X + y = 180°
x = 6 + 4y
6 + 4y + y = 180°
5y = 174°
y = 34.8
x = 6 + 4(34.8)
x = 145.2°
i am a mathematics teacher. if anything to ask please pm me
=±22
x
=
±
2
x
2
Using the fact that 2=ln2
2
=
e
ln
2
:
=±ln22
x
=
±
e
x
ln
2
2
−ln22=±1
x
e
−
x
ln
2
2
=
±
1
−ln22−ln22=∓ln22
−
x
ln
2
2
e
−
x
ln
2
2
=
∓
ln
2
2
Here we can apply a function known as the Lambert W function. If =
x
e
x
=
a
, then =()
x
=
W
(
a
)
.
−ln22=(∓ln22)
−
x
ln
2
2
=
W
(
∓
ln
2
2
)
=−2(∓ln22)ln2
x
=
−
2
W
(
∓
ln
2
2
)
ln
2
For negative values of
x
, ()
W
(
x
)
has 2 real solutions for −−1<<0
−
e
−
1
<
x
<
0
.
−ln22
−
ln
2
2
satisfies that condition, so we have 3 real solutions overall. One real solution for the positive input, and 2 real solutions for the negative input.
I used python to calculate the values. The dps property is the level of decimal precision, because the mpmath library does arbitrary precision math. For the 3rd output line, the -1 parameter gives us the second real solution for small negative inputs. If you are interested in complex solutions, you can change that second parameter to other integer values. 0 is the default number for that parameter.
Answer: x= 34
Step-by-step explanation:
Given: The measurement of the angles of the quadrilateral are as
First angle=88°
Second angle=108°
Third angle= 2x°
Forth angle =(3x-6)°
Now, The interior angles formed by the sides of a quadrilateral have measures that sum to 360°.
Therefore,
![88+108+2x+(3x-6)=360\\\Rightarrow196+5x-6=360\\\Rightarrow\ 5x=360-190\\\Rightarrow\ x=\frac{170}{5}\\\Rightarrow\ x=34](https://tex.z-dn.net/?f=88%2B108%2B2x%2B%283x-6%29%3D360%5C%5C%5CRightarrow196%2B5x-6%3D360%5C%5C%5CRightarrow%5C%205x%3D360-190%5C%5C%5CRightarrow%5C%20x%3D%5Cfrac%7B170%7D%7B5%7D%5C%5C%5CRightarrow%5C%20x%3D34)
C.6 i think, sorry if it’s wrong but my reasoning was that 50 + 58 = 108 and the interior of a triangle is 180 degrees so then you would subtract 180 - 108 = 72, then i did some guess work plugging in the different answers into the equation and 11 x 6 + 6 = 72 which was the missing angle from before