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If [tex][tex]$z=15$[/tex][/tex], what would the expression [tex][tex]$z^2-2z+15$[/tex][/tex] be equal to?

A. 205
B. [tex]210[/tex]
C. 215
D. 220


Sagot :

To solve the expression [tex]\( z^2 - 2z + 15 \)[/tex] given [tex]\( z = 15 \)[/tex], let's substitute [tex]\( z \)[/tex] with 15 and work through the calculation step-by-step.

1. Substitute [tex]\( z \)[/tex] with 15 in the expression:
[tex]\[ 15^2 - 2 \cdot 15 + 15 \][/tex]

2. Calculate [tex]\( 15^2 \)[/tex]:
[tex]\[ 15^2 = 225 \][/tex]

3. Calculate [tex]\( -2 \cdot 15 \)[/tex]:
[tex]\[ -2 \cdot 15 = -30 \][/tex]

4. Combine the results:
[tex]\[ 225 - 30 + 15 \][/tex]

5. Calculate [tex]\( 225 - 30 \)[/tex]:
[tex]\[ 225 - 30 = 195 \][/tex]

6. Finally, add 15 to the result:
[tex]\[ 195 + 15 = 210 \][/tex]

Thus, the value of the expression [tex]\( z^2 - 2z + 15 \)[/tex] when [tex]\( z = 15 \)[/tex] is [tex]\( 210 \)[/tex].

The correct answer is B) 210.