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

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

6 0

3 years ago

HELP 5 STAR + THANKS What series of transformations from △ABC to △DEF shows that △ABC≅△DEF ? a reflection across the y-axis

nirvana33 [79]

In the given triangle, the verteces are A(-4, 1), B(-6, 5), C(-1, 2).
A refrection across the x-axis will result in A'(-4, -1), B'(-6, -5), C'(-1, -2)
A translation of 1 unit to the right will result in A"(-3, -1), B"(-5, -5), C"(0, -2)
A translation of 1 unit down will result in A"'(-3, -2), B"'(-5, -6), C"'(0, -3) which corresponds to points DEF.
Therefore, the series of transformation required to transform ABC to DEF are <span>a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down.</span>

7 0

3 years ago

Please help!! It’s for chemistry

sergey [27]

I can help, which question do you need help in?

4 0

4 years ago

Can someone just help me on number 6 please???

Mandarinka [93]

Just do ittt write 200 words

4 0

3 years ago