Sure, let's go through the calculations one by one.
### c) [tex]\( (-20) + (-1) + (+21) + (+23) + (-4) + (-100) \)[/tex]
1. Start by adding the negative numbers:
[tex]\[ (-20) + (-1) + (-4) + (-100) = -125 \][/tex]
2. Now add the positive numbers:
[tex]\[ (+21) + (+23) = +44 \][/tex]
3. Add the results together:
[tex]\[ -125 + 44 = -81 \][/tex]
So, the result for part (c) is:
[tex]\[ c = -81 \][/tex]
### d) [tex]\( (-90) + (-75) + (54) - (-12) - (-45) + (34) \)[/tex]
1. Start by adding the negative numbers:
[tex]\[ (-90) + (-75) = -165 \][/tex]
2. Rewrite the subtraction as addition:
[tex]\[ - (-12) = +12 \][/tex]
[tex]\[ - (-45) = +45 \][/tex]
3. Add the positive numbers including the converted subtractions:
[tex]\[ 54 + 12 + 45 + 34 = 145 \][/tex]
4. Add the results together:
[tex]\[ -165 + 145 = -20 \][/tex]
So, the result for part (d) is:
[tex]\[ d = -20 \][/tex]
### e) [tex]\( (-76) + (-21) - (-38) + (-87) + (-31) - (-89) + (+17) \)[/tex]
1. Start by adding the negative numbers:
[tex]\[ (-76) + (-21) + (-87) + (-31) = -215 \][/tex]
2. Rewrite the subtractions as additions:
[tex]\[ - (-38) = +38 \][/tex]
[tex]\[ - (-89) = +89 \][/tex]
3. Add the positive numbers including the converted subtractions:
[tex]\[ 38 + 89 + 17 = 144 \][/tex]
4. Add the results together:
[tex]\[ -215 + 144 = -71 \][/tex]
So, the result for part (e) is:
[tex]\[ e = -71 \][/tex]
### f) [tex]\( (-10) - (-23) + (-92) - (+56) + (12) - (-123) + (-98) \)[/tex]
1. Rewrite the subtractions as additions:
[tex]\[ - (-23) = +23 \][/tex]
[tex]\[ - (-123) = +123 \][/tex]
2. Start by adding the negative numbers:
[tex]\[ (-10) + (-92) + (-56) + (-98) = -256 \][/tex]
3. Add the positive numbers including the converted subtractions:
[tex]\[ 23 + 12 + 123 = 158 \][/tex]
4. Add the results together:
[tex]\[ -256 + 158 = -98 \][/tex]
So, the result for part (f) is:
[tex]\[ f = -98 \][/tex]
Therefore, the values are:
[tex]\[ \boxed{c = -81, d = -20, e = -71, f = -98} \][/tex]
