Answer:
(4+7i)-2i(2+3i) = 10+3i
Step-by-step explanation:
We need to find the expression that is equivalent to the complex number 10+3i.
Option 1. 2i(4-5i)+(1-7i)
=8i-10i²+1-7i
∵ i² = -1
=8i-10(-1)+1-7i
=8i+10+1-7i
=11+i (incorrect)
Option 2. (4+7i)-2i(2+3i)
=4+7i-4i-6i²
=4+7i-4i-6(-1)
=4+7i-4i+6
=10+3i (Correct)
Option 3. (-3+5i)-3i(4+5i)
= (-3+5i)-12i-15i²
= -3+5i-12i-15(-1)
= -3+5i-12i+15
=12-7i (incorrect)
Option 4. 3i(4+7i)+(11+2i)
= 12i+21i²+11+2i
=12i+21(-1)+11+2i
= 12i-21+11+2i
=14i-10 (incorrect)
Hence, the correct option is (B).
Answer:
Three-fourths
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
∠QSR≅∠XZY ---> given problem
∠QRS≅∠XYZ ---> given problem
so
△QRS ~ △XYZ ----> by AA Similarity theorem
Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
That means

∠Q≅∠X
∠R≅∠Y
∠S≅∠Z
<em>In the right triangle XYZ</em>
Find the tangent of angle X
---> opposite side angle X divided by adjacent side angle X
substitute the given values
Simplify
Remember that
∠Q≅∠X
so
therefore
---->Three-fourths