(2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i)

Answers

Answer 1

Answer:

50+50i

Step-by-step explanation:

Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.

Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)

On expansion

(3 - i)(3 + i)

=  9+3i-3i-i²

= 9-(-1)

= 9+1

(3 - i)(3 + i) = 10

For the expression (2 + i)(1 - i), we have;

(2 + i)(1 - i)

= 2-2i+i-i²

= 2-i+1

= 3-i

Multiplying 3-i with the last expression (1 + 2i)

(2 + i)(1 - i)(1 + 2i)

= (3-i)(1+2i)

= 3+6i-i-2i²

= 3+5i-2(-1)

= 3+5i+2

= 5+5i

Finally,  [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]

= 10(5+5i)

= 50+50i

Hence,  (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i


Related Questions

Let u = , v = . Find u + v. (1 point)

Answers

Answer:

i couldnt find a solution to the equation all i could get is u +v

Step-by-step explanation:

what were you trying to say when you said "let u="

Answer:

4.8

Step-by-step explanation:

(-3,4) + (8,2) = 4.8

how many 4 digit numbers can be formed if repetitions are not allowed and the numbers always end with 3?
- 405
- 450
- 540
- 504

Answers

Answer:

448

Step-by-step explanation:

we have four spaces

_ _ _ _ but we know that they end in 3

_ _ _ 3 so the question changes how many 3 digit numbers can be formed without repetion and 3

so the first one has 8 options 1,2,4,5,6,7,8,9 we can have 0 here.

the second one 8 we count 0

the third 7 so we have

8*8*7*1=448

dont know why it doesn't fit.

-4.1=8(y-5) it says solve equation

Answers

[tex]\text{Solve for y:}\\\\-4.1=8(y-5)\\\\\text{Use the distributive property}\\\\-4.1=8y-40\\\\\text{Add 40 to both sides}\\\\35.9=8y\\\\\text{Divide by 8}\\\\\boxed{4.4875=y}\\\\[/tex]

Answer: See below

Explanation:
-4.1 = 8(y-5)
-4.1 = 8y - 40
-8y = -40 + 4.1
-8y = -35.9
Y = -35.9/-8
Y = 35.9/8

Solve the inequality for x.
7 > 2x+9

Answers

Answer:

x<-1

Step-by-step explanation:

[tex]7 > 2x+9\\\\\mathrm{Switch\:sides}\\\\\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\2x+9-9<7-9\\\\2x<-2\\\\\frac{2x}{2}<\frac{-2}{2}\\\\x<-1[/tex]

A man has two sons, one twice as old as the other. The man is four times as old as the older boy. In three years he will be five times as old as the younger boy. Find their present ages.

Answers

Answer:

Man's present age: 32 years

Older son's present age: 8 years

Younger sons present age: 4 years

Step-by-step explanation:

Let their present ages be represented by:

Man = a

Older boy = b

Younger boy = c

A man has two sons, one twice as old as the other:

b = 2 × c

b = 2c......... Equation 1

The man is four times as old as the older boy:

a = 4 × b

a = 4b.......Equation 2

In three years he will be five times as old as the younger boy:

a + 3 = 5 (c + 3)

a + 3 = 5c + 15........Equation 3

Since b = 2c and a = 4b

Subtitute 2c for b in Equation 2

a = 4b

a = 4 × 2c

a = 8c

Subtitute 8c for a in Equation 3

a + 3 = 5c........Equation 3

8c + 3 = 5c + 15

Collect like terms

8c - 5c = 15 - 3

3c = 12

c = 4

Therefore since c, represents the present age of the younger son, the younger son is 4 years old

b = 2c

b = 2 × 4

b = 8

Since b is the present age of the older son, the older son is 8 years old

a = 4b

b = 8

a = 4 × 8

a = 32

Since a is the present age of the man, the man is 32 years old

Therefore,

Man's present age: 32 years

Older son's present age: 8 years

Younger sons present age: 4 years

Look at the pattern below. step 1 with 1 square step 2 with 3 squares step 3 with 6 squares step 4 with 10 squares How many squares will be in the pattern in step 6

Answers

Answer:

21 squares

Step-by-step explanation:

Here in this question, we are given a pattern and we want to determine what the values in that pattern will be at a specific step.

We proceed as follows;

What we can see in this pattern is that the difference in number of squares between a pattern and the next pattern increases by the addition of the next integer to the number of squares we have in the last pattern.

Thus for step 5, we shall be adding the next integer( 5) to the number of squares ;

That would be 10 + 5 = 15 squares

For step 6, we shall be adding the next integer (6) to the number of squares in step 5.

That would be 15 + 6 = 21 squares

How we got the initial next integer?

step 1 = 1 square

step 2 = 3 squares ( integer difference of 2)

step 3 = 6 squares ( integer difference of 3)

step 4 = 10 squares ( integer difference of 4)

so;

step 5 = 15 squares ( integer difference of 5)

step 6 = 21 squares( integer difference of 6)

761.8 x 10^-8 Express the number in scientific notation. A) 7.618 x 10^-6 B) 7.618 x 10^-8 C) 7.618 x 10^2 D) 7.618 x 10^6

Answers

Answer:

[tex]\huge\boxed{A)\ 7.618\times10^{-6}}[/tex]

Step-by-step explanation:

The scientific notation:

[tex]a\cdot10^n[/tex]

where

[tex]1\leq a<10;\ n\in\mathbb{Z}[/tex]

We have

[tex]761.8\times10^{-8}[/tex]

We need to move the decimal point two places to the left.

[tex]\underbrace{(7.618\times10^2)}_{=761.8}\times10^{-8}=7.618\times(10^2\times10^{-8})[/tex]

use

[tex]a^n\cdot a^m=a^{n+m}[/tex]

[tex]=7.618\times10^{2+(-8)}=7.618\times10^{-6}[/tex]

Answer:

a

Step-by-step explanation:

Does anyone know this

Answers

Answer: Choice D) Domain: all real numbersRange: y > -100 (not [tex]y \ge -100[/tex])Type of function: exponential

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

Explanation:

The graph goes on forever to the left and right. This means any real number x can be plugged into the function to get some output y. The domain is the set of all real numbers. In interval notation, we would say [tex](-\infty, \infty)[/tex] which is another way of saying [tex]-\infty < x < \infty[/tex]

The range is y > -100 because the exponential graph steadily approaches this horizontal asymptote. Think of it like an electric fence you cannot touch. Since we never actually get to this y value, this means y = -100 is not part of the range. Your teacher made a typo when they wrote [tex]y \ge -100[/tex] and instead they should have written [tex]y > -100[/tex]. So basically y can be anything larger than -100. The graph may look like it eventually reaches y = -100 itself, but it's actually just getting closer and closer to this y value. To write the range in interval notation, we would say [tex](-100, \infty)[/tex]

This function is exponential because it has the general shape all exponential growth functions do. We have a fairly flat part with very slow growth at first, but then as time goes on, the growth rate increases dramatically resulting in the very steep curve.

Quartic polynomials are 4th degree polynomials. They have the same end behavior as quadratic functions do, since both are even degree polynomials. We don't have a quartic here because the left end behavior isn't going off to positive infinity as the right end behavior is.

90 to the nearest tenth

Answers

Answer:

90

Step-by-step explanation:

90 has 0 ones so it is already rounded.

Answer:

90

Step-by-step explanation:

Hey there!

Well 90.000 to the nearest tenth is just 90 because there is decimal places to round.

Hope this helps :)

If f(x) = 2(x − 5), find f(8). 4 6 8 16

Answers

Answer:

f(8) = 6

Step-by-step explanation:

Plug in 8 as x in the function:

f(x) = 2(x − 5)

f(8) = 2(8 - 5)

f(8) = 2(3)

f(8) = 6

Answer:

[tex]\large \boxed{\mathrm{6}}[/tex]

Step-by-step explanation:

[tex]f(x)=2(x-5)[/tex]

Replace x with 8 to find f(8).

[tex]f(8)=2(8-5)[/tex]

Evaluate.

[tex]f(8)=2(3)[/tex]

[tex]f(8)=6[/tex]

If an octagon is 24, how many is a pentagon?

Answers

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Hi my lil bunny!

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If an octagon is 24, how many is a pentagon?

Ans : Pentagon has 5 sides.

( A five-sided shape is called a pentagon. A six-sided shape is a hexagon, a seven-sided shape a heptagon, while an octagon has eight sides. The names of polygons are derived from the prefixes of ancient Greek numbers. )

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●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

The pentagon is 15, when octagon is 24.

What is Polygon?

A polygon is a figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (means many) and gon (means sides).

Polygon with 8 sides known as Octagon and polygon with 5 sides known as Pentagon.

Here, given that, Octagon = 8 sides = 24

So, 1 side= 3

Then, we get, pentagon = 5 sides = (5×3) = 15

Hence, the pentagon is 15.

To learn more on Polygon click:

https://brainly.com/question/15324224

#SPJ2

Pls answer this urgently

Answers

Answer:

The pic there has a step by step explanation

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

        Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\frac{(3^-2)^2 * (5^2)^-3 * ( t ^-3)^2 }{( 3^-2) ^5 ( 5^3) ^-2 ( t ^-4)^3}[/tex]

[tex]= \frac{\frac{1}{1265625^t12} }{1}[/tex]

[tex]= \frac{\frac{1}{992640625^t6} }{1}[/tex]

[tex]= \frac{992640625^t6}{1265625}[/tex]

[tex]= \frac{922640625tttttt}{1265625}[/tex]

[tex]= 729t^6[/tex]

Answer : [tex]729t^6[/tex]

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If this helped you, could you maybe give brainliest..?

❀*May*❀

GIVE ME A REAL ANSWER PLEASE! IT IS DUE NOW! Factor completely 3x^2 + 5x + 1.
(3x + 1)(x + 1)
(3x + 5)(x + 1)
(3x − 5)(x + 1)
Prime

Answers

Answer:

prime

Step-by-step explanation:

3x^2 + 5x + 1

it can't be factorizes with rational numbers

Answer:

Prime

Step-by-step explanation:

3x^2 + 5x + 1

3x^2  factors in to 3x and x

1 factors into 1 and 1

( 3x   + 1) ( x+1)

We need to verify the middle is 5

3x+1x = 4x

so this is not true

We cannot factor this so it is prime

7. Verify the following: i) (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0 ii) (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc iii) (p – q) (p² + pq + q²) = p³ – q³. EXPLAIN

Answers

1. (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0

We know that (a+b)(a-b) = a²-b²

(ab + bc)(ab -bc) can be written as b² - c²

(bc + ca)(bc -ca) can be written as c² - a²

(ca + ab)(ca - ab) can be written as a² - b²

a²b² - b²c² + b²c² - c²a² + c²a² - a²b²

→ a²b² - a²b² - b²c² + b²c² - c²a² + c²a²

→ 0

2. (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc

→ a³ + ab² + ac² -a²b - abc -ca² + a²b + b³ + bc² - ab² - b²c - abc + a²c + b²c + c³ - abc - bc² - c²a

→ a³ + b³+ c³ + (- abc - abc - abc) + (ab² - ab² )+ (ac² - ca² ) -(a²b + a²b )+ (bc² - bc² )+ (a²c - c²a) + (b²c - b²c)

→ a³+b³+c³ - 3 abc .

3. (p – q) (p² + pq + q²) = p³ – q³.

→ p³ + p²q + pq² - p²q - pq² - q³

→ p³ - q³ +(p²q - p²q) + (pq² - pq²)

→ p³ - q³

help help help me plZZZZZ ill give you brainly ;DDD

Answers

Answer:

the answer is 60.7

Step-by-step explanation:

60 to has a between numbers like given in the picture

so as number line it's

60.1 . 60.2 60.3 60.4 60.5 60.6 60.7 60.8 and continue

if u get any 3 digit number like 600 to 650 in number line

u do it like it the same 600.1 600.2.... and go on

Answer:

63½ or 63.5

Step-by-step explanation:

65-60=5

10points=5

1point=?

1×5/10= ½

that means the sequence continues after adding ½ i.e

60..60½...61...61½...62...62½...63...63½...64..64½...65

you have been asked the 8th number which is 63½

what do anthropologist study and why​

Answers

Answer:

Anthropologists study human societies and cultures and the development of them from the past and present. They study this to analyze the differences and evolutions that us as humans have.

Could someone clarrify this for me Factor completely 3x^2 + 2x − 1. (3x + 1)(x − 1) (3x + 1)(x + 1) (3x − 1)(x + 1) (3x − 1)(x − 1)

Answers

Answer:

(3x-1) (x+1)

Step-by-step explanation:

3x^2 + 2x − 1

3x^2 factors into 3x and x

-1 factors into -1 and 1

We want a postive 2x

(3x-1) (x+1)

Answer:

(3x-1)(x+1)

Step-by-step explanation:

3x² + 2x − 1

when factorizing , first look at the constant number( in this case it is 1 prime number), then find the GCF if found.

(3x        )(x      )     first step : 3x*x=3x^2

(3x-      ) (x+   )      the sign for the constant is minus so the factoring has to be minus and plus on each side

(3x-1)(x+1)   look at the 2x it has positive sign, means the sign is plus:

3x-1

x+1

                        regular standard multiplication

3x(x)-1(x)+1(3x)-1

3x²+2x-1

How do we solve 56x + 79 if x = 23? (30 points!) GIVE A GOOD EXPLANATION, NOT JUST AN ANSWER, WHO EVER DOES IT FIRST GETS BRAINLIEST.

Answers

Hello friend!

The answer is: 1367

First, since x = 23, we rewrite the problem.

56(23) + 79 = ?

Now we need to figure out 56 time 23

56 times 23 = 1288

Now we have 1288 + 79.

1288 + 79 = 1367

Answer:

1,367

Explanation:

Step 1 - Input the value of x in the given expression

56x + 79

56(23) + 9

Step 2 - Multiply fifty six by twenty three

56(23) + 79

56 × 23 + 79

1,288 + 79

Step 3 - Add

1,288 + 79

1,297

Therefore, the answer to the given expression is 1,367.

please can someone help me solve this.. please help!!​

Answers

Step-by-step explanation:

Hello,

Firstly just look to triangle BDE,

Here, you will find that,

140° = y+80° {the exterior and opposite interior angle of a triangle is equal}.

or, y= 140°-80° {shifting 80° to another side and subtracting it.}

Therefore, the value of y is 60°.

now, let's simply work with line EB or EG. we get;

angle GEF + y=180° { being a linear pair}.

or, angle GEF + 60°= 180°

or, angle GEF = 180°-60°

Therefore, the value of angle GEF = 120°.

now, looking in triangle EFG, we get;

angle GEF + 35°+x= 180° { the sum of interior angle of a triangle is 180°}.

or, 120°+35°+ x= 180°

or, x= 180°- 155°

Therefore, the value of x is 25°.

now, lastly finding the value of "z"

We find that x= z {being vertical opposite angle}

or, z =25°

Therefore, the value of z is 25°.

So, the values are,

x=25°

y=60°

and z= 25°

Hope it helps...

Brian invested his savings in two investment funds. The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit. How much did he invest in Fund B, if both funds together returned a 2% profit?

Answers

Answer: Brian invested $16000 in Fund B .

Step-by-step explanation:

Let x be the amount Brian invested in Fund B.

Given, The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit.

i.e. profit on Fund A = 4% of 8000 = 0.04 ×8000 = $320

Profit on Fund B = 1% of x = 0.01x

Together they earn 1% profit, i.e. Combined profit = 2% of (8000+x)

= 0.02(8000+x)

As per question,

Combined profit=Profit on Fund A+Profit on Fund B

[tex]\Rightarrow\ 0.02(8000+x) =320+0.01x\\\\\Rightarrow\ 0.02(8000) +0.02x=320+0.01x\\\\\Rightarrow\ 160+0.02x=320+0.01x\\\\\Rightarrow\ 0.02x-0.01x=320-160\\\\\Rightarrow\ 0.01x=160\\\\\Rightarrow\ x=\dfrac{160}{0.01}\\\\\Rightarrow\ x=16000[/tex]

Hence, Brian invested $16000 in Fund B .

If a box of cat food can feed 5 cats for 4 days how long can a box of cat food & cat?

Answers

Answer:

HOME CARE & WELLNESS BASIC PET CARE HOW LONG CAN YOU SAFELY LEAVE A CAT ALONE?

BASIC PET CARE

How Long Can You Safely Leave a Cat Alone?

How Long Can You Safely Leave a Cat Alone?

People who live with cats know that they're not nearly as aloof or independent as alleged. Although cats don't require daily walks like dogs, your presence matters to them… and not only because you have the ability to open a can, fill a water bowl and clean a litter box.

Still, there may be times when you must leave your adult cat for overnight or longer. (Kittens younger than four months should not be left alone for more than four hours. Older than that, they can handle another hour or so. When they reach six months, they can tolerate an eight-hour day without company.)

The length of time you can leave a grown-up cat alone depends on the cat, his diet and your environment. Cats who eat dry food that you can make readily available may be left on their own for 24-48 hours as long as fresh water is accessible as well. Beyond that time frame, water may get too dirty to drink and the litter box full.

To prepare for leaving your cat alone, take steps to make your absence as low‐stress on him as possible. This should include a conversation with your veterinarian.

Answer:

31

Step-by-step explanation:

multiple 5 into 7 that is equal to I week than find the answer that is equal to 35 and minas it by 4 that is equal to 31

A man bought a car for 15000GH cedis . He later sold it at a profit of 25% .What was his selling price.

Answers

Answer:

3750 GH cedis

Step-by-step explanation:

Step-by-step explanation:

100%=15000GH cedis

125%=?

125×15000/100

18750GH cedis

Please help me answer I need an answer asap:3

Answers

Answer:

please mark my answer brainliest

Step-by-step explanation:

it's 115

Answer:

115 degrees.

Step-by-step explanation:

< DBC = (180 - 40) / 2 = 70    ( as it is a base angle of an isosceles Δ)

< EBD = 45 degrees ( as the diagonal of a square bisects 90 degree <).

So < EBC = 70 + 45 = 115 degrees.

what is 136 1/50% of 231

Answers

Answer:

Step-by-step explanation:

136 1/50 % of 231 = 6801/50 % * 231

                             [tex]=\frac{6801}{50*100}*231\\\\\\=\frac{1571031}{5000}[/tex]

                             = 314.2062

Astrid is in charge of building a new fleet of ships. Each ship requires 40 4040 tons of wood, and accommodates 300 300300 sailors. She receives a delivery of 4 44 tons of wood each day. The deliveries can continue for 100 100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 21002100 sailors.

Answers

Answer:

10 ships

Step-by-step explanation:

did it on Khan and

There can be many ways to solve this problem. Here, we will do this by thinking about units.

Let's say that Astrid can build

x

ships

xshipsx, start text, s, h, i, p, s, end text if she receives deliveries of wood for the maximum possible number of days, which is

100

days

100days100, start text, d, a, y, s, end text. How can we relate these two quantities with an equation?

100

days

y

ships

day

=

x

ships

 

100days⋅y

day

ships

=xships

So in order to find the number of ships

x

xx, we need to figure out the value of

y

yy, which is the rate of ships per day.

Hint #22 / 4

Notice what other information we are given:

40

tons

ship

40

ship

tons

40, start fraction, start text, t, o, n, s, end text, divided by, start text, s, h, i, p, end text, end fraction

300

sailors

ship

300

ship

sailors

300, start fraction, start text, s, a, i, l, o, r, s, end text, divided by, start text, s, h, i, p, end text, end fraction

4

tons

day

4

day

tons

4, start fraction, start text, t, o, n, s, end text, divided by, start text, d, a, y, end text, end fraction

2100

sailors

2100sailors2100, start text, s, a, i, l, o, r, s, end text

Which of these quantities can help us calculate a rate whose units are

ships

day

day

ships

start fraction, start text, s, h, i, p, s, end text, divided by, start text, d, a, y, end text, end fraction?

Hint #33 / 4

We can combine the following quantities:

4

tons

day

40

tons

ship

=

4

40

tons

day

ships

ton

=

0.1

ships

day

 

 

=

40

ship

tons

4

day

tons

=

40

4

 

day

tons

ton

ships

=0.1

day

ships

Now we can plug that in the original equation:

100

days

0.1

ships

day

=

x

ships

10

ships

=

x

ships

 

100days⋅0.1

day

ships

10ships

 

=xships

=xships

Hint #44 / 4

In conclusion, assuming Astrid receives the maximum possible amount of wood, she can build

10

1010 ships.

Solve the system of equations algebraically. 5x-3y=6 and 6x-4y=2 a. many solutions c. no solution b. (8,14) d. (9,13)

Answers

Answer:

d. (9, 13)

Step-by-step explanation:

5x-3y=6  /*6

6x-4y=2  /*(-5)

30x - 18y = 36

-30x +20y = - 10

            2y = 26

              y = 13

5x-3y=6

5x - 3*13 = 6

5x - 39 = 6

5x = 45

x = 9

(9, 13)

Can guys please help me, please solve E

Answers

Answer:

Step-by-step explanation:

h(x)=12/x

h(a)= 12/a  ( a is a variable number just replace x with a)

Mr Lim, Mr Tan and Mr Chan have $8650 altogether. Mr Lim has $450 more than Mr Tan. Mr Chan has twice as much money as Mr Tan. How much money does Mr Lim have?​

Answers

Answer:

Mr. Lim will have $2500

Step-by-step explanation:

Given:

The total amount of money which Mr. Lim, Mr. Tan and Mr. Chan is $8650;

Mr. Lim has $450 more than what Mr. Tan has;

Mr. Chan has double the amount of money than what Mr. Tan has.

Therefore, if we assume that the amount of money Mr. Tan has as x, then...

Total money = Mr. Tan + Mr. Lim + Mr. Chan

therefore,

8650 = x + (x + 450) + 2x

8650 = x + 2x + x + 450

8650 = 4x + 450

8650 - 450 = 4x

8200 = 4x

8200/4 = x

2050 = x

As we assumed earlier, x will be equal to the amount of money Mr. Tan has and the question is asking us how much money Mr. Lim has. To find this out, you have to add $450 to the amount of money Mr. Tan has which is $2050. This is because the question also gives us that Mr. Lim has $450 more that Mr. Tan.

I hope this helped you :)

using the property of squares find the value of the following 24 square - 23 square

Answers

Answer:

47

Step-by-step explanation:

Using the follwing property

[tex]x^{2} -y^2=(x+y)(x-y)[/tex]

in which x=24 and y=23

so

[tex]24^2-23^2=(24-23)(24+23)\\=1(47)\\=47[/tex]

Answer:

47

Step-by-step explanation:

Lets say 24 is x and 23 is y.

the equation would be x^2 - y^2

this is = to (x-y)(x+y)

substitute the numbers in

(24-23)(24+23)

which simplifies to

(1)(47)

which equals 47

anyone know how to solve a functions equation such as x^2-x-x <0

Answers

Answer:

Step-by-step explanation:

[tex]x^{2} -x-x<[/tex] 0

[tex]x^{2} -2x[/tex] < 0

x^2-2x+1<1

(x-1)^2<1

-1<x-1<1

0<x<2

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

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