Please answer the everything thank you ! i'll mark the brainlest!!!!! :)

Mathematics

1 answer:

kari74 [83]2 years ago

4 0

Answer:

1. a. 2 KM ; b. 9000 m

2. a. 9 L ; b. 3000 g

3. a. 6000 ml ; b. 9

4. a. 60 mm ; b. 4000 m

5. a. 1 km ; b. 2 kg

6. a. 5 ; b. 4 m

7. a. 4000 ml ; b. 3000

8. a. 10 kg ; b. 20 mm

9. a. 10 km ; b. 9kg

10. a. 4 kg ; 8 l

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The product of (3 − 4i) and____is 25.

LiRa [457]

$(3-4i)(a+bi)=25\qquad\text{use FOIL method}\\\\(3)(a)+(3bi)+(-4i)(a)+(-4i)(bi)=25+0i\\\\3a+3bi-4ai-4bi^2=25+0i\\\\3a+3bi-4ai-4b(-1)=25+0i\\\\3a+3bi-4ai+4b=25+0i\\\\(3a+4b)+(3b-4a)i=25+0i\\.\qquad\qquad\qquad\qquad\Downarrow\\\\3a+4b=25\ and\ 3b-4a=0\\\\3b-4a=0\qquad\text{add 4a to both sides}\\\\3b=4a\qquad\text{divide both sides by 3}\\\\b=\dfrac{4}{3}a\qquad\text{substitute it to the first equation}\\\\3a+4\left(\dfrac{4}{3}a\right)=25\\\\3a+\dfrac{16}{3}a=25\qquad\text{multiply both sides by 3}$

$9a+16a=75\\\\25a=75\qquad\text{divide both sides by 25}\\\\\boxed{a=3}\qquad\text{put the value of a to}\ b=\dfrac{4}{3}a:\\\\b=\dfrac{4}{3}(3)\\\\\boxed{b=4}\\\\Answer:\ \boxed{(3-4i)\underline{(3+4i)}=25}$