Solve for x: 5/8=x-1/9 a. 37/8 b. 23/4 c. 11/2 d. 53/8

4 answers
Question:

Solve for x: 5/8=x-1/9
a. 37/8
b. 23/4
c. 11/2
d. 53/8

Answers

53/72

Step-by-step explanation:

5/8 = x - 1/9

+1/9       +1/9

5/8 + 1/9 = x

9(5/8)  + 8(1/9)

45/72 + 8/72

x= 53/72

** CORRECTIONS: Q1: It's 2x^3-29x+12; Q2,3,4,5,6: All conditions have ≠ symbol; Q7: it's (12x^2+32x+16); Q10: Option D should be divided by x^4; **

(1) Given:

Width = W = x+4

Area = A = [tex]2x^3-29x+12[/tex]

Length = L = ?

Since the pool is rectangular in shape:

area = width * length

A = W * L

Substitute:

[tex]2x^3-29x+12 = (x+4) * L \\ L =\frac{2x^3-29x+12}{x+4}[/tex]

The long division is attached with the answer (below in the picture). Hence the correct answer is [tex]2x^2-8x+3[/tex] (Option C)

(2) Given expression:

[tex]\frac{x}{6x-x^2} \\ \frac{x}{x(6-x)} \\ \frac{1}{6-x}[/tex]

Where x ≠ 6. (Option B)

(3) Given :

[tex]\frac{-12 x^{4} }{x^{4}+8 x^{5} }[/tex]

Now simplify:

[tex]\frac{-12 x^{4} }{x^{4}+8 x^{5} }= \frac{-12 x^{4} }{ x^{4}(1+8x)}= \frac{-12}{1+8x}[/tex]

Where x ≠ -1/8 (Option A)

(4) Given:

[tex]\frac{x+5}{x^{2}+6x+5}[/tex]

Simplify:

[tex]\frac{x+5}{x^{2}+6x+5}= \frac{x+5}{(x+1)(x+5)}= \frac{1}{x+1}[/tex]

Where x ≠ -1 (Option A)

(5) Given:

[tex]\frac{x^{2}-3x-18} {x+3}[/tex]

Simplify:

[tex]\frac{x^{2}-3x-18} {x+3}= \frac{(x-6)(x+3)}{x+3}= \frac{x-6}{1}=x-6[/tex] where x≠6 (Option C)

(6) Given:

[tex]\frac{2}{3a} .\frac{2}{a^2}[/tex]

Simplify:

[tex]\frac{4}{3a^{1+2}} = \frac{4}{3a^{3}}[/tex]

Where a ≠ 0 (Option C)

(7) Mathematically:

[tex]\frac{x-5}{4x + 8} * (12x^2+32x+16)[/tex]

Simplify:

[tex]\frac{x-5}{4x + 8} * (12x^2+32x+16) \\ \frac{x-5}{4(x + 2)} * 12x^2 + \frac{x-5}{4(x + 2)} * 32x + \frac{x-5}{4(x + 2)} * 16 \\ \frac{x-5}{(x + 2)} * 3x^2 + \frac{x-5}{(x + 2)} * 8x + \frac{x-5}{(x + 2)} * 4 \\ \frac{(x-5)(3x^2 + 8x + 4x) }{(x+2)} \\ \frac{(x-5)(3x^2 -6x - 2x + 4x) }{(x+2)} \\ \frac{(x-5)(3x+2)(x+2) }{(x+2)} \\ =(x-5)(3x+2)[/tex]

(Option C)

(8) Simplify:

[tex]\frac{( \frac{x^{2}-16} {x-1}) }{(x+4)} \\ \frac{( \frac{(x+4)(x-4)} {x-1}) }{(x+4)} \\ = \frac{(x-4)} {(x-1)}[/tex]

(Option A)

(9) Simplify:

[tex]\frac{ \frac{x^2+2x+1}{x-2}}{\frac{x^2-1}{x^2-4 }} \\ \frac{ \frac{(x+1)(x+1)}{x-2}}{\frac{(x+1)(x-1)}{(x-2)(x+2) }} \\ \frac{ \frac{(x+1)}{1}}{\frac{(x-1)}{(x+2) }} \\ = \frac{(x+1)(x+2)}{(x-1)}[/tex]

(Option A)

(10) Given:

[tex]\frac{24 w^{10}+8w^{12} }{4 x^{4} }[/tex]

Simplify:

[tex]\frac{24 w^{10}+8w^{12} }{4 x^{4} }= \frac{24w^{10} }{4 x^{4} } + \frac{8 w^{12} }{4 x^{4} } = \frac{6w^{10} }{x^{4} }+ \frac{2w^{12} }{x^{4}}= \frac{6w^{10}+2w^{12} }{ x^{4}}[/tex]

(Option D)

(11) Given:

[tex]\frac{-6m^{9}-6m^{8}-16m^{6} }{2m^{3} }[/tex]

Simplify:

[tex]\frac{-6m^{9}-6m^{8}-16m^{6} }{2m^{3} } = \frac{-2m^{6}(3m^{3}+3m^{2}+8)}{2m^{3} } = -m^{3}(3m^{3}+3m^{2}+8)\\ = -3m^{6}-3m^{5}-8m^{3}[/tex]

(Option C)

(12) Simplify:

[tex]\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)} \\ \frac{(-4x+28)(x-2)}{(x+7)(x-7)} = \frac{-4(x-7)(x-2)}{(x+7)(x-7)} = \frac{-4x+8}{x+7}[/tex]

(Option A)

(13) Simplify:

[tex]\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)}[/tex]

(Option A)

(14) Simplify:

[tex]\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)}[/tex]

(Option B)

(15) Simplify:

[tex]\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)}[/tex]

(Option D)

(16) Given:

4/x + 5/x = -3

Simplify:

(4+5)/x = -3

-3x = 9

x = -3 (Option C)

(17) Simplify:

[tex]\frac{1}{3x-6} - \frac{5}{x-2} = 12 \\ \frac{(x-2)-5(3x-6)}{(3x-6)(x-2)} = 12 \\ \frac{(x-2)-5*3(x-2)}{(3x-6)(x-2)} = 12 \\ \frac{-14(x-2)}{(3x-6)(x-2)} = 12 \\ \frac{-14}{(3x-6)} = 12\\ -14 = 12(3x-6) \\ -14 = 36x - 72 \\ 36x = 58 \\ x=\frac{29}{18}[/tex]

(Option D)

(18) Simplify:

[tex]\frac{1}{x} - \frac{6}{x^2} = -12 \\ \frac{x - 6}{x^2} = -12 \\ x-6 = -12x^2 \\ 12x^2 + x - 6 = 0 \\ 12x^2 + 9x - 8x - 6 = 0 \\ 3x(4x + 3) -2(4x + 3) =0 \\ (3x-2)(4x+3) =0 \\ = x =\frac{2}{3} , x =\frac{-3}{4}[/tex]

(Option C)

(19) Dorothy's rate (alone) will be:

[tex]R_D =\frac{1}{6}[/tex]

Rosanne's rate (alone) will be:

[tex]R_R =\frac{1}{8}[/tex]

If both work together, add both the rates:

[tex]R_T = R_D + R_R = \frac{1}{6} + \frac{1}{8} = \frac{7}{24}[/tex] (in 1/hours)

To find the hours, flip the rate:

[tex]\frac{24}{7} = 3.43[/tex] hours (Option B)

(20) As pressure (p) is inversely proportional with volume (v):

p = k/v (where k is constant of proportionality)

k = pv

Find constant using initial values:

k = (104)(108)

k = 11232

Now new pressure is:

p = k/v = 11232/432 = 26 Pa (Option A)

(21)

x: 1,3,5,10

y: 4,12,20,40

Direct variation is the value of y increases with x. So,

y = 4x

If x = 1,y=4(1)=4

If x = 3,y=4(3)=12

If x = 5,y=20

If x = 10,y=40 (Option A)

(22) [tex]\frac{3}{4x+64}[/tex]

If x=-16,4(-16) + 64 = 0;denominator will become zero,which means that there will be discontinuity at x = -16. Hence, x=-16 (Option C) should be excluded.


[tex]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[/tex]

the answer for x will be -1/2

even though thats not one of your answer choices

Step-by-step explanation:

Question 1

To find the width of the rectangle, we divide the area by the length
[tex]2x^{3}-29x+12[/tex]÷[tex]x+4[/tex]
We use the method of long division to get the answer. The method is shown in the first diagram below

 [tex]2x^{2}-8x+3[/tex]

Question 2:
[tex]\frac{x}{6x-x^{2} } = \frac{x}{x(6-x)} = \frac{1}{6-x}[/tex]

Question 3:
[tex]\frac{-12 x^{4} }{x^{4}+8 x^{5} }= \frac{-12 x^{4} }{ x^{4}(1+8x)}= \frac{-12}{1+8x}[/tex]

Question 4: 
[tex]\frac{x+5}{x^{2}+6x+5}= \frac{x+5}{(x+1)(x+5)}= \frac{1}{x+1}[/tex]

Question 5:
[tex]\frac{x^{2}-3x-18} {x+3}= \frac{(x-6)(x+3)}{x+3}= \frac{x-6}{1}=x-6[/tex]

Question 6:
[tex]\frac{2}{3a}[/tex]×[tex]\frac{2}{a^{2}}[/tex]=[tex]\frac{4}{3a^{3} }[/tex] where [tex]a \neq 0[/tex]

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

Question 8:
[tex]( \frac{x^{2}-16} {x-1})[/tex]÷[tex](x+4)[/tex]
[tex]( \frac{ x^{2}-16 }{x-1})[/tex]×[tex]\frac{1}{x+4}[/tex]
[tex]\frac{(x+4)(x-1)}{x-1}[/tex]×[tex]\frac{1}{x+4}[/tex]
Cancelling out [tex]x+4[/tex] we obtain [tex]\frac{x+1}{x-1}[/tex]

Question 9:
[tex]\frac{x^{2}+2x+1} {x-2}[/tex]÷[tex]\frac{x^{2-1} }{x^{2}-4 }[/tex]
[tex]\frac{ x^{2}+2x+1 }{x-2}[/tex]×[tex]\frac{x^{2}-4 }{x^{2}-1}[/tex]
Factorise all the quadratic expression gives
[tex]\frac{(x+1)(x+1)}{x-2}[/tex]×[tex]\frac{(x-2)(x+2)}{(x+1)(x-1)}[/tex]
Cancelling out [tex](x+1)[/tex] and [tex](x-2)[/tex] gives a simplest form
[tex]\frac{(x+1)(x+2)}{x-1}[/tex]

Question 10:

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

Question 11:

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

Question 12:

[tex]\frac{-4x}{x+7} - \frac{8}{x-7} = \frac{-4x(x-7)-8(x+7)}{(x+7)(x-7)}[/tex]
[tex]\frac{-4 x^{2} +28x-8x-56}{(x+7)(X-7)}= \frac{-4 x^{2} +20x-56}{(x+7)(x-7)}[/tex]
Factorising the numerator expression
[tex]\frac{(-4x+28)(x-2)}{(x+7)(x-7)} = \frac{-4(x-7)(x-2)}{(x+7)(x-7)}[/tex]
Cancelling out [tex]x-7[/tex] gives the simplified form
[tex]\frac{-4x+8}{x-7}[/tex]

Question 13:

[tex]\frac{3}{x-3} - \frac{5}{x-2}= \frac{x3(x-2)-5(x-2)}{y(x-3)(x-2)}[/tex]
[tex]\frac{3x-6-5x+15}{(x-3)(x-2)}= \frac{-2x+9}{(x-3)(x-2)}[/tex]

Question 14:

[tex]\frac{9}{x-1}- \frac{5}{x+4}= \frac{9(x+4)-5(x-1)}{(x-1)(x+4)}[/tex][tex]\frac{9x+36-5x+5}{(x-1)(x+4)}= \frac{4x+41}{(x-1)(x+4)}[/tex]

Question 15:

[tex]\frac{-3}{x+2}- \frac{(-5)}{x+3}= \frac{-3(x+3)-(-5)(x+2)}{(x+2)(x+3)}[/tex]
[tex]\frac{-3x-9+5x+10}{(x+2)(x+3)}= \frac{2x+1}{(x+2)(x+3)}[/tex]

Question 16:

[tex]\frac{4}{x}+ \frac{5}{x}=-3[/tex]
[tex]\frac{9}{x}=-3[/tex]
[tex]x=-3[/tex]

Question 17:

[tex]\frac{1}{3x-6}- \frac{5}{x-2}=12[/tex]
[tex]\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)}[/tex]

Question 18

[tex]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[/tex]

Similar Solved Works

5 answers

Read this excerpt from 'Ormuzd and Arimanes.'Ormuzd, the king of light, and Arimanes, the prince of darkness, both emanated from the Eternal One, and

Read this excerpt from "Ormuzd and Arimanes." Ormuzd, the king of light, and Arimanes, the prince of darkness, both emanated from the Eternal One, and consequently were brothers. Arimanes, who was the second emanation, became jealous of Ormuzd, the first born. How does this incident provoke a deci...
4 answers

Yo i got a doggg

Yo i got a doggg [tex]Yoooooooo i got a doggg[/tex]...
4 answers

Please help i don't understand ​

Please help i don't understand ​ [tex]Please help i don't understand ​[/tex]...
4 answers

Is anyone bored? could they do 37 pages of notes for my AP world history

Is anyone bored? could they do 37 pages of notes for my AP world history...
6 answers

Meredith notices that different plant fertilizers are made up of different chemicals. some fertilizers are high in nitrogen.

Meredith notices that different plant fertilizers are made up of different chemicals. some fertilizers are high in nitrogen. other fertilizers are high in phosphorus. meredith hypothesizes that nitrogen-rich fertilizers are best to grow fruit crops such as strawberries. when she is designing her exp...
4 answers

30 points for a full answer! you will now judge the contributions that african americans, native americans, and women made

30 points for a full answer! you will now judge the contributions that african americans, native americans, and women made to the american revolution by ranking each group. the group you believe made the largest contribution you will rank #1, the group you believe made the smallest contribution you...
4 answers

PLSS HELPP!! I WILL MARK BRAINLIEST FOR BEST ANSWEATTACK ON FORT SUMTER MARKED START OF WARPART B: Which detail from the

PLSS HELPP!! I WILL MARK BRAINLIEST FOR BEST ANSWE ATTACK ON FORT SUMTER MARKED START OF WARPART B: Which detail from the text best supports the answer to Part A?A. “Who were Sumter’s defenders? Just 82 soldiers — including members of themilitary band — aided by about 40 workmen employed at...
3 answers

If f(x) = 3x2 – 2 and g(x) = 2x + 4, find (f- g)(x).

If f(x) = 3x2 – 2 and g(x) = 2x + 4, find (f- g)(x)....
10 answers

Identify the 5 characteristics of a free market economy. Government ownership of property / resources Competition Private ownership

Identify the 5 characteristics of a free market economy. Government ownership of property / resources Competition Private ownership of property / resources Profit motive Centrally-planned economy Individual choice Consumer sovereignty Lack of consumer choice...
4 answers

The people attending a movie showing on saturday had the ages: 43, 46, 49, 50, 52, 54, 78, 47. what

The people attending a movie showing on saturday had the ages: 43, 46, 49, 50, 52, 54, 78, 47. what is the outlier of these ages?...
10 answers

Help please im going to fail. answer choices are in the picture

Help please im going to fail. answer choices are in the picture [tex]Helpppp please im going to fail. answer choices are in the picture[/tex]...
4 answers

A diamond merchant received a shipment of 1/3 of a pound of diamonds. She divided the diamonds into 3 equal lots and sold

A diamond merchant received a shipment of 1/3 of a pound of diamonds. She divided the diamonds into 3 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot?...
3 answers

Find the output, y, when the input, x, is 4Y=25-3x

Find the output, y, when the input, x, is 4 Y=25-3x [tex]Find the output, y, when the input, x, is 4 Y=25-3x[/tex]...
6 answers

Apex plz i’m almost done if i get this all right

Apex plz i’m almost done if i get this all right [tex]Apex plz i’m almost done if i get this all right[/tex]...
10 answers

Which expressions are equivalent to 2(4x−3)+3x−12(4x−3)+3x−1 select each correct answer. a.11x−711x−7

Which expressions are equivalent to 2(4x−3)+3x−12(4x−3)+3x−1 select each correct answer. a.11x−711x−7 b.4(3x−1)−x−34(3x−1)−x−3 c.2(3x−3)+5x−12(3x−3)+5x−1 d.5x−15x−1 e.8x+3x−48x+3x−4 f.2(4x+3x)−4...
4 answers

Ns for Reflection: Why did the Japanese look for revenge against the Chinese at Nanking?

Ns for Reflection: Why did the Japanese look for revenge against the Chinese at Nanking?...
4 answers

Victoria needs $299 to purchase a music player. She earns $4.50 per hour from her neighbor for babysitting. She has already saved

Victoria needs $299 to purchase a music player. She earns $4.50 per hour from her neighbor for babysitting. She has already saved $75. Which inequality bestrepresents the minimum number of hours she will have to babysit to earn enough money to purchase the music player?...
1 answer

Which of the following is the solution to |-12X-15|<_7

Which of the following is the solution to |-12X-15|<_7...
4 answers

What is an odd number

What is an odd number...
4 answers

Write and solve an inequality. To cover a rectangular region of her yard, Penny needs at least 145 square feet of sod. The length

Write and solve an inequality. To cover a rectangular region of her yard, Penny needs at least 145 square feet of sod. The length of the region is 14.5. Let the width be x. The inequality is...

-- 0.015268--