Fill in the Table Below for the Corresponding x

The sum of the fractions 2/y-3 and 6/y+3 is equal to their

Sphinxa [80]

Step-by-step explanation:

Move expression to the left side and change its sign

5

y

−

3

+

10

y

2

−

y

−

6

−

y

+

2

=

0

Write

−

y

as a sum or difference

5

y

−

3

+

10

y

2

+

2

y

−

3

y

−

6

−

y

+

2

=

0

Factor out

y

and

−

3

from the expression

5

y

−

3

+

10

y

(

y

+

2

)

−

3

(

y

+

2

)

−

y

+

2

=

0

Factor out

y

+

2

from the expression

5

y

−

3

+

10

(

y

+

2

)

(

y

−

3

)

−

y

+

2

=

0

Write all numerators above the least common denominator

5

(

y

+

2

)

+

10

−

y

(

y

−

3

)

(

y

+

2

)

(

y

−

3

)

=

0

Distribute

5

and

−

y

through the parenthesis

5

y

+

10

+

10

−

y

2

+

3

y

(

y

+

2

)

(

y

−

3

)

=

0

Collect the like terms

8

y

+

20

−

y

2

(

y

+

2

)

(

y

−

3

)

=

0

Use the commutative property to reorder the terms

−

y

2

+

8

y

+

20

(

y

+

2

)

(

y

−

3

)

=

0

Write

8

y

as a sum or difference

−

y

2

+

10

y

−

2

y

+

20

(

y

+

2

)

(

y

−

3

)

=

0

Factor out

−

y

and

−

2

from the expression

−

y

(

y

−

10

)

−

2

(

y

−

10

)

(

y

+

2

)

(

y

−

3

)

=

0

Factor out

−

(

y

−

10

)

from the expression

−

(

y

−

10

)

(

y

+

2

)

(

y

+

2

)

(

y

−

3

)

=

0

Reduce the fraction with

y

+

2

−

y

−

10

y

−

3

=

0

Determine the sign of the fraction

−

y

−

10

y

−

3

=

0

Simplify

10

−

y

−

3

=

0

When the quotient of expressions equals

0

, the numerator has to be

0

10

−

y

=

0

Move the constant,

10

, to the right side and change its sign

−

y

=

−

10

Change the signs on both sides of the equation

y

=

10

Check if the solution is in the defined range

y

=

10

,

y

≠

3

,

y

≠

−

2

∴

y

=

10

6 0

3 years ago

Read 2 more answers

How to write 5/10 as a decimal

prisoha [69]

You write it as 0.5. Just divide both numbers

5 0

3 years ago

Read 2 more answers

A rectangle has a length of (x+10) centimeters and a width of x centimeters. If the perimeter is 32 centimeters, what is the len

I am Lyosha [343]

Given:

Length of rectangle = (x+10) cm

Width of the rectangle = x cm

Perimeter = 32 cm

To find:

The length of the rectangle.

Solution:

We know that,

$Perimeter=2(l+w)$

Where, l is length and w is width.

Substituting the values, we get

$32=2((x+10)+x)$

$32=2(2x+10)$

$32=4x+20$

Subtract 20 from both sides.

$32-20=4x$

$12=4x$

Divide both sides by

$3=x$

So, the length is

$3+10=13$

Therefore, the length of the rectangle is 13 cm.

7 0

2 years ago

A car is traveling at a speed of 25 meters per second what is the cars speed in kilometers per hour how many kilometers will the

Likurg_2 [28]

Answer:

90 km/h
180 km

Step-by-step explanation:

There are 1000 m in 1 km, and 3600 s in 1 h, so the speed conversion is ...

$\dfrac{25\,m}{s}\cdot\dfrac{1\,km}{1000\,m}\cdot\dfrac{3600\,s}{1\,h}=\dfrac{90\,km}{h}$

The car's speed is 90 km/h.

__

In 2 hours, the car will travel ...

distance = speed · time = (90 km/h)(2 h) = 180 km

7 0

3 years ago

Please please help me out

Inessa [10]

Answer:

26.6 m

Step-by-step explanation:

Given the figures are similar

linear ratio = a : b

area ratio = a² : b²

here

area ratio = 16 : 25, then

linear ratio = 4 : 5 ( square root of both area ratio parts )

let the perimeter of the larger figure be x, then by proportion

$\frac{4}{21.3}$ = $\frac{5}{x}$ ( cross- multiply )

4x = 106.5 ( divide both sides by 4 )

x ≈ 26.6

Hence perimeter of larger figure is approximately 26.6 m

3 0

3 years ago

Fill in the Table Below for the Corresponding x - valuesxy-2024