Answer:
ΔABC ~ ΔDEC
Step-by-step explanation:
Given : DE║AB
Statements Reasons
1). DE║AB 1). Given
2). ∠CDE ≅ ∠CAB 2). Corresponding angles
[Since DE║AB and AC is the transverse]
3). ∠CED ≅ ∠CBA 3). Corresponding angles
[Since DE║AB and BC is the transverse]
4). ΔABC ~ ΔDEC 4). By AA property of similarity
Hence ΔABC is similar to ΔDEC.
Answer: Option C - Construction Y because point E is the circumcentre of triangle LMN.
Point E is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.
Step-by-step explanation:
Before solving an algebra problem, it sometimes helps to get a geometric picture of what's happening. Geometry says that three points determine a circle - in other words, given three points that are not
all on the same line, there is exactly one circle which passes through all 3. Finding the point equidistant from the 3 points is the same thing as finding the center of the circle that passes through all of them (since all points on a circle are equidistant from the center).
Our points are L, M and N. Draw the lines LM, LN and MN to form a triangle. Now construct the perpendicular bisectors of any two of the lines, and their intersection, point E, will be the center of this circle.
As shown in the Construction Y because E is the circumcentre of triangle LMN.
This is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.
QED!
The change from 3/4 to 4/10 is found by obtaining and applying the LCD:
15/20 to 8/20 is a negative change, and the amount of the change was -7/20.
We compare this result to the original value, 15/20, to obtain the percentage change in the fraction:
-7/20
----------- = -7/15 = -0.467 => -46.7%
15/20
Answer: 350 adult tickets
Step-by-step explanation:
(omg I remember this question!)
- a stands for the number of adult tickets sold
student tickets : a + 65
<em>the equation for the prob: </em>
765 = a + (a + 65)
<em>solve:</em>
combine 'like terms'
1.) 765 = a + a + 65
2.) 765 = 2a + 65
<u>- 65 - 65 </u>
700= 2a
divide by 2
700/2 = 2a/2
<em>(700/2 = 350) </em>
<em>(the "2" in 2a is cancelled out by the other 2)</em>
<u>350 = a </u>