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Law Incorporation [45]
3 years ago
8

Which of the following statements is true?

Mathematics
2 answers:
N76 [4]3 years ago
6 0
Every square is a rhombus
sashaice [31]3 years ago
5 0

Answer:

every square is a rhombus

Step-by-step explanation:

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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}

6 0
3 years ago
The ratio of the width to the length of a painting is 3 to 7. If the painting is 42 in. long how wide is it
belka [17]

If length is 42 inches, then width is 18 inches.

Step-by-step explanation:

We are given ratio of width to the length of a painting i.e 3 to 7. If the painting is 42 inches long, then how wide it is?

Solving:

\frac{width}{length}=\frac{width}{length}\\ \frac{3}{7}=\frac{w}{42}\\  Cross\,\,multiply:\\3*42=w*7\\126=w*7\\w=\frac{126}{7}\\w=18

So, If length is 42 inches, then width is 18 inches.

Keywords: Ratio

Learn more about Ratio at:

  • brainly.com/question/9880052
  • brainly.com/question/10781917
  • brainly.com/question/2707032

#learnwithBrainly

8 0
2 years ago
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