if 3/4 of a number is added to 5/4 it gives the same result as taking 7/8 of the number from 20 ⅓. Find the number​

Answers

Answer 1

Given:

[tex]\dfrac{3}{4}[/tex] of a number is added to [tex]\dfrac{5}{4}[/tex] it gives the same result as taking [tex]\dfrac{7}{8}[/tex] of the number from [tex]20\dfrac{1}{3}[/tex].

To find:

The unknown number.

Solution:

Let x be the unknown number.

[tex]\dfrac{3}{4}[/tex] of a number is added to [tex]\dfrac{5}{4}[/tex] it gives the same result as taking [tex]\dfrac{7}{8}[/tex] of the number from [tex]20\dfrac{1}{3}[/tex].

[tex]\dfrac{5}{4}+\dfrac{3}{4}x=20\dfrac{1}{3}-\dfrac{7}{8}x[/tex]

[tex]\dfrac{5+3x}{4}=\dfrac{61}{3}-\dfrac{7}{8}x[/tex]

[tex]\dfrac{5+3x}{4}=\dfrac{488-21x}{24}[/tex]

Multiply both sides by 24.

[tex]6(5+3x)=488-21x[/tex]

[tex]30+18x=488-21x[/tex]

[tex]18x+21x=488-30[/tex]

[tex]39x=458[/tex]

Divide both sides by 39.

[tex]x=\dfrac{458}{39}[/tex]

Therefore, the required number is [tex]\dfrac{458}{39}[/tex].


Related Questions

How much would $500 invested at 5% interest compounded continuously be worth after 4 years? Round your answer to the nearest cent

Answers

Answer:

$610.70

Step-by-step explanation:

[tex]a = pe^{rt}[/tex]

a = 500 [tex]e^{.05 * 4}[/tex]

a = $610.70

Which of the following are square roots of the number below? Check all that
apply.
196
A. -14
B. 196^1/2
C. 14
D. 98
E. 7
F. -196^1/2

Answers

Answer:

B. 196^1/2

C. 14

Step-by-step explanation:

Square root of 196=14

196^1/2=14

Leonardo is solving the equation 4 (x minus one-fifth) = 2 and two-thirds. His work is shown. Where is his error?

Answers

Answer:

Step 3

Step-by-step explanation:

Leonardo is solving the equation 4 (x minus one-fifth) = 2 and two-thirds. His work is shown. Where is his error?

Given :

4(x - 1/5) = 2 2/3

Open the bracket

4x - 4/5 = 2 2/3

Add 4/5 to both sides

4x - 4/5 + 4/5 = 8/3 + 4/5

Lcm of 3 and 5 = 15

4x = (40 + 12) / 15

4x = 40/15 + 12/15

4x = 52/15

Multiply by 1/4

4x * 1/4 = 52/15 * 1/4

x = 52 / 60

x = 13 / 15

Hence, the error is in step 3

15/5 * 3 = 12

Rather ; Leonardo wrote 16

If (2,1) is the midpoint of the line segment ST and the coordinates of S are (5,4), find the coordinates of T.

Answers

Answer:

Step-by-step explanation:

The formula to find the midpoint of a segment is

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] and we have the midpoint and we also have a coordinate of (5, 4). Let's let x₁ = 5 and y₁ = 4. Filling in what we have:

[tex](2,1)=(\frac{5+x_1}{2},\frac{4+y_2}{2})[/tex] and we'll deal with the x terms first. The x coordinate of the midpoint is 2, so:

[tex]2=\frac{5+x_2}{2}[/tex] and multiply both sides by 2 to get rid of the denominator to get:

4 = 5 + x₂ so

x₂ = -1. Going on to the y coordinate. The y coordinate of the midpoint is 1, so:

[tex]1=\frac{4+y_2}{2}[/tex] and again multiply both sides by 2 to get rid of the denominator to get:

2 = 4 + y₂ so

y₂ = -2

The coordinates of T are (-1, -2)

En una radio, 1/8 del dia esta destinado a emitir publicidad. Del total de publucidad, 3/5 corresponden a comerciales de univercidades. En esta radio,¿que fraccion del tiempo diario corrsponde a publicidad de univercidades.

Answers

Respuesta:

3/40

Explicación paso a paso:

Dado :

Fracción de tiempo diario dedicado a publicidad = 1/8

Del tiempo diario dedicado a publicidad, 3/5 corresponde a comerciales de universidad

Fracción del tiempo diario dedicado a la publicidad de las universidades:

3/5 de 1/8

3/5 * 1/8 = (3 * 1) / (5 * 8) = 3/40

AYUDAAAA, LES DOY CINCO ESTRELLAS SI LO RESUELVEN BIEN

Answers

dividido por la epotenusa es 7 :v

Find a solution to the following system of equations –5x + 2y = 9 3x + 5y = 7

Answers

Answer: (-1, 2)

Step-by-step explanation:

Let's start by solving for x in

[tex]-5x+2y=9\\-5x+2y+-2y=9+-2y\\-5x=9+-2y\\\frac{-5x}{-5} =\frac{9+-2y}{-5} \\x=\frac{2}{5} y+\frac{-9}{5}[/tex]

We can now sub this value of x in 3x+5y=7 and solve

[tex]3x+5y=7\\3(\frac{2}{5} y+\frac{-9}{5})+5y=7\\(3)(\frac{2}{5} y)+(3)(\frac{-9}{5})+5y=7\\\frac{6}{5} y+\frac{-27}{5}+5y=7\\\frac{6}{5} y+\frac{25}{5}y +\frac{-27}{5}=7\\\frac{31}{5} y+\frac{-27}{5}=7\\\frac{31}{5} y+\frac{-27}{5}+\frac{27}{5}=7+\frac{27}{5}\\\frac{31}{5} y=\frac{62}{5} \\\frac{\frac{31}{5} y}{\frac{31}{5}} =\frac{\frac{62}{5} }{\frac{31}{5}} \\y=2[/tex]

Now we can sub in 2 for y in one of the equations

[tex]3x+5(2)=7\\3x+10=7\\3x+10-10=7-10\\3x=-3\\\frac{3x}{3} =\frac{-3}{3} \\x=-1[/tex]

x=-1 and y=2 giving us the point (-1, 2)

An amount of 25,000 is borrow for 15 years at 5.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

Answers

Answer: [tex]55,811.91[/tex]

Step-by-step explanation:

Given

Principal amount is 25,000

Time Period is [tex]t=15\ yr[/tex]

Rate of interest [tex]r=5.5\%[/tex]

Amount in compound interest is given by

[tex]\Rightarrow A=P\left(1+r\%\right)^t[/tex]

Insert the values

[tex]\Rightarrow A=25,000(1+\dfrac{5.5}{100})^{15}\\\\\Rightarrow A=25,000(1.055)^{15}\\\Rightarrow A=55,811.91[/tex]

Therefore, [tex]55,811.91[/tex] must be paid back

Andrew lives at an altitude of 135 feet, and his friend Lisa lives at an altitude of -10 feet.

Andrew or Lisa residence is higher than Andrew or Lisa
residence.

Answers

Answer:

Andrew's residence is higher

find the sum or difference of the following ( simplify all answers)
a) 1/5 + 3/5=
b) 5/8-1/8=
c) 8/9 + 4/9 =
d) 3/5+ 1/10=
e) 2/3 +3/4=
f) 4/5- 1/3= ​

Answers

A) 4/5
B) 1/2
C) 4/3
D) 7/10
E) 17/12
F) 17/15

A 4-column table with 4 rows. Column 1 is labeled number of friends with entries 3, 5, 7, 9. Column 2 is labeled Carnival Cost with entries 51.5, 75.5, 99.5, 123.5. Column 3 is labeled Aquarium Cost with entries 43.5, 72.5, 101.5, 130.5. Column 4 is labeled Wave Pool Cost with entries 50.25, 61.25, 85.75, 110.25.
Gale wants to compare the cost of the events.

Aquarium: $14.50 each ticket

Carnival: c = 15.5 + 12f

Wave pool: $16.75 each, but $12.25 each for groups larger than 4

Which of the claims Gale makes is true?
The table represents all possibilities.
The carnival always costs the least.
The Aquarium always costs the most.
(7, 101.5) is an ordered pair used to represent the aquarium cost.

Answers

Answer:

D.(7, 101.5) is an ordered pair used to represent the aquarium cost.

Hope it helps :)

Step-by-step explanation:

Answer: it is d - (7, 101.5) is an ordered pair used to represent the aquarium cost

Step-by-step explanation: got it right on edge 2022

PLEASE HELP!!! PLEASE!!!

What is my average speed if I travel x mph for t hrs and then y mph for t hrs?

Thanks!

Answers

Answer:

Average speed = [tex]\frac{(x+y)}{2}[/tex] miles per hour

Step-by-step explanation:

Formula to calculate the average speed of an object is,

Average speed = [tex]\frac{\text{Total distance covered}}{\text{Time taken to cover this distance}}[/tex]

If I travel with the speed of x mph for t hours,

Total distance covered = Speed × Time

                                       = [tex]x\times t[/tex]

                                       = [tex]xt[/tex] miles

Similarly, if I travel with the speed y mph for t hours,

Total distance covered = [tex]yt[/tex] miles

Total distance covered by me = [tex](xt+yt)[/tex] miles

Total time taken to cover this distance = [tex]t+t[/tex]

                                                                 = [tex]2t[/tex] hours

Therefore, expression for the average speed will be,

Average speed = [tex]\frac{xt+yt}{2t}[/tex]

                          = [tex]\frac{(x+y)t}{2t}[/tex]

                          = [tex]\frac{x+y}{2}[/tex] miles per hour

what is the sum of all the exterior angle of a polygon ​

Answers

Answer:

From what I learn it is 360 degrees

Any help is appreciated!!!!

Answers

Answer:

D

Step-by-step explanation:

because 3x - 12y = 15 has only numbers that are divisible by 3 leaving just one single x term, and the other terms simply reduce their used numbers to still integer numbers (4 and 5).

this makes it easier to be used in the other equation.

Helpppppp and explain toooo thankyouuuu

Answers

Step 1: Distribute

5x + 10 - 3x > 7 - 4x + 12

Step 2: Combine like terms

2x + 10 > -4x + 19

Step 3: Move all variable terms to one side, and all constants to the other

6x + 10 > 19

6x > 9

Step 4: Divide

x > 9 / 6

x > 1.5

Hope this helps!

An on-demand movie company charges 52.95 per movie plus a monthly fee of $39.95. Which expression represents
the yearly cost for x movie rentals?
295x+39.95
39.95x295
2958-39 95(12)
295x3995(12)
Hurry I'm being timed !

Answers

Answer:

52.95x + 39.95(12)

Step-by-step explanation:

Answer:

52.95 x + 39.95 (12)

Step-by-step explanation:

cost per movie = 52.95

a monthly subscription is 39.95 and there are 12 months in a year so it would be 39.95 x 12

the x would be dependent on the amount of movie rentals and therefore the cost of the rentals = 52.95 x

What is the slope of the line? What is the y-intercept of the line? y = 1/2x + 7

Answers

Answer:

slope= 1/2

y-intercept= 0,7

Answer:

slope = 1/2 or 0.5, the y-intercept is (0,7)

Step-by-step explanation:

Find the measure of the missing angle using the triangle angle sum theorem

Answers

Answer:

m∠60

Step-by-step explanation:

30 + 90 = 120

180-120=60

Answer:

x = 60°

Step-by-step explanation:

A triangle is equal to 180°

Make an equation and solve:

30° + 90° + x = 180°

120° + x = 180°

x = 180° - 120°

x = 60°

Hello can someone help me with this problem

Answers

no lol do it yourself

Help me please guys

Answers

Answer:

1st box is -4

2nd box is -4

3rd box is 3

4th box is -1

Answer: 15x squared -4x-3

rewrite the expression

15x squared + 5x-9x-3

factor the expressions

5x × (3x+1)-3(3x+1)

factor the expression

solution

(3x + 1) × (5x - 3)

I need help
Please
I hate math

Answers

Hey
Here it is

We can do this exercise in two ways

1°) We can make an expression:

3 markers ———> 5,79$
13 markers ——> x $

So x = ( 13 x 5,79 )/ 3

2°) 3/5,79 = 13/x

So x = ( 13 x 5,79 )/ 3

Answer: C

You want to randomly arrange 4 discs in a CD rack. What is the probability that the rack ends up in alphabetical order

Answers

Answer:

The probability is 1/24

Step-by-step explanation:

The total number of possible arrangements is;

4! = 4 * 3 * 2 * 1 = 24

Now, out of all these, there is only one possible correct alphabetical arrangement

so, to get this probability, we have to divide 1 by the total number of possible arrangements

we have this simply as 1/24

what is the value of x? no links.

Answers

Answer:

X= 115 is the answer

because it is corresponding angel they are equal

Answer:

X = 115 since the x and the other angle looks like they correspond to each other

Step-by-step explanation:

Find each measure

Please help me

Answers

Answer:

11. 90

12. 90

13. 90

14. 90

15. 180

16. 135

17. 225

18. 270

Step-by-step explanation:

Answer:

BC=90

AC=90

AE=90

EB=90

ACB=180

AD=135

CBF=225

ADC=270

Step-by-step explanation:

for numbers 11-14 they're all linear pairs which means they're each 90 degrees

and as long as O is the center point, all the arcs are the same value as the degree.

for numbers 16-17 you can assume that line FO and DO bisects the right angles which makes them 45 degrees

and for 18, you just multiply 3 and 90 degrees

if x = 3 and y = 2, then the value of ( x - y )(x² + xy + y²) is
(a) 31 (b) 19 (c) 1 (d) 25 ​

Answers

Answer:

19

Step-by-step explanation:

(3-2)(3^2+3x2+2^2)

(1)(9+6+4)

(1)(19)

[tex]\displaystyle\bf \underbrace{ (x-y)(x^2+xy+y^2)}}_{x^3-y^3}=3^3-2^3=19\\\\Answer: b)19[/tex]

HELP WILL GIVE BRAINLIEST

Answers

Answer:

A.   hexagonal prism

Step-by-step explanation:

The box has 2 congruent hexagons as bases, and 6 congruent rectangles as sides.

Answer: hexagonal prism

[tex]\text{Solve for 'x'.}\\\\3x + 15 = 33\\\\\\text{Thank you.}[/tex]

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]x=6[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\3x + 15 = 33\\--------------\\\rightarrow 3x + 15 - 15 = 33 - 15\\\\\rightarrow 3x = 18\\\\\rightarrow \frac{3x=18}{3}\\\\\rightarrow \boxed{x = 6}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

x=6

Step-by-step explanation:

3x+15=33

or as, 3x=33-15

or as, 3x=18

x=18/3=6

so we got 6 is the answer

find the estimates for the following:

Answers

Answer:

Hope it helps

Step-by-step explanation:

Ava’s gross pay is $2,500 per month. Her deductions include the following:

Federal income tax $290

State income tax $85

Social Security $112

Medicare $35

What is Ava’s net pay each month?

Answers

$1,978

Explanation:

Gross pay is what’s made before taxes and necessary deductions, net pay is after taxes and necessary deductions. So we minus the deductions to find the net pay. The equation is 2,500 - 290 - 85 - 112 - 35 = ? . The answer is $1,978.

I hope this helps. Please mark me the Brainliest, it’s not necessary but I put time and effort into every answer and I would appreciate it greatly. Have a great day, stay safe and stay healthy ! :)

Five students are lined up in a row. How
many arrangements could be made if
the position of the last boy remains
unchanged?
(WAEC)​

Answers

Step-by-step explanation:

16 arrangement can be done

The 24 arrangements could be made if the position of the last boy remains unchanged.

Arrangement

Arrangement is a plans or preparations for a future event.

How to solve this problem?

The steps are as follow:

Given, Five students are lined up in a rowWe have make the arrangment such that last boy should remain unchangedTo find how many arrangements are possible in a set of objects, use the formula below, where x is the number of objects.

x! , where,! is factorial

x! is equal to x*(x-1)*(x-2)*(x-3)*…(x-(x-1))

In this case we have to take x equal to 4 because last boy to remain unchanged

∴ 4*3*2*1 = 24 arrangments

Therefore total 24 arrangements could be made if the position of the last boy remains unchanged.

Learn more about arrangment here:

https://brainly.com/question/251701

#SPJ2

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