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Mathematics 18 Online
Nicole:

http://prntscr.com/o01ijl

Nicole:

@Narad

Narad:

This is the same angle angle ACB = mAB You can convert the angle to radians as \[=\frac{ \pi }{ 180 }* \thetaº\]

Nicole:

so 102/180?

Narad:

don't forget to multiply by \[\pi\]

Nicole:

can you show me how the equation would look with the numbers plugged in

Narad:

\[\frac{ 102 }{ 180 }*\pi\]

Nicole:

okay so the answer is \[\frac{ 17π }{ 30 }\]

Nicole:

thats it?

Narad:

Yes

Nicole:

okay http://prntscr.com/o01o0d

Narad:

The angle subtended at the center of the circle is =360º And you have angle ACB + angle ADB =306º From this you can calculate angle ADB

Nicole:

so \[\frac{ 360 }{ 180 }*\]

Nicole:

π

Narad:

first, calculate 360º-306 and then convert to radians

Nicole:

thats 54

Narad:

Then convert this angle in radians

Narad:

Have you studied radians?

Nicole:

\[\frac{ 3\Pi }{ 10 }\]

Narad:

no, \[\frac{ 54 }{ 180 }*\pi\]

Narad:

Your answer is correct

Nicole:

Loll yes. okay. http://prntscr.com/o01t89

Narad:

The angle subtended at the center of a circle by a chord is twice the angle subtended at the cicrcumference of the circle by the same chord. \[2x= 360 -(x+45)\] Solve this equation for x?

Nicole:

x=105

Narad:

Yes

Nicole:

http://prntscr.com/o01w6l

Narad:

nº4 The angle subtended by a chord is the same at any point on the circumference. Therefore, \[x+2=3x-40\] Solve this equation for x?

Nicole:

x=21

Narad:

Yes

Nicole:

http://prntscr.com/o01xpd

Narad:

nº5 \[QR= LN\] \[5x-7=3x+9\] Solve this equation for x? Then, calculate \[5x-7\]

Nicole:

x=8

Narad:

yes, continue

Nicole:

then 33

Narad:

yes

Nicole:

http://prntscr.com/o021js

Narad:

nº6 \[QR= LN\] and \[OP= VW\] Therefore, \[x+y=6\] and \[3x-y=10\] Solve for x and y in the 2 equations?

Nicole:

x=10/3+y/3 y= -10+3x

Narad:

No, add the 2 equations

Nicole:

10/3+y/3 + -10+3x ?

Narad:

No, the original equations

Nicole:

x+y=6 + 3x−y=10

Narad:

Not like that \[x+y=6\] \[3x-y=10\] \[x+3x+y-y=6+10\]

Nicole:

x=4 y=4

Narad:

ok for x, Check for y?

Nicole:

still getting 4

Narad:

no, from the first equation

Nicole:

2

Narad:

yes, this method of solving simultaneous equation is called by elimination

Nicole:

got it so x = 4 and y=2 final?

Narad:

yes

Nicole:

okay http://prntscr.com/o02agv

Narad:

nº7 \[QR=LN\] \[OP=VW\] \[2x=y+12\] \[3x=19+y\] Solve for x and y in the 2 equations?

Nicole:

in the first equation x=y/2 +6 y= 2x-12

Nicole:

second equation x= 19/3+y/3 y= 3x-19

Narad:

then, y(1st)=y(2nd)

Nicole:

show me how it would look like please?

Narad:

\[2x-12=3x-19\]

Nicole:

x=7

Nicole:

but we have to find y

Narad:

yes, now y=?

Nicole:

4?

Narad:

no,

Nicole:

?

Narad:

y=2x-12

Nicole:

do we solve 2x-12?

Narad:

x=7 then y ?

Nicole:

6?

Narad:

\[y=2*7-12= \]

Nicole:

14

Nicole:

14-12=2

Narad:

14-12 =?

Nicole:

2

Narad:

Yes y=2

Nicole:

http://prntscr.com/o02hnz

Narad:

nº8 \[AB=BC\] \[3x+2= x+12\] Solve for x?

Nicole:

x=5

Nicole:

right?

Narad:

Yes

Nicole:

http://prntscr.com/o02jyz

Narad:

Give me some time to think about this?

Nicole:

OOkay

Narad:

nº9 In the triangle AEB \[45+70+180-x=180\] Solve this equation for x?

Nicole:

x=115

Nicole:

http://prntscr.com/o02op1

Narad:

nº10 Let angle A=x In the triangle ABE \[x+180-\frac{ 53 }{ 2 }+4=180\] Solve this equation for x?

Nicole:

x=45/2

Nicole:

right?

Narad:

Yes

Nicole:

http://prntscr.com/o02w46

Narad:

A parallelogram is a quadrilateral (four sided plane figure) with 2 pairs of parallel sides.

Nicole:

http://prntscr.com/o02ydx

Narad:

nº2 A square is regular quadrilateral, it has four equal sides and four equal angles (90º)

Nicole:

http://prntscr.com/o031oq

Narad:

A rectangle is parallelogram where all the angles are right angles, one with adjacent sides of unequal length.

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