Math babysitting help?

Question

My little brother needs help with his homework so I helped him and now I need to absolutely make sure that his answers are correct. Can you all help please?

Thank you,

5.) 4i(-3i+7)

6.) (3+2i)(9-7i)

7.) 4i/5+2i

8.) 3 + 5i/5-3i

9.) (-2 - the squre root of -36 squared

Answer 1

5. First: eliminate parenthesis-distribute the outer term with the terms in parenthesis...

(4i)(-3i) + (4i)(7)
- 12i^2 + 28i

Sec: i^2 becomes "-1" > replace "-1" with i^2

- 12(-1) + 28i
= 12 + 28i

6. (3 + 2i)(9 - 7i)
First: eliminate the parenthesis-use the foiling method...

(3)(9) + (3)(-7i) + (2i)(9) + (2i)(-7i)
27 + (-21i) + 18i + (14i^2)
27 - 21i + 18i + 14i^2
27 - 3i + 14i^2

Third: i^2 becomes "-1" > replace "-1" with i^2

27 - 3i + 14(-1)
27 - 3i + (-14)
27 - 14 - 3i
13 - 3i

7. 4i/5+2i

First: rationalize the denominator - multiply the conjugate (5 - 2i) of the denominator with the top & bottom...

(5 - 2i)(4i)/(5 - 2i)(5 + 2i)

Sec: eliminate parenthesis - distribute the outer terms with the terms in parenthesis...

[5(4i) - 2i(4i)]/[5(5)+5(2i)-2i(5) - 2i(2i)]

[20i - 8i^2]/[25 + 10i - 10i - 4i^2]

[20i - 8i^2]/[25 - 4i^2]

Third: the i^2 variables become "-1"...

20i - 8(-1)/25 - 4(-1)
20i + 8/25 + 4
20i + 8/29

8. please specify whether the numerator or, denominator needs to rationalized, from your book.

9. - 2 - V`(-36)^2

First: square "-36" in the radical sign...

- 2 - V`(-36)(-36)

- 2 - V`(1296)

Sec: find the square root of "1296"...

- 2 - 36
= -38

Answer 2

5.) 4i(-3i+7) = -12i^2 + 28i = -12(-1) +28i = 12 + 28i

6.) (3+2i)(9-7i) = 27-21i+18i -14i^2
= 27 -3i -(14)(-1) = 41-3i

7.) 4i/(5+2i) = 4i(5-2i)/[(5+2i)(5-2i)]
= (20i -8)/29

8.) 3 + 5i/(5-3i) = 5i(5+3i)/[5+3i)(5-3i)]
= (25i +15)/34

9.) (-2 - the squre root of -36) squared
= (-2 - 6i)^2 = 4 -24i +36i^2 = -32 -24i

Note: (a+bi)(a-bi) = a^2+b^2
In problem 9, I replaced a missing paretheses
In problems 7 and 8 Iinserted parentheses so that the denominators became (5+2i) and (5-3i) instead of 5 and 5 respectively.

Answer 3

I made some assumptions about parenthetical groupings that may or may not be correct - proceed accordingly!

Knowing that i = sqrt(-1) and that i^2 = -1, solve as follows:

5) 12 + 28i

6) (3+2i)(9-7i) = (27 + 18i -21i - 14i^2)
= 41 - 3i

7) (4i)(5-2i) / (5+2i)(5-2i)
= (20i - 8i^2) / (25 - 4i^2)
= (8 + 20i)/29

8) (3+5i)(5+3i) / (5-3i)(5+3i) = (15 + 25i + 9i -15) / 34
= 34i/34 = i

9) ( -2 - (6i) )^2
= (-2 -6i)(-2 - 6i) = (4 + 12i + 12i + 36i^2)
= 24i - 32

Answer 4

5.) 4i(-3i+7)
=-12i^2+28i

=12+28i

6.) (3+2i)(9-7i)
=27-21i+18i-14i^2
=27+14-3i
=41-3i


7.) 4i/5+2i
=14i/5

8.) 3 + 5i/5-3i
=3-10i/5

=3-2i


9.) (-2 - the squre root of -36 squared
(-2-sqrt(-36))^2
=4-36+4sqrt(-36)
=-32+4*6i

=-32+24i

Answer 5

a million. So Gerhart will pay 3.ninety 5, a million.40 5, and a million.10, for a finished of 6.50. to discover the proportion that the top is, you divide the top by using the value of the nutrition. a million.30/6.50 =.2, or 20%. 2. If the top is eighteen% of the bill, meaning that 6.40 8/X(the excellent bill) = .18 in case you go multiply, you get that 6.40 8/.18 = X, so X, the excellent bill, is 36 money. 3. 5.ninety 5 + 2.40 5 = 8.40 for the nutrition. 20 % of the nutrition is a million.sixty 8, so now the excellent is 10.08 for the nutrition and the top. The sales tax = 8.4 cases .05, which equals .40 two. for this reason, the excellent that she will pay is 10.08+.40 two=10.50. wish this helps!

Answer 6

your LITTLE brother!?
now when you say little... haah
not even i can do that...
good luck though!
xxxx