Answer:
m∠CAF is 28°
Step-by-step explanation:
The given parameters are;
EG = 3, EB = 8, A_F = 7, m∠EBG = 23°, ∠EGF 32°, and m∠CAE = 51°
From the diagram, we have;
m∠EBG = m∠EAD ; 
Given
Therefore, m∠EAD = 23°
m∠CAE = m∠CAF + m∠EAD Angle addition postulate
Therefore, we have;
51° = m∠CAF + 23°
m∠CAF = 51° - 23°
m∠CAF = 28°
If G is the incenter of ∆ABC, then GD = GF = GE.
Given, GD is 3x + 5 and GF is 6x - 4.
According to the above statement,
GD = GF
or, 3x + 5 = 6x - 4
or, 5 + 4 = 6x - 3x
or, 9 = 3x
or, 9/3 = x
or, 3 = x
The value of x is 3.
By putting the value of x in GD or GF, we get
GD = 3(3) + 5 = 9 + 5 = 14
GF = 6(3) - 4 = 18 - 4 = 14
Therefore, GE = <u>14</u>.
Answer:
57/100
Step-by-step explanation: 0.57 can also be written as 57/100 which is equal to 0.57
Answer:
<h3>The surface area in square meters that Darren has to paint is
</h3><h3>∴
</h3>
Step-by-step explanation:
Given that Darren is painting a wooden block is a rectangular prism
Its length is 12 cm ,width is 9 cm and height is 5 cm
<h3>To find the surface area in square meters that Darren has to paint :</h3>
Let l be the length, w be the width and h be the height
Then l=12 cm , w=9 cm and h=5 cm
The formula for the Surface area is
A=2(lw+wh+hl) square units
Substitute the values in formula we get,
A=2(12(9)+9(5)+5(12))
=2(108+45+60)
=2(213)
=426
<h3>∴
</h3><h3>∴ the surface area in square meters that Darren has to paint is
</h3>
So there is an identity we'll need to use to solve this:
cos(x+y) = cosxcosy - sinxsiny
replace the numerator with the right hand side of that identity and we get:
(cosxcosy - sinxsiny)/cosxsiny
Separate the numerator into 2 fractions and we get:
cosxcosycosxsiny- sinxsiny/cosxsiny
the cosx's cancel on the left fraction, the siny's cancel on the right fraction and we're left with:
cosy/siny - sinx/cosx
which simplifies to:
coty - tanx
