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Explanation:</h2><h2>
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The diagram for this problem is shown below. Point E is the intersection of the two diagonals and we know that:
![\angle BCE=\beta \\ \\ \angle DCE=\theta](https://tex.z-dn.net/?f=%5Cangle%20BCE%3D%5Cbeta%20%5C%5C%20%5C%5C%20%5Cangle%20DCE%3D%5Ctheta)
Every internal angle of any rectangle measures 90 degrees, so:
![\beta +\alpha=90 \\ \\ (4x-23)+(5+5x)=90 \\ \\ \\ Isolating \ x: \\ \\ (4x+5x)+(5-23)=90 \\ \\ 9x-18=90 \\ \\ 9x=108 \\ \\ x=\frac{108}{9}=12](https://tex.z-dn.net/?f=%5Cbeta%20%2B%5Calpha%3D90%20%5C%5C%20%5C%5C%20%284x-23%29%2B%285%2B5x%29%3D90%20%5C%5C%20%5C%5C%20%5C%5C%20Isolating%20%5C%20x%3A%20%5C%5C%20%5C%5C%20%284x%2B5x%29%2B%285-23%29%3D90%20%5C%5C%20%5C%5C%209x-18%3D90%20%5C%5C%20%5C%5C%209x%3D108%20%5C%5C%20%5C%5C%20x%3D%5Cfrac%7B108%7D%7B9%7D%3D12)
So:
![\beta=4x-23=4(12)-23=25^{\circ}](https://tex.z-dn.net/?f=%5Cbeta%3D4x-23%3D4%2812%29-23%3D25%5E%7B%5Ccirc%7D)
So the measure of angle BEC can be found as follows:
We know that triangle ΔCEB is an isosceles triangle because the diagonals of any rectangle measure the same. So
![\angle EBC=\beta](https://tex.z-dn.net/?f=%5Cangle%20EBC%3D%5Cbeta)
The sum of internal angles of any triangle add up to 180 degrees, so:
![\beta + \beta+\angle BEC=180^{\circ} \\ \\ 2\beta+\angle BEC=180^{\circ} \\ \\ \angle BEC=180^{\circ}-2\beta \\ \\ \angle BEC=180^{\circ}-2(25^{\circ}) \\ \\ \angle BEC=180^{\circ}-50^{\circ} \\ \\ \boxed{\angle BEC=130^{\circ}}}](https://tex.z-dn.net/?f=%5Cbeta%20%2B%20%5Cbeta%2B%5Cangle%20BEC%3D180%5E%7B%5Ccirc%7D%20%5C%5C%20%5C%5C%202%5Cbeta%2B%5Cangle%20BEC%3D180%5E%7B%5Ccirc%7D%20%5C%5C%20%5C%5C%20%5Cangle%20BEC%3D180%5E%7B%5Ccirc%7D-2%5Cbeta%20%5C%5C%20%5C%5C%20%5Cangle%20BEC%3D180%5E%7B%5Ccirc%7D-2%2825%5E%7B%5Ccirc%7D%29%20%5C%5C%20%5C%5C%20%5Cangle%20BEC%3D180%5E%7B%5Ccirc%7D-50%5E%7B%5Ccirc%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7B%5Cangle%20BEC%3D130%5E%7B%5Ccirc%7D%7D%7D)
Answer:
yes, 18 is a polynomial
Step-by-step explanation:
We have to show whether 18 is a polynomial or not
Polynomial is an expression involving variables and constants such that variables having non negative integer power.
Example
etc,
Thus, yes 18 is a polynomial
as 18 can be written as
where
and 0 is non negative integer,
Thus, yes 18 is a polynomial as it can be written as
having non negative integer power 0.
Answer:
86 thousand 5 hundred and 3
Step-by-step explanation:
Answer:
Let x = total number of apples picked by the prince
x=44
Step-by-step explanation:
1st troll payment
x-(0.5x+2)
x-0.5x-2
0.5x-2 (that is the amount of apples left after 1st troll payment)
2nd troll payment
(0.5x-2)-(0.5(0.5x-2)+2)
Simplifying,
(0.5x-2)-(0.25x-1+2)
(0.5x-2)-(0.25x+1)
0.5x-2-0.25x-1
0.25x-3 (apples remaining after 2nd troll payment)
3rd troll payment
(0.25x-3)-(0.5(0.25x-3)+2)=2
(0.25x-3)-(0.125x-1.5+2)=2
(0.25x-3)-(0.125x+0.5)=2
0.25x-3- 0.125x-0.5=2
0.125x-3.5=2
0.125x =2+3.5
0.125x=5.5
x=5.5/0.125 (divide both sides by 0.125)
=44 apples
Therefore total number of apples picked by the prince, x=44
3a) Answer: 84 degrees
Step-by-step explanation:
3x + 2(x+20)= 180 (total sum of angles in a triangle is 180 degrees)
5x+40 = 180
5x = 140
x= 28
3x= 28 x 3
= 84