Answer:
because AC and BD bis => AX = XC; BX = XD
ΔAXD ≅ ΔCXB (SAS) because: AX = CX
DX = BX
m∠AXD = m∠BXC ( 2 opposing angles)
because ΔAXD ≅ ΔCXB (SAS)
=> AD = BC and m∠DAX = m∠BCX
because m∠DAX = m∠BCX => AD//BC
ABCD has AD = BC and AD//BC => ABCD is a parallelogram
Step-by-step explanation:
Answer:
Susan sent 25 messages
Felipe sent 100 messages
Deon sent 35 messages
Step-by-step explanation:
160 = x + 4x + x + 10
160 = 6x + 10
6x = 150
x = 25
Answer:Robert's minimum age is 11 years.
Step-by-step explanation:
Let x represent George's age.
Let y represent Edward's age.
Let z represent Robert's age.
George is twice as old as Edward. It means that
x = 2y
Edward's age exceeds Robert's age by 4 years. It means that
z = y - 4
If the sum of the three ages is at least 56 years, it means that
x + y + z ≥ 56 - - - - - - - - - - 1
Substituting x = 2y and z = y - 4 into equation 1, it becomes
2y + y + y - 4 ≥ 56
4y - 4 ≥ 56
4y ≥ 56 + 4
y ≥ 60/4
y ≥ 15
z = y - 4 = 15 - 4
z ≥ 11
Answer:
y = 2/3x +6 for x< -3
y = 2/3x +1 for x> 3
Step-by-step explanation:
The graph is a line for x < -3
( - 6,2) and ( -3,4)
The slope is m= ( y2-y1)/(x2-x1)
m = ( 4-2)/(-3 - -6) = 2/ ( -3+6) = 2/3
The slope is 2/3
Using point slope form
y-y1 = m(x-x1) and the point ( -6,2)
y -2 = 2/3(x - -6)
y -2 = 2/3(x +6)
y-2 = 2/3 x +4
y = 2/3x +6 x< -3
The graph is a line for x > 3
(3,3) and ( 6,5)
The slope is m= ( y2-y1)/(x2-x1)
m = ( 5-3)/(6-3) = 2/ (3) = 2/3
The slope is 2/3
Using point slope form
y-y1 = m(x-x1) and the point (6,5)
y -5 = 2/3(x - 6)
y-5 = 2/3 x -4
y = 2/3x +1 x> 3
First you convert centimeters to meters which will be 35 centimeters-> 0.35 meters
Once you have that, you multiply String A's length (0.35 m) by 5 to find String B's length which will be 1.75 meters.
Now that you have the two lengths you multiply each by 17.
17 x 1.75 = 29.75 and 17 x 0.35 = 5.95
Now you just add 29.75 and 5.95 and you get your answer which is
35.7 meters
