1. a positive real number is 2 less than another. when 4 times the larger is added to the square of the smaller, the result is 49. find the numbers.

x=

−

2

+

3

√

5

y=

3

√

5

Step-by-step explanation:

Positive real number =  

x

Other number =  

y

First statement: A positive real number is 2 less than another.

Therefore  

y

=

x

+

2

Second statement: When 4 times the larger is added to the square of the smaller, the result is 49.

Since the larger number is  

y

, we know that "4 times the  

larger" means  

4

y

.

The square of the smaller would mean  

x

2

.

If you put them together, it would look like  

4

y

+

x

2

=

49

.

Now create a system of equations like the following:

y

=

x

+

2

4

y

+

x

2

=

49

.

From the first equation, we can understand the value of  

y

in terms of  

x

, which is  

x

+

2

.

Replace the  

y

in the second equation with  

x

+

2

.

4

(

x

+

2

)

+

x

2

=

49

Now that we have an equation with only one variable, solve for  

x

.

Below is a potential way one can solve this equation:

1. Expand the bracket.

4

x

+

8

+

x

2

=

49

2. Form a quadratic equation (

a

x

2

+

b

x

+

c

=

0

)

x

2

+

4

x

−

41

=

0

3, Use  

−

b

±

√

b

2

−

4

a

c

2

(

a

is 1,  

b

is 4,  

c

is -41.)

−

4

±

√

4

2

−

4

⋅

(

−

41

)

2

−

4

±

(

180

)

1

2

2

−

2

±

3

√

5

Since the answer must be a positive real number,  

x

will be  

−

2

+

3

√

5

If you place  

−

2

+

3

√

5

into  

y

=

x

+

2

:

y

=

−

2

+

3

√

5

+

2

You will get  

3

√

5

for  

y

.

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.

you would need to know all the numbers that are on there

step-by-step explanation: