Mathematics: What is the solution for 8 = x + 1?

Step-by-step explanation: Simplify for x by subtracting each side by 1;...

What is the solution for 8 = x + 1?, №18010253, 18.01.2022 00:41

Mathematics

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is an expression for the length of the pool? a. 2x^2+8x+3 b. 2x^2-8x-3 c. 2x^2-8x+3 d. 2x^2+8-3 2. simplify x/6x-x^2 a. 1/6-x; where x = 0,6 b. 1/6-x; where x=6 c. 1/6; where x=0 d. 1/6 3. simplify -12x4/x4+8x^5 a. -12/1+8x; where x= -1/8 b. -12/1+8x; where x= -1/8,0 4. simplify x+5/ x^2+6x+5 a. 1/x+1; where x= -1 b. 1/x+1; where x=-1, -5 5. simplify x^2-3x-18/x+3 a. x-3 b. x-6; where x= -3 c. x-6; where x= 6 d. 1/x+3; where x= -3 6. simplify 2/3a .

Step-by-step answer

P Answered by PhD

20

Question 1

To find the width of the rectangle, we divide the area by the length
$2x^{3}-29x+12$ ÷ x+4

We use the method of long division to get the answer. The method is shown in the first diagram below

$2x^{2}-8x+3$

Question 2:
$\frac{x}{6x-x^{2} } = \frac{x}{x(6-x)} = \frac{1}{6-x}$

Question 3:
$\frac{-12 x^{4} }{x^{4}+8 x^{5} }= \frac{-12 x^{4} }{ x^{4}(1+8x)}= \frac{-12}{1+8x}$

Question 4:
$\frac{x+5}{x^{2}+6x+5}= \frac{x+5}{(x+1)(x+5)}= \frac{1}{x+1}$

Question 5:
$\frac{x^{2}-3x-18} {x+3}= \frac{(x-6)(x+3)}{x+3}= \frac{x-6}{1}=x-6$

Question 6:
$\frac{2}{3a}$ × $\frac{2}{a^{2}}$ = $\frac{4}{3a^{3} }$ where $a \neq 0$

Question 7: (Question is not written well)
$\frac{x-5}{4x+8}$ × $(12x^{2}+32x+8)$
$\frac{12 x^{3}-28 x^{2} -152x-40 }{4x+8}$
By performing long division we get an answer $3 x^{2} -x-36$ with remainder of 248

Question 8:
$( \frac{x^{2}-16} {x-1})$ ÷ (x+4)

$( \frac{ x^{2}-16 }{x-1})$ × $\frac{1}{x+4}$
$\frac{(x+4)(x-1)}{x-1}$ × $\frac{1}{x+4}$
Cancelling out x+4

we obtain $\frac{x+1}{x-1}$

Question 9:
$\frac{x^{2}+2x+1} {x-2}$ ÷ $\frac{x^{2-1} }{x^{2}-4 }$
$\frac{ x^{2}+2x+1 }{x-2}$ × $\frac{x^{2}-4 }{x^{2}-1}$
Factorise all the quadratic expression gives
$\frac{(x+1)(x+1)}{x-2}$ × $\frac{(x-2)(x+2)}{(x+1)(x-1)}$
Cancelling out (x+1)

and

gives a simplest form
$\frac{(x+1)(x+2)}{x-1}$

Question 10:

$\frac{24 w^{10}+8w^{12} }{4 x^{4} }= \frac{24w^{10} }{4 x^{4} } + \frac{8 w^{12} }{4 x^{4} }$
Cancelling out the constants of each fraction
$\frac{6w^{10} }{x^{4} }+ \frac{2w^{12} }{x^{4}}= \frac{6w^{10}+2w^{12} }{ x^{4}}$

Question 11:

$\frac{-6m^{9}-6m^{8}-16m^{6} }{2m^{3} } = \frac{-2m^{6}(3m^{3}-3m^{2}-8)}{2m^{3} }$
Cancelling $2m^{3}$ gives us the simplified form
$-m^{3}(3m^{3}-3m^{2}-8) = -3m^{6}+3m^{5}+8m^{3}$

Question 12:

$\frac{-4x}{x+7} - \frac{8}{x-7} = \frac{-4x(x-7)-8(x+7)}{(x+7)(x-7)}$
$\frac{-4 x^{2} +28x-8x-56}{(x+7)(X-7)}= \frac{-4 x^{2} +20x-56}{(x+7)(x-7)}$
Factorising the numerator expression
$\frac{(-4x+28)(x-2)}{(x+7)(x-7)} = \frac{-4(x-7)(x-2)}{(x+7)(x-7)}$
Cancelling out x-7

gives the simplified form
$\frac{-4x+8}{x-7}$

Question 13:

$\frac{3}{x-3} - \frac{5}{x-2}= \frac{x3(x-2)-5(x-2)}{y(x-3)(x-2)}$
$\frac{3x-6-5x+15}{(x-3)(x-2)}= \frac{-2x+9}{(x-3)(x-2)}$

Question 14:

$\frac{9}{x-1}- \frac{5}{x+4}= \frac{9(x+4)-5(x-1)}{(x-1)(x+4)}$ $\frac{9x+36-5x+5}{(x-1)(x+4)}= \frac{4x+41}{(x-1)(x+4)}$

Question 15:

$\frac{-3}{x+2}- \frac{(-5)}{x+3}= \frac{-3(x+3)-(-5)(x+2)}{(x+2)(x+3)}$
$\frac{-3x-9+5x+10}{(x+2)(x+3)}= \frac{2x+1}{(x+2)(x+3)}$

Question 16:

$\frac{4}{x}+ \frac{5}{x}=-3$
$\frac{9}{x}=-3$
x=-3

Question 17:

$\frac{1}{3x-6}- \frac{5}{x-2}=12$
$\frac{(x-2)-5(3x-6)}{(3x-6)(x-2)} = \frac{x-2-15x+30}{(3x-6)(x-2)}= \frac{-14x+28}{(3x-6)(x-2)}$

Question 18

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is

Mathematics

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is an expression for the length of the pool? a. 2x^2+8x+3 b. 2x^2-8x-3 c. 2x^2-8x+3 d. 2x^2+8-3 2. simplify x/6x-x^2 a. 1/6-x; where x = 0,6 b. 1/6-x; where x=6 c. 1/6; where x=0 d. 1/6 3. simplify -12x4/x4+8x^5 a. -12/1+8x; where x= -1/8 b. -12/1+8x; where x= -1/8,0 4. simplify x+5/ x^2+6x+5 a. 1/x+1; where x= -1 b. 1/x+1; where x=-1, -5 5. simplify x^2-3x-18/x+3 a. x-3 b. x-6; where x= -3 c. x-6; where x= 6 d. 1/x+3; where x= -3 6. simplify 2/3a .

Step-by-step answer

P Answered by PhD

20

Question 1

To find the width of the rectangle, we divide the area by the length
$2x^{3}-29x+12$ ÷ x+4

We use the method of long division to get the answer. The method is shown in the first diagram below

$2x^{2}-8x+3$

Question 2:
$\frac{x}{6x-x^{2} } = \frac{x}{x(6-x)} = \frac{1}{6-x}$

Question 3:
$\frac{-12 x^{4} }{x^{4}+8 x^{5} }= \frac{-12 x^{4} }{ x^{4}(1+8x)}= \frac{-12}{1+8x}$

Question 4:
$\frac{x+5}{x^{2}+6x+5}= \frac{x+5}{(x+1)(x+5)}= \frac{1}{x+1}$

Question 5:
$\frac{x^{2}-3x-18} {x+3}= \frac{(x-6)(x+3)}{x+3}= \frac{x-6}{1}=x-6$

Question 6:
$\frac{2}{3a}$ × $\frac{2}{a^{2}}$ = $\frac{4}{3a^{3} }$ where $a \neq 0$

Question 7: (Question is not written well)
$\frac{x-5}{4x+8}$ × $(12x^{2}+32x+8)$
$\frac{12 x^{3}-28 x^{2} -152x-40 }{4x+8}$
By performing long division we get an answer $3 x^{2} -x-36$ with remainder of 248

Question 8:
$( \frac{x^{2}-16} {x-1})$ ÷ (x+4)

$( \frac{ x^{2}-16 }{x-1})$ × $\frac{1}{x+4}$
$\frac{(x+4)(x-1)}{x-1}$ × $\frac{1}{x+4}$
Cancelling out x+4

we obtain $\frac{x+1}{x-1}$

Question 9:
$\frac{x^{2}+2x+1} {x-2}$ ÷ $\frac{x^{2-1} }{x^{2}-4 }$
$\frac{ x^{2}+2x+1 }{x-2}$ × $\frac{x^{2}-4 }{x^{2}-1}$
Factorise all the quadratic expression gives
$\frac{(x+1)(x+1)}{x-2}$ × $\frac{(x-2)(x+2)}{(x+1)(x-1)}$
Cancelling out (x+1)

and

gives a simplest form
$\frac{(x+1)(x+2)}{x-1}$

Question 10:

$\frac{24 w^{10}+8w^{12} }{4 x^{4} }= \frac{24w^{10} }{4 x^{4} } + \frac{8 w^{12} }{4 x^{4} }$
Cancelling out the constants of each fraction
$\frac{6w^{10} }{x^{4} }+ \frac{2w^{12} }{x^{4}}= \frac{6w^{10}+2w^{12} }{ x^{4}}$

Question 11:

$\frac{-6m^{9}-6m^{8}-16m^{6} }{2m^{3} } = \frac{-2m^{6}(3m^{3}-3m^{2}-8)}{2m^{3} }$
Cancelling $2m^{3}$ gives us the simplified form
$-m^{3}(3m^{3}-3m^{2}-8) = -3m^{6}+3m^{5}+8m^{3}$

Question 12:

$\frac{-4x}{x+7} - \frac{8}{x-7} = \frac{-4x(x-7)-8(x+7)}{(x+7)(x-7)}$
$\frac{-4 x^{2} +28x-8x-56}{(x+7)(X-7)}= \frac{-4 x^{2} +20x-56}{(x+7)(x-7)}$
Factorising the numerator expression
$\frac{(-4x+28)(x-2)}{(x+7)(x-7)} = \frac{-4(x-7)(x-2)}{(x+7)(x-7)}$
Cancelling out x-7

gives the simplified form
$\frac{-4x+8}{x-7}$

Question 13:

$\frac{3}{x-3} - \frac{5}{x-2}= \frac{x3(x-2)-5(x-2)}{y(x-3)(x-2)}$
$\frac{3x-6-5x+15}{(x-3)(x-2)}= \frac{-2x+9}{(x-3)(x-2)}$

Question 14:

$\frac{9}{x-1}- \frac{5}{x+4}= \frac{9(x+4)-5(x-1)}{(x-1)(x+4)}$ $\frac{9x+36-5x+5}{(x-1)(x+4)}= \frac{4x+41}{(x-1)(x+4)}$

Question 15:

$\frac{-3}{x+2}- \frac{(-5)}{x+3}= \frac{-3(x+3)-(-5)(x+2)}{(x+2)(x+3)}$
$\frac{-3x-9+5x+10}{(x+2)(x+3)}= \frac{2x+1}{(x+2)(x+3)}$

Question 16:

$\frac{4}{x}+ \frac{5}{x}=-3$
$\frac{9}{x}=-3$
x=-3

Question 17:

$\frac{1}{3x-6}- \frac{5}{x-2}=12$
$\frac{(x-2)-5(3x-6)}{(3x-6)(x-2)} = \frac{x-2-15x+30}{(3x-6)(x-2)}= \frac{-14x+28}{(3x-6)(x-2)}$

Question 18

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is

Mathematics

Which table best represents the steps to solve the equation 8 + x over 3 = 4? (5 points) select one: a. step justification step 1: x over 3 = 4 + 8 the same number +8 can be added to both sides of the equation step 2: x over 3 = 12 adding 8 and 4 on the right hand side step 3: x = 12 ⋅ 3 the same number 3 can be multiplied on both sides of the equation step 4: x = 36 multiplying 12 and 3 on the right hand side b. step justification step 1 x over 3 = 4 − 8 the same number −8 can be added to both sides of the equation step 2: x over 3 = −4 adding

Step-by-step answer

P Answered by Specialist

10

The answer is -1/8 because u multiply both numerators by each other and both deminators by eachother and you get 15\120 then u simplify you do 15 divided by 15 and get 1and then 120 divided by 15 and get 8 and u get 1\8 as your answer

Mathematics

Which table best represents the steps to solve the equation 8 + x over 3 = 4? (5 points) select one: a. step justification step 1: x over 3 = 4 + 8 the same number +8 can be added to both sides of the equation step 2: x over 3 = 12 adding 8 and 4 on the right hand side step 3: x = 12 ⋅ 3 the same number 3 can be multiplied on both sides of the equation step 4: x = 36 multiplying 12 and 3 on the right hand side b. step justification step 1 x over 3 = 4 − 8 the same number −8 can be added to both sides of the equation step 2: x over 3 = −4 adding

Step-by-step answer

P Answered by Master

10

The answer is -1/8 because u multiply both numerators by each other and both deminators by eachother and you get 15\120 then u simplify you do 15 divided by 15 and get 1and then 120 divided by 15 and get 8 and u get 1\8 as your answer

Mathematics

Solve each equation and match them with the correct solution. Column A 1. large -3x=42 : large -3x=42 2. large frac{x}{-6}=-9 : large frac{x}{-6}=-9 3. large 5x=-105 : large 5x=-105 4. large x+37=-25 : large x+37=-25 5. large x-42=-15 : large x-42=-15 6. large x- left(-12 right)=-4 : large x- left(-12 right)=-4 7. large x- left(-6 right)=5 : large x- left(-6 right)=5 8. large 8-x=-12 : large 8-x=-12 9. large -9-x=-6 : large -9-x=-6 10. large -6+x=17 : large -6+x=17 11. large frac{x}{9}=-42 : large frac{x}{9}=-42 12. large -16=x-8 : large -16=x-8

Step-by-step answer

P Answered by PhD

1

The answer is below

Step-by-step explanation:

1) -3x = 42

Divide both sides by -3

-3x/ -3 = 42 / -3

x = -14

p.x=-14

2)

$\frac{x}{-6}=-9\\ \\Multiply\ both\ sides\ by\ -6\\\\\frac{x}{-6}*-6=-9*-6\\\\x=54$

j. x=54

3) 5x = 105

Divide both sides by 5

5x/ 5 = 105 / 5

x = 21

n. x=-21

4) x+37=-25

add -37 to both sides

x+37 - 37 =-25 - 37

x = -62

d. x=-62

5) x-42=-15

add 42 to both sides

x-42 + 42 =-15 + 42

x = 27

k. x=27

6)x - (-12) = -4

x + 12 = -4

add -12 to both sides:

x + 12 - 12 = -4 - 12

x = -16

f. x = -16

7) x - (-6) = 5

x + 6 = 5

add -6 to both sides:

x + 6 - 6 = 5 - 6

x = -1

r. x = -1

8)8-x = -12

8 - x + x + 12 = -12 + x = 12

x = 8 + 12

x = 20

c) x = 20

9) -9 - x = -6

x = -9 + 6

x = -3

s. x =-3

10) -6 + x = 17

x = 17 + 6

x = 23

a. x =23

11)

$\frac{x}{9} =-42\\multiply\ by \ 9\\\\x = 9*-42=-378$

b. x = -378

12) -16 = x - 8

x = -16 + 8

x = -8

q. x = -8

13) -25 = x + 17

x = -25 - 17

x = -42

h. x = -42

14) 36 = 8 - x

x = 8 - 36

x = -28

g. x = -28

15) -x + 6 = 11

x = 6 - 11

x = -5

m. x = -5

16) -x + 8 = 4

x= 8 - 4

x = 4

e. x =4

17) 16 = 4 -x

x = 4 - 16

x = -12

o: x = -12

18) 85 = -5x

x = 85/ -5

x = -17

l. x= -17

19) 21 = -x/7

x = 21 * -7

x = -147

i. x = -147

Mathematics

Solve each equation and match them with the correct solution. Column A 1. large -3x=42 : large -3x=42 2. large frac{x}{-6}=-9 : large frac{x}{-6}=-9 3. large 5x=-105 : large 5x=-105 4. large x+37=-25 : large x+37=-25 5. large x-42=-15 : large x-42=-15 6. large x- left(-12 right)=-4 : large x- left(-12 right)=-4 7. large x- left(-6 right)=5 : large x- left(-6 right)=5 8. large 8-x=-12 : large 8-x=-12 9. large -9-x=-6 : large -9-x=-6 10. large -6+x=17 : large -6+x=17 11. large frac{x}{9}=-42 : large frac{x}{9}=-42 12. large -16=x-8 : large -16=x-8

Step-by-step answer

P Answered by PhD

1

The answer is below

Step-by-step explanation:

1) -3x = 42

Divide both sides by -3

-3x/ -3 = 42 / -3

x = -14

p.x=-14

2)

$\frac{x}{-6}=-9\\ \\Multiply\ both\ sides\ by\ -6\\\\\frac{x}{-6}*-6=-9*-6\\\\x=54$

j. x=54

3) 5x = 105

Divide both sides by 5

5x/ 5 = 105 / 5

x = 21

n. x=-21

4) x+37=-25

add -37 to both sides

x+37 - 37 =-25 - 37

x = -62

d. x=-62

5) x-42=-15

add 42 to both sides

x-42 + 42 =-15 + 42

x = 27

k. x=27

6)x - (-12) = -4

x + 12 = -4

add -12 to both sides:

x + 12 - 12 = -4 - 12

x = -16

f. x = -16

7) x - (-6) = 5

x + 6 = 5

add -6 to both sides:

x + 6 - 6 = 5 - 6

x = -1

r. x = -1

8)8-x = -12

8 - x + x + 12 = -12 + x = 12

x = 8 + 12

x = 20

c) x = 20

9) -9 - x = -6

x = -9 + 6

x = -3

s. x =-3

10) -6 + x = 17

x = 17 + 6

x = 23

a. x =23

11)

$\frac{x}{9} =-42\\multiply\ by \ 9\\\\x = 9*-42=-378$

b. x = -378

12) -16 = x - 8

x = -16 + 8

x = -8

q. x = -8

13) -25 = x + 17

x = -25 - 17

x = -42

h. x = -42

14) 36 = 8 - x

x = 8 - 36

x = -28

g. x = -28

15) -x + 6 = 11

x = 6 - 11

x = -5

m. x = -5

16) -x + 8 = 4

x= 8 - 4

x = 4

e. x =4

17) 16 = 4 -x

x = 4 - 16

x = -12

o: x = -12

18) 85 = -5x

x = 85/ -5

x = -17

l. x= -17

19) 21 = -x/7

x = 21 * -7

x = -147

i. x = -147

Mathematics

Select all the equations that are true. 24 x − 8 = 8 ( 3 x − 1 ) 24 x − 8 = 8 ( 3 x − 1 ) 6 m − 15 = 3 ( 2 m − 5 ) 6 m − 15 = 3 ( 2 m − 5 ) − 7 x − 1 = − 1 ( 7 x + 1 ) − 7 x − 1 = − 1 ( 7 x + 1 ) 16 a + 24 b = 8 ( 8 a + 16 b ) 16 a + 24 b = 8 ( 8 a + 16 b ) − 8 x − 12 y − 16 = − 4 ( 2 x + 3 y + 4 ) − 8 x − 12 y − 16 = − 4 ( 2 x + 3 y + 4 )

Step-by-step answer

P Answered by PhD

24x - 8 = 8 ( 3 x - 1 )

6 m - 15 = 3 ( 2 m - 5 )

-7 x - 1 = - 1 ( 7 x + 1 )

-8 x -12 y - 16 = - 4 ( 2 x + 3 y + 4 )

Step-by-step explanation:

Required

Select which of the equation is true

24x - 8 = 8 ( 3 x - 1 )

Open the bracket on the right hand side

24x - 8 = 8 * 3 x - 8 *1

24x - 8 = 24x - 8

Both sides of the equation are equal.

Hence, this equation is true

6 m - 15 = 3 ( 2 m - 5 )

Open the bracket on the right hand side

6m - 15 = 3 * 2m - 3 * 5

6m - 15 = 6m - 15

Both sides of the equation are equal.

Hence, this equation is true

-7 x - 1 = - 1 ( 7 x + 1 )

Open the bracket on the right hand side

-7x - 1 = -1 * 7x -1 * 1

-7x - 1 = -7x -1

Both sides of the equation are equal.

Hence, this equation is true

16 a + 24 b = 8 ( 8 a + 16 b )

Open the bracket on the right hand side

16a + 24b = 8 * 8a + 8 * 16b

16a + 24b = 64a + 128b

Both sides of the equation are not equal.

Hence, this equation is false

-8 x -12 y - 16 = - 4 ( 2 x + 3 y + 4 )

Open the bracket on the right hand side

-8 x -12 y - 16 = - 4* 2 x -4 * 3 y -4 * 4

-8 x -12 y - 16 = -8x -12y -16

Both sides of the equation are equal.

Hence, this equation is true

Mathematics

Select all the equations that are true. 24 x − 8 = 8 ( 3 x − 1 ) 24 x − 8 = 8 ( 3 x − 1 ) 6 m − 15 = 3 ( 2 m − 5 ) 6 m − 15 = 3 ( 2 m − 5 ) − 7 x − 1 = − 1 ( 7 x + 1 ) − 7 x − 1 = − 1 ( 7 x + 1 ) 16 a + 24 b = 8 ( 8 a + 16 b ) 16 a + 24 b = 8 ( 8 a + 16 b ) − 8 x − 12 y − 16 = − 4 ( 2 x + 3 y + 4 ) − 8 x − 12 y − 16 = − 4 ( 2 x + 3 y + 4 )

Step-by-step answer

P Answered by PhD

24x - 8 = 8 ( 3 x - 1 )

6 m - 15 = 3 ( 2 m - 5 )

-7 x - 1 = - 1 ( 7 x + 1 )

-8 x -12 y - 16 = - 4 ( 2 x + 3 y + 4 )

Step-by-step explanation:

Required

Select which of the equation is true

24x - 8 = 8 ( 3 x - 1 )

Open the bracket on the right hand side

24x - 8 = 8 * 3 x - 8 *1

24x - 8 = 24x - 8

Both sides of the equation are equal.

Hence, this equation is true

6 m - 15 = 3 ( 2 m - 5 )

Open the bracket on the right hand side

6m - 15 = 3 * 2m - 3 * 5

6m - 15 = 6m - 15

Both sides of the equation are equal.

Hence, this equation is true

-7 x - 1 = - 1 ( 7 x + 1 )

Open the bracket on the right hand side

-7x - 1 = -1 * 7x -1 * 1

-7x - 1 = -7x -1

Both sides of the equation are equal.

Hence, this equation is true

16 a + 24 b = 8 ( 8 a + 16 b )

Open the bracket on the right hand side

16a + 24b = 8 * 8a + 8 * 16b

16a + 24b = 64a + 128b

Both sides of the equation are not equal.

Hence, this equation is false

-8 x -12 y - 16 = - 4 ( 2 x + 3 y + 4 )

Open the bracket on the right hand side

-8 x -12 y - 16 = - 4* 2 x -4 * 3 y -4 * 4

-8 x -12 y - 16 = -8x -12y -16

Both sides of the equation are equal.

Hence, this equation is true

Mathematics

The value of y varies directly with x, where LaTeX: y=50y = 50 when LaTeX: x=40x = 40. Find the value of x when y is 10. Group of answer choices LaTeX: x=8 x = 8 x = 8 x = 8 x = 8 x = 8 x = 8 x = 8 LaTeX: x=12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 LaTeX: x=1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 LaTeX: x=0

Step-by-step answer

P Answered by PhD

2

x= 8

Step-by-step explanation:

The equation of direct variation is

y = kx

When y = 50 when x = 40

50 = k* 40

Divide each side by 40

50/40 = k

5/4 = k

The equation is

y = 5/4x

Let y = 10

10 = 5/4x

Multiply each side by 4/5

4/5 * 10 = 5/4 x * 4/5

8 = x

Mathematics

Let x = 7.99999 . (a) is x 8 or is x = 8? x 8 it is neither; x 8 x = 8 x 8 and x = 8 it cannot be determined. correct: your answer is correct. (b) sum a geometric series to find the value of x. x = 8 correct: your answer is correct. (c) how many decimal representations does the number 8 have? 1 incorrect: your answer is incorrect. decimal representations (d) which numbers have more than one decimal representation? the integers all real numbers the rational numbers except for 0 all integers except for 0 all rational numbers that have a terminating

Step-by-step answer

P Answered by PhD

1

a) We showed in (b) that 7.9999... = 8

b) The sum of the geometric series that involves 7.9999... = 8

c) The number 8 has two decimal representations.

d) All real, rational numbers except for 0 have more than one decimal representations.

Step-by-step explanation:

x = 7.999999

To answer (a), we first evaluate (b)

b) We need to sum a geometric series to infinity to find the values of this expression.

7.99999 can be written as 7 + 0.9999

0.99999 is a geometric series that is essentially

0.99999... = 0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 +

The sum to infinity for a geometric series is given as S = a ÷ (1-r)

where

a = first term = 0.9

r = common ratio = (second term) ÷ (first term) = 0.09 ÷ 0.9 = 0.1

Sum of this geometric series to infinity

= 0.9 ÷ (1 - 0.1) = 0.9 ÷ 0.9 = 1

0.9999... = 1

7.99999 = 7 + 0.99999... = 7 + 1 = 8

c) how many decimal representations does the number 8 have?

As shown in (b), 8 has 2 decimal representations, the one we know and this newly proven one.

d) which numbers have more than one decimal representation?

All real, rational numbers except for 0 have more than one decimal representations.

Hope this Helps!!!

What is the solution for 8 = x + 1?

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