Answer:
Step-by-step explanation
there are 80 boxes in total
If the student got a true statement, it is an identity
example, ending with x=x or 10=10 means it is an identity
if the student ended up with a false statement, there is no solution
example, 10=2
Answer:
GCD(343,550) = 1
LCM(343,550) = 188650
GCD(89,110) = 1
LCM(89,110) = 9790
GCD(870,222) = 6
LCM(870,222) = 32190
Step-by-step explanation:
a) GCD(343,550)
343 - 550 | 1
...
There are no values for which both 343 and 550 are divisible by, so GCD(343,550)=1.
LCM(343,550)
343 - 550 | 2
343 - 275 | 5
343 - 55 | 5
343 - 11 | 7
49- 11 | 7
7 - 11 | 7
1 - 11 | 11
1 - 1
So LCM(343,550) = 2*5*5*7*7*7*11 = 188650
b) GCD(89,110)
Again, as in a), there are no values for which 89 and 110 are divisible by. So GCD(89,110) = 1.
LCM(89,110)
89 - 110 | 2
89 - 55 | 5
89 - 11 | 11
89 - 1 | 89
1 - 1
So LCM(89,110) = 2*5*11*89 = 9790
c) GCD(870,222)
870 - 222 | 2
435 - 111 | 3
145 - 37
There are no numbers for which 145 and 37 are both divisible by, so the algorithm ends there, and GCD(870,222) = 2*3 = 6
LCM(870,222)
870 - 222 | 2
435 - 111 | 3
145 - 37 | 5
29 - 37 | 29
1 - 37 | 37
1 - 1
So LCM(870,222) = 2*3*5*29*37 = 32190
Answer:
19
Step-by-step explanation:
Operations of functions:
h(x) = f(z) + g(z)
h(x) = (2z³ - 3z) + (-3z² + 1)
Simplify or expand:
(2z³ - 3z) + (-3z² + 1)
Determine the sign
2z³ - 3z - 3z² + 1
Rewrite the expression
2z³ - 3z² - 3z + 1
Calculate:
Substitute z = 3 into
2z³ - 3z² - 3z + 1
Substitute
2 × 3³ - 3 × 3² - 3 × 3 + 1
Calculate
19
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