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saw5 [17]
3 years ago
10

Geometry Bisects Help

Mathematics
1 answer:
Orlov [11]3 years ago
5 0

Answer:

<h2>m∠ABC = 72</h2>

Step-by-step explanation:

\text{If}\ \overrightarrow{BD}\ \text{bisects}\ \angle ABC,\ \text{then}\ \angle ABD\cong\angle DBC\to m\abgle ABD=m\angle DBC.\\\\\text{We have}\ m\angle ABD=12x+24\ \text{and}\ m\angle DBC=20x+16.\\\\\text{Make the equation:}\\\\12x+24=20x+16\qquad\text{subtract 24 from both sides}\\\\12x=20x-8\qquad\text{subtract}\ 20x\ \text{from both sides}\\\\-8x=-8\qquad\text{divide both sides by (-8)}\\\\x=1\\\\m\angle ABC=m\angle ABD+m\angle DBC=2m\angle ABD

m\angle ABD=12x+24\\\\\text{Put}\ x=1\ \text{to the equation:}\\\\m\angle ABD=12(1)+24=12+24=36\\\\m\angle ABC=(2)(36)=72

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Step-by-step explanation:

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A rectangular prism has a volume of 729ft^3. The length width and height are the same. What is the length of each side
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3 years ago
Evaluate the expression and write your answer in the form a + bi. 1) (2-6i)+(4+2i)2) (6+5i)(9-2i)3) 2/(3-9i)4) (3 − 5i)(7 − 2i)
laiz [17]

Answer:

Step-by-step explanation:

Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.

1) (2-6i)+(4+2i)

open the parenthesis

= 2-6i+4+2i

collect like terms

= 2+4-6i+2i

= 6-4i

2)  (6+5i)(9-2i)

= 6(9)-6(2i)+9(5i)-5i(2i)

= 54-12i+45i-10i²

= 54+33i-10i²

In complex number i² = -1

= 54+33i-10(-1)

= 54+33i+10

= 54+10+33i

= 64+33i

3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i

= 2/3-9i*3+9i/3+9i

=2(3+9i)/(3-9i)(3+9i)

= 6+18i/9-27i+27i-81i²

= 6+18i/9-81(-1)

= 6+18i/9+81

= 6+18i/90

= 6/90 + 18i/90

= 1/15+1/5 i

4) For (3 − 5i)(7 − 2i)

open the parenthesis

= 3(7)-3(2i)-7(5i)-5i(-2i)

= 21-6i-35i+10i²

= 21-6i-35i+10(-1)

= 21-41i-10

= 11-41i

4 0
4 years ago
M−4=2m what's the value of m
romanna [79]

Answer:

m=-4

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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