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

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

6 0

3 years ago

Which expression is equivalent to 10x2y + 25x2?

babymother [125]

$10 x^{2} y +25 x^{2} = 5 x^{2} ( \frac{10 x^{2} y +25 x^{2} }{5 x^{2} }) = 5 x^{2} ( \frac{10 x^{2} y}{5 x^{2} } + \frac{25 x^{2} }{5 x^{2} } ) = 5 x^{2} ( \frac{2y}{1} + \frac{5}{1} )$

Answer A 5x² * ( 2y + 5)

7 0

3 years ago

Read 2 more answers

Sine is opposite divided by hypotenuse. So the sine of an angle times the hypotenuse is the length of the opposite side. What is

valkas [14]

Answer:

10 m

Step-by-step explanation:

opposite = sin30° × 20 = $\frac{1}{2}$ × 20 = 10 m

7 0

1 year ago