One number is 5 times another. The sum of their reciprocals is 2/5. Determine the smaller number.

Answers

Answer 1
Answer: so x=5y
reciprocal of x=1/x then

sum of reciprocals means 1/x+1/y=2/5
subsitute x=5y for x in 1/x+1/y=2/5 and get
1/5y+1/y=2/5
multiply 1/y by 5/5 to make it 5/5y so you can add since the denomenators (bottom number) are the same

1/5y+5/5y=2/5
6/5y=2/5
multiply both sides by 5y
6=2y
divide both sides by 2
3=y
put this into x=5y so 
x=5(3)
x=15
y=3

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Liquid A has a density of 0.7g/cm^3liquid B has a density of 1.6g/cm^3

140g of liquid A is and 128g of liquid B are mixed to make liquid C

work out the density of liquid C

Answers

density is defined as mass per unit volume

in this case liquids A and B with 2 different densities are mixed and we are asked to find the density of the liquid C


liquid A has a density of 0.7 g/cm³

mass of liquid A added is 140 g

therefore volume of liquid A added is - 140 g / 0.7 g/cm³ = 200 cm³


liquid B has a density of 1.6 g/cm³

mass of liquid B added is 128 g

volume of liquid B added is - 128 g / 1.6 g/cm³ = 80 cm³


the total mass of liquid C after adding liquid A and B = 140 g + 128 g = 268 g

total volume in liquid C - 200 cm³ + 80 cm³ = 280 cm³

density of liquid C = mass / volume

= 268 g / 280 cm³ = 0.957 g/cm³

density of liquid C - 0.957 g/cm³

\rho = (m)/(V) \Rightarrow V=(m)/(\rho)
ρ - density, m - mass, V - volume

Liquid A:
\rho=0.7 \ (g)/(cm^3) \nm=140 \ g \n\n V=(140 \ g)/(0.7 \ (g)/(cm^3))=200 \ cm^3

Liquid B:
\rho=1.6 \ (g)/(cm^3) \nm=128 \ g \n\n V=(128 \ g)/(1.6 \ (g)/(cm^3))=80 \ cm^3

Liquid C:
m=140 \ g + 128 \ g=268 \ g \nV=200 \ cm^3 + 80 \ cm^3=280 \ cm^3 \n \n\rho=(268 \ g)/(280 \ cm^3) \approx 0.96 \ (g)/(cm^3)

The density of liquid C is approximately 0.96 g/cm³.

Fifty pounds of a cement-and-sand mixture is 40% sand.How many pounds of sand must be added for the resulting mixture to be 60% sand?

Answers

To get the answer you would have to multiply fifty by .4 to get 20. now you know that 20 is 2/5 of the bad and 1/5 must be 10. So you would multiply 10 by 3 to get to 3/5 so you can have 60%. The final answer is 30

Chris Built a rectangular snow fort with a perimeter of 24 feet. The length of the fort was 8 feet less than 3 times the width. What was the length (x) and width (y) of the fort

Answers

The length of a rectangular snow fort is 7 feet and the width of a rectangular snow fort is 5 feet.

Given that, Chris Built a rectangular snow fort with a perimeter of 24 feet.

What is the perimeter of a rectangle?

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Let x be the length of a rectangular snow fort and y be the width of a rectangular snow fort.

The length of the fort was 8 feet less than 3 times the width.

y=3x-8

Now, 2(y+x)=24

⇒ 3x-8+x=12

⇒ 4x=20

⇒ x=5

So, y=3x-8=7

Therefore, the length of a rectangular snow fort is 7 feet and the width of a rectangular snow fort is 5 feet.

To learn more about the perimeter of a rectangle visit:

brainly.com/question/15287805.

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We set up an equation for this.  P = 2L + 2W.24 = 2(3W-8) + 2W
24 = 6W + 2W -16
32 = 8W
W = 4.

L = 3W-8
L = 3 (4) -8
L = 12-8
L = 4

if on January 1st 2015 you decided to read 1001 Nights over the next 1001 Nights on which date would you finally finish

Answers

Well, one year is 365 days, and a leap year is every 4 years with an extra day, making leap years 366 days. 2016 is the nearest leap year. So, We take 365 from 1001 to get 636 days. Now it is January 1st 2016. So, subtract 366 from 636 to get 270 days. It is now January 1st 2017. There are 31 days in December, 30 in November, and 31 in October. Adding these together, you get 92. Subtracting 92 from 365, we get 273. So three days before October 1st is when you end. There are 30 days in September, so taking three away gives us the night of the 27th of September, 2017. So, the date you finish, if staying on a schedule of reading a bit each night, would be the night of September 27th, 2017, which is a Wednesday.

Half of a number decreased by 8 is -3

Answers

Answer: 10

Step-by-step explanation: work your way backwords. first add 8 to get 5. Then half is 1/2, so you then multiplt by 2. hope this helped! sorry for short explanation

What is the retail price of a couch at a furniture store that has a wholesale price of $115 and is marked up by 75 percent?

Answers

Answer:

The retail price of the couch is $ 201.25.

Step-by-step explanation:

Given, the wholesale price of the couch = $ 115,

Marked up rate = 75 %,

So, the total marked up = 75 % of wholesale price

= 75 % of $ 115

=(75* 115)/(100)

=(8625)/(100)

\$ 86.25

Hence, the retail price of the couch = The wholesale price + Total marked up

= $ 115 + $ 86.25

= $ 201.25

You would multiply the $115 by 1.75 to get $201.25 for the retail price