Answer:
Center (-5,4) radius 3
Step-by-step explanation:
The standard equation of a circle is
(x-h)^2+(y-k)^2=r^2
where the center is (h,k) and r is the radius
so h=-5 in this case and k is 4
r^2=9 so r=3
Answer:
Step-by-step explanation:
First, write an equation. 55x+40=190.
X represents the hours the electrician works. The 55 represents the $55 that she charges for each hour she works. The +40 for the $40 that was the price just to come to your house. The 190 is the total cost. Now, solve that equation.
55x+40=190
55x=150
x=2.72727272...
So the answer is 2.727 hours. It can be rounded as needed or turned into a decimal, 2 8/11.
Volume in terms of pi =V=πr2h
Answer:
ΔASA ≅ ΔASA
Step-by-step explanation:
<h3>Given</h3>
1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.
2) Regular pentagon PENTA with side lengths 9 m
<h3>Find</h3>
The area of each figure, rounded to the nearest integer
<h3>Solution</h3>
1) The area of a trapezoid is given by
... A = (1/2)(b1 +b2)h
... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77
The area of BEAR is about 77 cm².
2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...
... A = (1/2)ap
... A = (1/2)(s/(2tan(180°/n)))(ns)
... A = (n/4)s²/tan(180°/n)
We have a polygon with s=9 and n=5, so its area is
... A = (5/4)·9²/tan(36°) ≈ 139.36
The area of PENTA is about 139 m².
