Answer:
The proof is explained step-wise below :
Step-by-step explanation :
For better understanding of the solution see the attached figure :
Given : ABCD is a Parallelogram ⇒ AB ║ DC and AD ║ BC
Now, F lies on the extension of DC. So, AB ║ DF
To Prove : ΔABE is similar to ΔFCE
Proof :
Now, in ΔABE and ΔFCE
∠ABE = ∠FCE ( alternate angles are equal )
∠AEB = ∠FEC ( Vertically opposite angles )
So, by using AA postulate of similarity of triangles
ΔABE is similar to ΔFCE
Hence Proved.
Answer:
A. 
B. 
Step-by-step explanation:
Consider the equation
A. This equation has no solutions when the coefficients at x are the same and the free coefficients are not the same.
First, use distributive property:
So, the equation is
This equation has no solutions when
B. The equation has infinitely many solutions when the coefficients at x are the same and the free coefficients are the same too.
So, the equation
has infinitely many solutions when
In other cases, the equation has a unique solution
Answer:
Part A: Kimberly
Part B:
Becca = 22.5 miles, Kimberly = 25 miles
Step-by-step explanation:
Part A:
Given that Becca runs at a constant speed of 4.5 miles per hour, use the table to find the constant speed that Kimberly runs, and compare who runs faster.
Let x = time
y = distance
k = speed = y/x
Equation for each person can be written as: y = kx
Therefore:
✔️Equation for Becca if k = 4.5
y = 4.5x
✔️Find k (speed) of Kimberly using (2, 10):
Speed (k) = y/x
k = 10/2
k = 5 miles per hour
Equation for Kimberly would be:
y = 5x
Comparing their speed, Kimberly runs faster because she covers more miles per hour than Becca does.
Part B:
For Becca, substitute x = 5 into Becca's equation, y = 4.5x
Thus:
y = 4.5*5 = 22.5 miles
For Kimberly, substitute x = 5 into Kimberly's equation, y = 5x
Thus:
y = 5*5 = 25 miles
Let the daily played number of pop songs be P, the number of rock songs be R and the number of hip-hop songs be H.
i)
"A radio station plays a total of 272 pop, rock, and hip-hop songs during a day"
means that : P+R+H=272
ii)
"The number of pop songs is 3 times the number of rock songs. "
so, P=3R
iii)
"The number of hip-hop songs is 32 more than the number of rock songs."
means: H=32+R
iv)
since both P and H can be written in terms of R, we have:
P+R+H=272
(3R)+R+(32+R)=272
3R+R+32+R=272
5R+32=272
5R=272-32=240
R=240/5=48
vi)
thus: P=3R=3*48=144, H=32+R= 32+48=80
Answer:
48 Rock, 144 Pop and 80 Hip-hop
SeconAnswer:
Step-by-step explanation:
First question answer is 390.66 m
1 mile_1609.34 m
1000m=1km
2km=2x1000=2000m
2000km - 1609.34m=390.66m
Se ond question 6x10000=60000cm2
