The answer is d 160 tickets.
Answer:
1/14
Step-by-step explanation:
A) x + y = 110
x - y = 40
B) Melvin swims for 35 minutes every day.
C) It is not possible
Step-by-step explanation:
Step 1:
Let x denote the duration for which Melvin plays tennis and y denote the duration for which he swims
Step 2 :
Part A :
Given that the total duration for which he plays and tennis is 110 minutes
so we have x + y = 110
Also given that he plays tennis for 40 minutes more than he swims
So, x = y+ 40 =>x-y = 40
So the linear pair of equations are
x + y = 110
x-y = 40
Step 3 :
Part B
Solving the above 2 equations we have
y+40+y = 110 = > 2y+ 40 = 110 = > y = 2y = 70 = >35
x = y+40 = 35+ 40 = 75
So Melvin plays tennis for 75 minutes and swims for 35 minutes every day.
Step 4 :
Part C
Given he plays and swims for 110 mins exactly, i.e x + y = 110
If Melvin plays tennis for 70 minutes , then x = 70, then the time for which he can swim is 110 - 70 = 40 mins.
He gets only 40 mins for swimming which is not 40 mins more than he plays tennis .
So this case is not possible.
Answer: Kara should have written the proportion in step 1 as;
Start Fraction 12 Over 72 End Fraction = Start Fraction 14 Over x End Fraction (that is 12/72 = 14/x)
Step-by-step explanation: The two similar triangles are given with the following dimensions;
Triangle VXW with side VW = 12 and side VX = 14. Also Triangle ZXY with side YZ = 72 and side XZ = x.
For two triangles to be similar, then there must be a similarity ration that is consistent with all sides in both triangles. This means if in the first triangle a side measures 1 unit and the similar side in the other triangle measures 5 units, then the ratio of similarity of corresponding sides shall be ratio 1 : 5. So for every corresponding side in the second triangle the measurement shall be times five of the side that corresponds in the first triangle.
Therefore, in triangle VXW and triangle ZXY, the corresponding sides are as follows;
VX = ZX
VW = ZY
XW = XY
What Kara did was as follows;
VX/ZY = VW/ZX
Which translates to 14/72 = 12/x
This was a wrong calculation because the side that corresponds to VX is ZX and not ZY.
The correct step should therefore have been;
VW/ZY = VX/ZX
12/72 = 14/x (Step 1)
12x = (72) (14) {Step 2}
x = 1008/12 (Step 3)
x = 84 (Step 4)
20 inches is 400
10 inches is 200
5 iches is 100
So 20+10+5=35
Which means 400+200+100= 700
So the frequency of a 35 inch string is 700 cycles per second
