Answer:
18π ft^2
Step-by-step explanation:
The area of the circle is
pi *r^2
pi * 12^2
144pi
The part that is shaded is 45 degrees
An entire circle is 360 degrees
The fraction that is shaded is 45/360 = 1/8
Multiply the area by the fraction that is shaded
1/8 * 144 pi
18 pi
Answer:
13 carnations
Step-by-step explanation:
Assuming you meant 2/5 because 2.5 would mean there are more roses in the vase than there are flowers in the vase, heres how to solve this.
Understanding
Each fraction is referring to "flowers" not "remaining flowers" and as such each time we will be comparing to the total.
2/5 of the total flowers are roses. This is written in words as for every 5 flowers two are roses, which means we will multiply 2 by how many sets of five we have in 30 flowers.
(30/5) x 2 =
(6) x 2 = 12 roses
Though with fractions its written as 30/1*2/5 which is the same as (30 x 2)/5
60/5 = 12 roses
Following this logic for every 6 flowers one is a daisy.
30/1 * 1/6 = (30 x 1)/6 = 30/6 = 5 daisies
Because the rest are carnations we want to subtract the amount of daisies and roses from the total amount of flowers to find the remaining flowers.
30 - 5 - 12 = 13 carnations
Hope this helps,
The required values are ~
Refer to attachment for solution ~
<h3>Answer:</h3>
- ABDC = 6 in²
- AABD = 8 in²
- AABC = 14 in²
<h3>Explanation:</h3>
A diagram can be helpful.
When triangles have the same altitude, their areas are proportional to their base lengths.
The altitude from D to line BC is the same for triangles BDC and EDC. The base lengths of these triangles have the ratio ...
... BC : EC = (1+5) : 5 = 6 : 5
so ABDC will be 6/5 times AEDC.
... ABDC = (6/5)×(5 in²)
... ABDC = 6 in²
_____
The altitude from B to line AC is the same for triangles BDC and BDA, so their areas are proportional to their base lengths. That is ...
... AABD : ABDC = AD : DC = 4 : 3
so AABD will be 4/3 times ABDC.
... AABD = (4/3)×(6 in²)
... AABD = 8 in²
_____
Of course, AABC is the sum of the areas of the triangles that make it up:
... AABC = AABD + ABDC = 8 in² + 6 in²
... AABC = 14 in²
