Answer:
a = 4 b = 5
Step-by-step explanation:
8a + 12b = 92......eqn 1
6a - 4b = 4......eqn 2
multiply eqn 2 by 3
18a - 12b = 12.....eqn 2
add eqn 1 and 2 to eliminate b
26a = 104
a = 4
put a = 4 into eqn 2
18(4) - 12b = 12
72 - 12b = 12
72 - 12 = 12b
60 = 12b
5 = b
Answer:
Step-by-step explanation:
hello :
the point-slope formula is :
y - y_1 = m(x - x_1) the point is A(x_1 , y_1 ) , m : the slope
in this exercice : x_1 = 6 y_1 = 8 m = -2
so : y - 8 = -2(x - 6) ...an equation for this line .
7d = 56 minus the x in the middle
<u>0.</u><u>3</u><u>7</u><u>5</u>
Answer:
Solution given:
For 1st box.
probability of not getting blue is:2/4=1/2
For second box
probability of not getting blue is:1/4
total probability=½*¼=0.375
Given:
Regular polygon.
Side length = 18 in
To find:
The area of the regular polygon.
Solution:
Let us first find the apothem (length from center to side).
<u>Apothem formula:</u>
![$a=\frac{s}{2 \tan \left(\frac{180^\circ}{n}\right)}](https://tex.z-dn.net/?f=%24a%3D%5Cfrac%7Bs%7D%7B2%20%5Ctan%20%5Cleft%28%5Cfrac%7B180%5E%5Ccirc%7D%7Bn%7D%5Cright%29%7D)
where s is side length and n is number of sides.
number of sides (n) = 6
![$a=\frac{18}{2 \tan \left(\frac{180^\circ}{6}\right)}](https://tex.z-dn.net/?f=%24a%3D%5Cfrac%7B18%7D%7B2%20%5Ctan%20%5Cleft%28%5Cfrac%7B180%5E%5Ccirc%7D%7B6%7D%5Cright%29%7D)
![$a=\frac{9}{\tan (30^\circ)}](https://tex.z-dn.net/?f=%24a%3D%5Cfrac%7B9%7D%7B%5Ctan%20%2830%5E%5Ccirc%29%7D)
The value of ![\tan \left(30^{\circ}\right)=\frac{\sqrt{3}}{3}](https://tex.z-dn.net/?f=%5Ctan%20%5Cleft%2830%5E%7B%5Ccirc%7D%5Cright%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B3%7D)
![$a=\frac{9}{\frac{\sqrt{3}}{3}}](https://tex.z-dn.net/?f=%24a%3D%5Cfrac%7B9%7D%7B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B3%7D%7D)
in
<u>Area of regular polygon:</u>
![$A=\frac{1}{2} \times p \times a](https://tex.z-dn.net/?f=%24A%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20p%20%5Ctimes%20%20a)
where p is perimeter of polygon and a is apothem.
![$A=\frac{1}{2} \times (6\times 18) \times 9\sqrt{3}](https://tex.z-dn.net/?f=%24A%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%286%5Ctimes%2018%29%20%5Ctimes%20%209%5Csqrt%7B3%7D)
![$A=54 \times 9\sqrt{3}](https://tex.z-dn.net/?f=%24A%3D54%20%5Ctimes%20%209%5Csqrt%7B3%7D)
square inches.
The area of the regular polygon is 841.78 square inches.