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2 years ago

The sum of two numbers is 9. And the sum of their reciprocals is 1/2.find the numbers

1 answer:

7 0

Set up a system of equations:

x + y = 9
1/x +1/y = 1/2

The easiest way to solve would be substitution.
x + y = 9 can be solved for y:

y = 9 - x

Then plug this into the second equation and solve for x:

1/x + 1/(9-x) = 1/2
(9-x) + x = x(9-x)/2
9 = (9x-x²)2
18 = 9x - x²
x² - 9x + 18 = 0
(x-6)(x-3) = 0
x = 6, 3

You can check your answer by plugging the two numbers back into both of the equations:

6 + 3 = 9
1/6 + 1/3 = 1/2

The two numbers are 6 and 3.

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3 numbers that are less than 2 and greater then -1

Viefleur [7K]

Three numbers less than 2, but greater than -1 are:

1.5 (I don't know if that counts as a number specifically)

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3 years ago

The average weight of a newborn panda is 0.2, or 2/10 pound. Between what two integers is the weight of a newborn panda?

sweet-ann [11.9K]

Answer:

$\frac{2}{10}$ lies between 0 and 1.

Step-by-step explanation:

We must have in mind that given average weight of a newborn panda is a non-integer rational number, such that lies between two integer rational number. In other words, this number must satisfy the following condition:

$n < \frac{a}{b} < n +1$ , $n, a, b \in \mathbb{N}_{O}$

$\mathbb{N}_{O} = \mathbb{N}\,\cup\,{\{0\}}$

Which is now developed mathematically to deduce a useful expression to find integers:

1) $n < \frac{a}{b} < n +1$ Given

2) $n \cdot 1 < \frac{a}{b} < n\cdot 1 + 1$ Modulative property

3) $n \cdot (b\cdot b^{-1}) < a\cdot b^{-1} < n \cdot (b\cdot b^{-1}) + b\cdot b^{-1}$ Existence of Multiplicative inverse/Definition of division.

4) $(n\cdot b)\cdot b^{-1} < a\cdot b^{-1}< [(n+1)\cdot b] \cdot b^{-1}$ Commutative, Associative and Distributive properties.

5) $n\cdot b < a < (n+1)\cdot b$ Compatibility with Multiplication/Existence of Multiplicative Inverse/Modulative Property/Result.

If we know that $a = 2$ and $b = 10$ , the following inequation is formed:

$10\cdot n < 2 < 10\cdot (n+1)$

It is quite evident to conclude that $\frac{2}{10}$ lies between 0 and 1.

6 0

3 years ago

Which ones have been translated ?thank you

WITCHER [35]

Answer:

looks like D! Have a nice day :D

7 0

2 years ago

What is the surface area of a cube whose edges are 11 inches long?

Dennis_Churaev [7]

Surface area is the total area of the surface. A cube has 6 surface, and each surface is the same. Each surface is a 11 by 11 square. Therefore there will be 6 11in. x 11in. surfaces. The math would be 11x11x6 =726.

8 0

3 years ago

Read 2 more answers

Jenny and her children went to the SeaWorld.She purchased adult ticket for herself and children tickets for her 2 boys. Tickets

dangina [55]

Given:

She purchased adult ticket for herself and children tickets for her 2 boys.

Cost of one adult ticket = $39.99

Cost of one child ticket = $19.99

To find:

The expression to represent the total cost of the tickets Jenny purchased.

Solution:

Let x represent the number of adult ticket purchase

and y represent the number of child tickets purchase.

Cost of one adult ticket = $39.99

Cost of one child ticket = $19.99

Total cost = 39.99x + 19.99y

Therefore, the expression for total cost is 39.99x + 19.99y.

She purchased one adult ticket and 2 child tickets.

Substitute x=1 and y=2 in the above expression.

Total cost = 39.99(1) + 19.99(2)

= 39.99 + 39.98

= 79.97

Therefore, the required expression to represent the total cost of the tickets Jenny purchased is 39.99(1) + 19.99(2) and total cost is $79.97.

3 0

2 years ago