What algebraic expression must be subtracted from the sum of y2 + 5y - 1 and 3y2-2y + 4 to give 2y2 + 7y-2 as the result

The required expression is 2y² - 4y + 5.

Step-by-step explanation:

We have to find the sum of first 2 expressions and then subtracting an expression, let us consider a, to give the third expression. We have to find a.

y² + 5y -1 + 3y² - 2y + 4

We have to group the like terms and doing the addition as,

= y² + 3y² + 5y -2y -1 + 4

= 4y² + 3y + 3

Now we have to subtract an expression a from the above sum to get the third expression.

4y² + 3y + 3 - a = 2y² + 7y - 2

Now we have to group the terms as,

a = 4y² + 3y + 3 - (2y² + 7y - 2)

  = 4y² + 3y + 3 - 2y² - 7y + 2

Rearranging the terms as,

a = 4y² - 2y² + 3y - 7y + 3 + 2

   = 2y² - 4y + 5

So the required expression is 2y² - 4y + 5.

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.