Answer:
x = 12
(2x + 1)° = 25°
(5x + 5)° = 65°
Step-by-step explanation:
By the property of a triangle,
Sum of all angles of a triangle is 180°
In the given right triangle,
(2x + 1)° + 90° + (5x + 5)°= 180°
7x + 96 = 180
7x = 180 - 96
x = ![\frac{84}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B84%7D%7B7%7D)
x = 12
Angle (2x + 1)° = 2(12) + 1 = 25°
Angle (5x + 5)° = 5(12) + 5 = 65°
Therefore, all three angles of the right triangle are 25°, 90° and 65°.
Step-by-step explanation:
464.5cm³
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Answer:
5x+6y=60
Step-by-step explanation:
x= $5 per pound of second type of seed
y=$6 per pound of first types of seed
Question - Answer
a) 1/2 L = 4
b) 1/2 L x 4 = 2
c) 5/6 x 2 = 1 4/6 L OR 1.67 L
d) 2/3 L = 3 beakers with 2/3 OR 5 beakers with 2/3 and 5/6
e) <1/3 L = 3 beakers
I believe that is the answer.
Answer:
See explanation
Step-by-step explanation:
a) To prove that DEFG is a rhombus, it is sufficient to prove that:
- All the sides of the rhombus are congruent:
![|DG|\cong |GF| \cong |EF| \cong |DE|](https://tex.z-dn.net/?f=%7CDG%7C%5Ccong%20%7CGF%7C%20%5Ccong%20%7CEF%7C%20%5Ccong%20%7CDE%7C)
- The diagonals are perpendicular
Using the distance formula; ![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![|DG|=\sqrt{(0-(-a-b))^2+(0-c)^2}](https://tex.z-dn.net/?f=%7CDG%7C%3D%5Csqrt%7B%280-%28-a-b%29%29%5E2%2B%280-c%29%5E2%7D)
![\implies |DG|=\sqrt{a^2+b^2+c^2+2ab}](https://tex.z-dn.net/?f=%5Cimplies%20%7CDG%7C%3D%5Csqrt%7Ba%5E2%2Bb%5E2%2Bc%5E2%2B2ab%7D)
![|GF|=\sqrt{((a+b)-0)^2+(c-0)^2}](https://tex.z-dn.net/?f=%7CGF%7C%3D%5Csqrt%7B%28%28a%2Bb%29-0%29%5E2%2B%28c-0%29%5E2%7D)
![\implies |GF|=\sqrt{a^2+b^2+c^2+2ab}](https://tex.z-dn.net/?f=%5Cimplies%20%7CGF%7C%3D%5Csqrt%7Ba%5E2%2Bb%5E2%2Bc%5E2%2B2ab%7D)
![|EF|=\sqrt{((a+b)-0)^2+(c-2c)^2}](https://tex.z-dn.net/?f=%7CEF%7C%3D%5Csqrt%7B%28%28a%2Bb%29-0%29%5E2%2B%28c-2c%29%5E2%7D)
![\implies |EF|=\sqrt{a^2+b^2+c^2+2ab}](https://tex.z-dn.net/?f=%5Cimplies%20%7CEF%7C%3D%5Csqrt%7Ba%5E2%2Bb%5E2%2Bc%5E2%2B2ab%7D)
![|DE|=\sqrt{(0-(-a-b))^2+(2c-c)^2}](https://tex.z-dn.net/?f=%7CDE%7C%3D%5Csqrt%7B%280-%28-a-b%29%29%5E2%2B%282c-c%29%5E2%7D)
![\implies |DE|=\sqrt{a^2+b^2+c^2+2ab}](https://tex.z-dn.net/?f=%5Cimplies%20%7CDE%7C%3D%5Csqrt%7Ba%5E2%2Bb%5E2%2Bc%5E2%2B2ab%7D)
Using the slope formula; ![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
The slope of EG is ![m_{EG}=\frac{2c-0}{0-0}](https://tex.z-dn.net/?f=m_%7BEG%7D%3D%5Cfrac%7B2c-0%7D%7B0-0%7D)
![\implies m_{EG}=\frac{2c}{0}](https://tex.z-dn.net/?f=%5Cimplies%20m_%7BEG%7D%3D%5Cfrac%7B2c%7D%7B0%7D)
The slope of EG is undefined hence it is a vertical line.
The slope of DF is ![m_{DF}=\frac{c-c}{a+b-(-a-b)}](https://tex.z-dn.net/?f=m_%7BDF%7D%3D%5Cfrac%7Bc-c%7D%7Ba%2Bb-%28-a-b%29%7D)
![\implies m_{DF}=\frac{0}{2a+2b)}=0](https://tex.z-dn.net/?f=%5Cimplies%20m_%7BDF%7D%3D%5Cfrac%7B0%7D%7B2a%2B2b%29%7D%3D0)
The slope of DF is zero, hence it is a horizontal line.
A horizontal line meets a vertical line at 90 degrees.
Conclusion:
Since
and
, DEFG is a rhombus
b) Using the slope formula:
The slope of DE is ![m_{DE}=\frac{2c-c}{0-(-a-b)}](https://tex.z-dn.net/?f=m_%7BDE%7D%3D%5Cfrac%7B2c-c%7D%7B0-%28-a-b%29%7D)
![m_{DE}=\frac{c}{a+b)}](https://tex.z-dn.net/?f=m_%7BDE%7D%3D%5Cfrac%7Bc%7D%7Ba%2Bb%29%7D)
The slope of FG is ![m_{FG}=\frac{c-0}{a+b-0}](https://tex.z-dn.net/?f=m_%7BFG%7D%3D%5Cfrac%7Bc-0%7D%7Ba%2Bb-0%7D)
![\implies m_{FG}=\frac{c}{a+b}](https://tex.z-dn.net/?f=%5Cimplies%20m_%7BFG%7D%3D%5Cfrac%7Bc%7D%7Ba%2Bb%7D)