex]

Therefore, the required explicit formula for the second recursive formula is [tex]f(n)=5+5(n-1)[/tex].

The third recursive formula is:

[tex]f(1)=5[/tex]

[tex]f(n)=f(n-1)+3[/tex] for [tex]n\geq 2[/tex].

It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:

[tex]f(n)=5+(n-1)3[/tex]

[tex]f(n)=5+3(n-1)[/tex]

Therefore, the required explicit formula for the third recursive formula is [tex]f(n)=5+3(n-1)[/tex].

Find the distance between the
following points using the
Pythagorean theorem: (5, 10)
and (10, 12)

Answers

Answer:

[tex]\displaystyle d = \sqrt{29}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)

Algebra II

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

Step-by-step explanation:

*Note:

The distance formula is derived from the Pythagorean Theorem.

Step 1: Define

Identify

Point (5, 10)

Point (10, 12)

Step 2: Find distance d

Substitute in points [Distance Formula]:                                                         [tex]\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}[/tex][√Radical] (Parenthesis) Subtract:                                                                   [tex]\displaystyle d = \sqrt{5^2 + 2^2}[/tex][√Radical] Evaluate exponents:                                                                       [tex]\displaystyle d = \sqrt{25 + 4}[/tex][√Radical] Add:                                                                                                  [tex]\displaystyle d = \sqrt{29}[/tex]

The height, h, in metres, of a rocket t seconds after it is launched is approximately modelled by the quadratic relation h = 80t - 16t2. To the nearest second, how long is the rocket in the air?

Answers

Answer: 5 s

Step-by-step explanation:

Given

Height of the rocket can be modelled as [tex]h=80-16t^2[/tex]

Rocket will land on earth when it's height becomes 0

[tex]\Rightarrow 80t-16t^2=0\\\Rightarrow t(80-16t)=0\\\\\Rightarrow t=0\ \text{or}\ t=\dfrac{80}{16}=5\ s[/tex]

Neglecting 0 value

Thus, rocket remains in air for 5 s.

Please i need the correct answer, no funny business.

Answers

Answer:

Age of the spear head = 6349 years.

Step-by-step explanation:

Expression to be used to calculate the age of the spear head,

[tex]N_t=N_0e^{-kt}[/tex]

Here, [tex]N_t[/tex] = Final amount of C-14

[tex]N_0[/tex] = Initial amount

[tex]k[/tex] = 0.0001

[tex]t[/tex] = Time in years

If [tex]N_t[/tex] = 53% of [tex]N_0[/tex] = [tex]N_0\times (0.53)[/tex]

[tex]0.53N_0=N_0e^{-0.0001\times t}[/tex]

[tex]0.53=e^{-0.0001t}[/tex]

[tex]\text{ln}(0.53)=\text{ln}(e^{-0.0001t})[/tex]

[tex]-0.634878=(-0.0001)t[/tex]

[tex]t=6348.78[/tex] years

[tex]t[/tex] ≈ [tex]6349[/tex] years

Therefore, age of the spear head = 6349 years.

How do you solve this problem?

Answers

9514 1404 393

Answer:

  -19.2

Step-by-step explanation:

Fill in the given values and do the arithmetic.

  [tex]\displaystyle x\ \blacksquare\ y=\frac{x}{y}-xy\\\\4\ \blacksquare\ 5=\frac{4}{5}-4\cdot5=0.8-20\\\\\boxed{4\ \blacksquare\ 5=-19.2}[/tex]

Can someone please help me with this I’m struggling

Answers

Answer:

Equation:  [tex]70=(x+3)x[/tex]

x = -10 or x = 7

x = 7 (width can't be negative)

x + 3 = 10

Step-by-step explanation:

Represent the width of the rectangle by  x.  "The length of a rectangle EXCEEDS the width by 3" means the length is 3 LONGER than the width, so the length is represented by the expression  x + 3.

Area = (length)(width)

70 = (x + 3)x

Multiply out the right side.

[tex]70=x^2+3x\\x^2+3x-70=0[/tex]

Factor the left side.

[tex](x+10)(x-7)=0[/tex]

Each binomial could equal 0, so

[tex]x+10=0 \text{ or }x-7=0\\x=-10\text{ or }x=7[/tex]

The negative solution does not make sense as the width of a rectangle.

x = 7, making the length, x + 3 = 10

Answer:

Pls mark this as brainiest

Step-by-step explanation:

Area of the rectangle = length x breadth

consider 'x' to be width

therefore length = x+3

area = (x+3)*x

Area = 70 square

x = 7

x+3 = 7+3

      = 10

verification

7 x 10

= 70

the polygons in each pair are similar. find the missing side length.​

Answers

Given:

The polygon in the given figure are similar.

To find:

The missing side length.​

Solution:

We know that the corresponding sides of similar figures are proportional.

The given polygons are similar, so the their corresponding sides are proportional.

[tex]\dfrac{x}{15}=\dfrac{32}{40}=\dfrac{32}{40}[/tex]

So, the missing values in the equation of proportion are 15, 40, 32 respectively.

On solving the above equation, we get

[tex]\dfrac{x}{15}=\dfrac{4}{5}=\dfrac{4}{5}[/tex]

[tex]\dfrac{x}{15}=\dfrac{4}{5}[/tex]

[tex]x=\dfrac{4}{5}\times 15[/tex]

[tex]x=12[/tex]

Therefore, the value of x is 12.

Help anyone can help me do this question,I will mark brainlest.​

Answers

Answer:

Answer is in attached image

I hope it help...

Please help!!!!!!!!!!!!!!

Answers

Answer:

choice A is the answer

Step-by-step explanation:

[tex]5 + 2.75s \leqslant 21 \\ 2.75s \leqslant 21 - 5 \\ s \leqslant 16 \div 2.75 \\ s \leqslant 5.82[/tex]

but since we only can have a whole number in the number of stops, she can only travel 5 stops with the money she has.

What’s the answer? I don’t understand the question and I came to see if you all can help

Answers

Answer:

15/2 that is the answer man

factor x^2-3x-28 using the x method

Answers

Answer:

[tex] {x}^{2} - 7x + 4x - 28 \\ = x(x - 7) + 4(x - 7) \\ = (x - 7)(x + 4)[/tex]

in 1990 sausage cost an average of $2.42 per pound. In 1994 it cost 51.35 per pound. What was the percent of depreciation (percent of decrease)?
*(show your work)*​

Answers

Answer:

Cumulative price change 105.96%

Average inflation rate 2.36%

Converted amount ($100 base) $205.96

Price difference ($100 base) $105.96

CPI in 1990 130.700

Step-by-step explanation:

match the absolute value functions with their vertices

Answers

Answer:

Vertex: (5, 2/3) - > f(x) = 3/5 |x - 5| + 2/3
Vertex: (-1, -3/7) - > f(x) = 1/2 |x + 1| - 3/7
Vertex: (0, -4/5) - > f(x) = 1/2 |x| - 4/5
Vertex: (2/5, 5/3) - > f(x) = 3/2 |x - 2/5| + 5/3

Step-by-step explanation:

I need to know the transformation of the shape

Answers

Answer:

is there anything underneath it? it says which of the following

Step-by-step explanation:

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Duval Co. issues four-year bonds with a $100,000 par value on January 1, 2019, at a price of $95,952. The annual contract rate is 7%, and interest is paid semiannually on June 30 and December 31.1. Prepare a straight-line amortization table like Exhibit 14.7 for these bonds.2. Prepare journal entries to record the first two interest payments.3. Prepare the journal entry for maturity of the bonds on December 31, 2022 (assume semiannual interest is already recorded). ITALIAN 7. The expression denim can be translated as let's have breakfast VERO/FALSO8. The verb 'mangiare can be translated as to eat, VERO/FALSO9.What does Bere mean A polynomial has one root that equals 2 + i. Name one other root of thispolynomial. name three dangerouse objects Your best friend has just been suspended from school for truancy.write a letter to her expressing your displeasure and advising her to turn a new leaf explain chlorination of methane cho dy s a[] c n phn t v dy s b[]c m phn t l cc cc s nguyn dng nh hn 1000 . Gi tp hp A l tp cc s khc nhau trong a[], tp hp B l cc s khc nhau trong b[] The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour period, one defective circuit board was found. (a) Find the probability that it was produced during the first hour of operation during that period. (Round your answer to four decimal places.) (b) Find the probability that it was produced during the last hour of operation during that period. (Round your answer to four decimal places.) (c) Given that no defective circuit boards were produced during the first five hours of operation, find the probability that the defective board was manufactured during the sixth hour. (Round your answer to four decimal places.) Cu 27:I.. say this much for him; he's very generous.A. could B. may C. might D. will What is the last country to introduce television? The points A,B,C and D divide the line segment AD in the ratio 4:3:1 , respectively , and AD = 72cm . What is the length of BD? Choose which is a statistical question: What arethe ages of the students in this class? or Howmany pennies equal 1 dollar? Explain. write your answer in simplest radical form Human Population Growth and OverpopulationCan someone please help me I don't understand what I have to do. Find an equation of the line having the given slope and containing the given point m= - 8, (2,5) The equation of the line is y= (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression) Question 4 of 20Which energy transfer occurs when a cube of ice is placed in a glass ofwater?A. The chemical energy of the ice is transferred to the liquid water.B. The nuclear energy in the water molecules is released from the iceinto the liquid water.C. Gravitational potential energy is transferred from the liquid waterto the ice.O D. Thermal energy is transferred from the liquid water to the ice.SUBMIT Klog earns $6.30 per hour. He worked 3.5 hours each day Monday through Friday plus 4 on Saturday. How much did he earn altogether? Write an equation and solve it to answer each question. A pile of 55 coins consisting of nickels and dimes is worth $3.90. Find the number of each. I only need the equation plz. WILL MARK BRAINLIEST. 1. Find the word which has a different sound in the part underlined. Read the words aloud 1. A. Volunteer B. Committee C. Guarantee D. Degree 2. A. Chemistry B. Chemical C. Charity D. Mechanic 3. A. Architect B. Church C. Childhood D. Change 4. A. Collage B. Cave C. Cycle D. Cancel 5. A. Child B. Provide C. Mind D. Think If (5^(k-1))+(5^(k+1)) = m, what is 2*5^k in terms of m?If [tex]5^k^-^1+5^k^-^1=m[/tex], what is [tex]2*5^k[/tex] in terms of m?A) 5mB) 5m2C) 5m13D) 5m26