Question

Please help me with algebra 2 questions!

Answer 1

5B; 7B; 1,024; see answer

Explanation:

5.

We can see from the table that

a1 = 5

a2= 5·2 = 10

a3= 5·2·2 = 5·2² = 20

a4 = 5·2·2·2 = 5·2³ = 40

...

`a_(n) = 5*2^(n-1)`

7.

Is given that the filter removes 90% of contaminated air

after run 1 :

100% air

90% contamination removed for 100% air

100% is 10%+10%+10%+10%+10%+10%+10%+10%+10%+10%

10% is still contaminated air

after run 2:

10% air

90% contamination removed for 10% air

10% is 1%+1%+1%+1%+1%+1%+1%+1%+1%+1%

1% is still contaminated air

after run 3:

1% air

90% contamination removed for 1% air

1% is .1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%

.1% is still contaminated air

11.

Figure 1 = 1 piece

Figure 2 = 4 pieces

Figure 3 = 4² = 16

...

`Figure 6 = 4^((6-1)) = 4^(5) = 1024`

12.

`(c+d)^(6) \\`

-we know that the coefficients should be 1, 6, 15, 20, 15, 6, 1

-we start with c to the lowest power 0 and d to the highest power 6 and end with d to the lowest power 0 and c to the highest power 6

`(c+d)^(6) = 1*c^(0) d^(6) +6*c^(1) d^(5) +15*c^(2) d^(4) +20*c^(3) d^(3) +15*c^(4) d^(2) +6*c^(5) d^(1) +1*c^(6) d^(0)`

-we simplify to have the final answer:

`(c+d)^(6 ) = d^(6) +6cd^(5) +15c^(2) d^(4) +20c^(3) d^(3) +15c^(4) d^(2) +6c^(5) d+c^(6)`