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zzz [600]
2 years ago
11

Lines EC and HF are parallel CDG is congruent to dgh what is the measure of CDG

Mathematics
1 answer:
Verizon [17]2 years ago
5 0
Angle ADC and EDG are congruent(vertical angles)
Same side interior angles are =180
2x+4x-30=180
6x-30=180
6x=210
x=35
CDG is congruent to DGH(alternate interior)
4x-30
4(35)-30
140-30
=110
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Quick algebra 1 question for 10 points!
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<u>Answer:</u>

○ x = -7

<u>Step-by-step explanation:</u>

Given the equation:

10(x + 10) - 4 = 11 - 5(2x + 11),

to solve for x, we have to rearrange the equation to make x its subject.

10(x + 10) - 4 = 11 - 5(2x + 11)

⇒ 10x + 100 - 4 = 11 - 10x -55      [expand brackets]

⇒ 10x + 96 = -44 - 10x

⇒ 10x + 10x + 96 = -44                   [add 10x to both sides]

⇒ 20x + 96 = -44

⇒ 20x = -44 - 96                             [subtract 96 from both sides]

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6 0
2 years ago
Read 2 more answers
Rationalize the denominator of sqrt -49 over (7 - 2i) - (4 + 9i)
zubka84 [21]
\sqrt{ \frac{-49}{(7-2i)-(4+9i) } } &#10;

This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:

\frac{ \sqrt{-49}}{7-2i-4-9i}

See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result: 

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Now, the \sqrt{-49} must be respresented as an imaginary number, and using the multiplication of radicals, we can simplify it to \sqrt{49}  \sqrt{-1}
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In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely: x^2 - y^2 =(x+y)(x-y)
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.

\frac{7i (3+11i)}{(3-11i)(3+11i)}

See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how (3-11i)(3+11i)= 3^2 -(11i)^2 therefore, we can finally write:

\frac{7i(3+11i)}{3^2 - (11i)^2 }

I'll let you take it from here, all you have to do is simplify it further.
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Step-by-step explanation:

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