Answer:
x = 5 and y = 7
Step-by-step explanation:
Given that,
PT = x+2, TR=y, QT=2x, TS=y+3
We need to find the value of x and y.
The diagonal of a parallelogram bisect each other. It means,
PT = TR and QT = TS
ATQ,
y = x+2 ...(1)
and
y+3 = 2x ....(2)
Subtracting equation (1) and (2).
y-(y+3) = x+2-2x
y-y-3 = 2-x
-3 = 2-x
x = 2+3
x = 5
Put the value of x in equation (1).
y = 5 + 2
y = 7
Hence, the values of x and y are x = 5 and y = 7.
Step-by-step explanation:
Input:The definition of input is something entered into a machine or other system
Output:The act of turning out
Answer:
The length of DF must be between 21 and 53.
Step-by-step explanation:
In a triangle, the length of two sides added together must exceed the length of the 3rd side. So, since EF is the shortest of the two givens, we know that EF + DF must be greater than DE. So we can plug in these numbers to find the minimum.
EF + DF > DE
16 + DF > 37
DF > 21
Now, for the upper maximum, we know that the two given lengths must be greater than the length of DF. So again, we can solve for the maximum using the amounts.
DE + EF > DF
37 + 16 > DF
53 > DF
With these two in mind, we know that DF must be between 21 and 53
Answer:
Original number 26.
Step-by-step explanation:
xy - two-digit number
1) x + y = 8
2) Original two-digit number can be written as
10*x + y
3) If the digits interchanged yx,
then the new number can be written as
10*y + x
4) Double the original number is
2*(10*x + y)
5) New number is 10 more than double the original number
(10*y + x) - (2*(10*x + y)) = 10
6) Now we have the system of 2 equations:
x + y = 8
(10*y + x) - (2*(10*x + y)) = 10 -----> 10y + x - (20x + 2y) = 10 ---> 8y - 19x = 10
x = 8 - y
8y - 19(8 - y) = 10
8y - 152 +19y = 10
27y = 162
y = 6
x = 8 - y = 8 - 6 = 2
x = 2
So, x =2, y = 6.
Original number 26.
Check:
Original number 26.
New number 62.
Double of the original number = 2*26= 52.
New number is 10 more than double the original number :
62 - 52 = 10 True
