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jolli1 [7]
2 years ago
6

The difference between two numbers is 3 and their sum is 7. Find the numbers

Mathematics
1 answer:
lubasha [3.4K]2 years ago
8 0

Answer:

The numbers are 8 and 5

Step-by-step explanation:

The two numbers are

8

and

5

.

Explanation:

Consider the two numbers as

x

and

y

. From the given data, we write:

x

−

y

=

3

x

+

y

=

13

From the first equation, we determine a value for

x

.

x

−

y

=

3

Add

y

to both sides.

x

=

y

+

3

In the second equation, substitute

x

with

(

y

+

3

)

.

x

+

y

=

13

(

y

+

3

)

+

y

=

13

Open the brackets and simplify.

y

+

3

+

y

=

13

2

y

+

3

=

13

Subtract

3

from each side.

2

y

=

10

Divide both sides by

2

.

y

=

5

In the first equation, substitute

y

with

5

.

x

−

y

=

3

x

−

5

=

3

Add

5

to each side.

x

=

8

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. Denise has multiplied (2r – 3)(2r + 3) to get 4r2 – 9. After looking at her work, Hyder says her solution must be incorrect be
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Answer:

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Step-by-step explanation:

One of the methods of solving the given equation [(2r – 3)(2r + 3)] is the FOIL method

Using the FOIL method (Used for multiplying binomials)

F stands for first

O stands for outer

I stands for inner

L stands for last

In this method, it means we will first multiply the first terms followed by multiplying the outer term, then multiplying the inner terms and finally, the last terms.

So, for the equation  (2r – 3)(2r + 3)

First : (2r)(2r) = 4r²

Outer : (2r)(+3) = 6r

Inner : (–3)(2r) =  – 6r

Last :  (–3)(+3) =  – 9

Adding the results we get

4r² + 6r – 6r – 9 (+6r and – 6r cancels out)

= 4r² – 9

∴ (2r – 3)(2r + 3) = 4r² – 9

Hence, Denise answer is correct

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Step-by-step explanation:

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