Consider this quadratic expression. x² – 10x + c + 11 – c

What value of c is needed to complete the square for this expression?
A. 10
B. 20
C. 25
D. 100

Step-by-step explanation:

Given this quadratic expression.

x² – 10x + c = 0

We are to find the value c that will make the expression a perfect square'

Using the completing the square method

Add the square of the half of coefficient of x

Coefficient of x = -10

Half of -10 = 1/2(-10) = -5

Square of -5 = (-5)^2 = 25

Hence the value of c to complete the expression is 25

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

hope this !

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}