Find the values of a and b such that

x^2 + 2x - 7 = (x+a)^2 + b

The values of a and b are 1 and -8

Step-by-step explanation:

Let us solve the question by comparing the two sides.

∵ x² + 2x - 7 = (x + a)² + b

→ Let us solve the bracket on the right side

∵ (x + a)² = (x)(x) + 2(x)(a) + (a)(a)

∴ (x + a)² = x² + 2ax + a²

→ Substitute it in the right side above

∴ x² + 2x - 7 = x² + 2ax + a² + b

→ Compare the like terms on both sides (terms of x², terms of x

   and numerical terms)

∵ The terms of x are 2x and 2ax

→ Equate them

∵ 2x = 2ax

→ Divide both sides by 2x

∴ =

∴ 1 = a

∴ The value of a = 1

∵ The numerical terms are -7 and a² + b

→ Equate them

∵ -7 = a² + b

→ Substitute a by 1

∴ -7 = (1)² + b

∴ -7 = 1 + b

→ Subtract 1 from both sides

∵ -7 - 1 = 1 - 1 + b

∴ -8 = b

∴ The value of b = -8

∴ The values of a and b are 1 and -8

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540