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3 years ago

Two numbers have a product of 20. The second number is three less than twice the first number. What are the two numbers?

Mathematics

1 answer:

yan [13]3 years ago

4 0

Answer:

4 and 5

Step-by-step explanation:

xy = 20

x = 2y - 3

(2y-3)y = 20

2y^2 - 3y = 20

2y^2 - 3y - 20 = 0

Solve the quadratic equation

you get y = 4, -5/2

Use 5 since it is one of the options

xy = 20, y = 4

x = 5

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The UK has an area of 243,610km2 and a population of 6.41 x 107. Calculate the population density the United Kingdom. Answer to

hodyreva [135]

Answer: Population density the United Kingdom $=2.63\times10^2$

A= 2.63

B= 2

Step-by-step explanation:

We know that, to calculate the population density, we will divide the population by the size of the area.

i.e. $\text{Population density}=\dfrac{\text{Population size}}{\text{Area}}$

Given : Area of UK = 243,610 km²1

Population = $6.41 \times 10^7$

Then, the population density the United Kingdom would be :

$\text{Population density}=\dfrac{6.41 \times 10^7}{243,610}\\\\=\dfrac{64100000}{243610}=263.125487459\\\\\approx263=2.63\times10^2$

On comparing to $A\times10^B$ , we get

A= 2.63

B= 2

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The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number

andreyandreev [35.5K]

Answer:

Step-by-step explanation:

let the 2 digit number be ab = 10a + b ( considering place value )

The reversed 2 digit number is ba = 10b + a

The sum of the 2 digit number is

a + b = 12 ( subtract b from both sides )

a = 12 - b → (1)

Expressing as an equation

ba = ab + 54 , that is

10b + a = 10a + b + 54

Substitute a = 12 - b into the equation

10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides

9b + 12 = 120 - 10b + b + 54

9b + 12 = - 9b + 174 ( add 9b to both sides )

18b + 12 = 174 ( subtract 12 from both sides )

18b = 162 ( divide both sides by 18 )

b = 9

Substitute b = 9 into (1)

a = 12 - 9 = 3

Thus

the original 2 digit number = ab = 39

The reversed 2 digit number = ba = 93

which is 54 more than the original number

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3 years ago