Answer:
17
Step-by-step explanation:
Given expression:
[tex]|-3d-6|+|-5-d^2|[/tex]
To evaluate for d = -3, substitute d = -3 into the expression:
[tex]\implies |-3(-3)-6|+|-5-(-3)^2|[/tex]
[tex]\textsf{Apply exponent rule} \quad a\cdot a=a^2:[/tex]
[tex]\implies |(-3)^2-6|+|-5-(-3)^2|[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^2=a^2:[/tex]
[tex]\implies |3^2-6|+|-5-3^2|[/tex]
[tex]\implies |9-6|+|-5-9|[/tex]
Subtract the numbers:
[tex]\implies |3|+|-14|[/tex]
[tex]\textsf{Apply absolute rule} \quad |a|=a, \quad a\geq 0[/tex]
[tex]\implies 3+|-14|[/tex]
[tex]\textsf{Apply absolute rule} \quad |-a|=a, \quad a > 0[/tex]
[tex]\implies 3+14[/tex]
Add the numbers:
[tex]\implies 17[/tex]
