1. (7 − 3i) • (2 − i)
It is simplified as follows:
14 - 7i -6i - 3
11 - 13i
2. <span>(−5 + 3i) • (1 − 2i)
</span><span>It is simplified as follows:
</span><span>-5 + 10i + 3i + 6
1 + 13i
3. (1 + 3i) + (2 − 5i)
</span><span>It is simplified as follows:
</span>1 + 3i + 2 − 5i<span>
3 - 2i
4. (6 + 2i) − (8 − 3i)
</span><span>It is simplified as follows:
</span><span>6 + 2i − 8 + 3i
</span>-2 + 5i
We can solve by figuring the area of the rectangle then add it to the area of the semicircle.
Area of the rectangle: length · width = 6 · 10 = 60 ft²
Area of the semicircle: (πd²)/8 = (3.14 · 6²)/8 = (3.14 · 36)/8 = 14.13 ft²
Total area of the figure: 60 + 14.13 = 74.13 ft² ≈ 74 ft²
Let
rA--------> radius of the circle A
rB-------> radius of the circle B
LA------> <span>the length of the intercepted arc for circle A
</span>LB------> the length of the intercepted arc for circle B
we have that
rA/rB=2/3--------> rB/rA=3/2
LA=(3/4)<span>π
</span>
we know that
if <span>Both circle A and circle B have a central angle , the ratio of the radius of circle A to the radius of circle B is equals to the ratio of the length of circle A to the length of circle B
</span>rA/rB=LA/LB--------> LB=LA*rB/rA-----> [(3/4)π*3/2]----> 9/8π
the answer is
the length of the intercepted arc for circle B is 9/8π
Answer:
a
Step-by-step explanation:
Add 2 to each side
Subtract 4 from each side
Divide 8 by each side
The correct answer is: [A]: " x + 2y = -11 " .
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Explanation:
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First, we narrow down to choices:
[A]: "x + 2y = -11 ; and: [D]: "2x + y = -10 " ;
since these are the only answer choices that the point "(-3, -4) pass through.
Now, write these in "slope-intercept form" (a.k.a. "point-slope form"); that is:
y = mx + b ;
and see which one has the slope of "(-1/2)" (i.e. "m = -1/2") ;
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Start with Answer choice [A]: "x + 2y = -11 " ;
↔ 2y + x = -11 ;
Subtract "x" from each side:
2y + x − x = -11 − x ;
to get: 2y = -11 − x ;
↔ 2y = -11 + (-x) ;
↔ 2y = -x + (-11) ;
↔ 2y = -1x − 11 ;
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Divide EACH SIDE of the equation by "2" ;
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2y / 2 = (-1x − 11) / 2 ;
to get: y = (-1/2)x − (11/2).
So: Answer choice: [A]: should be the correct answer .
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Let us try Answer choice: [D] ; just to rule out this possible answer:
" 2x + y = -10 " ;
↔ y + 2x = -10 ;
Subtract "2x" from EACH SIDE of the equation ;
y + 2x − 2x = -10 − 2x ;
y = -10 − 2x ;
↔ y = -10 + (-2x) ;
↔ y = -2x + (-10) ;
↔ y = -2x − 10 ;
The slope of: Answer choice [D]: is "-2" ; NOT "(-1/2)".
So; we confirm that: Answer choice: [D]: is INCORRECT.
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So the correct answer is: Answer choice: [A]: " x + 2y = -11 " .
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