Answer:the plane in still air is 904 km/h
the rate of the wind is 104 km/h
Step-by-step explanation:
Let x represent the rate or speed of the plane in still air.
Let y represent the rate or speed of the wind.
Flying against the wind, an airplane travels 4000 kilometers in 5 hours. This means that the total speed of the airplane would be (x - y) km/h
Distance = speed × time
Therefore
4000 = 5(x - y)
4000 = 5x - 5y - - - - - - - - -1
Flying with the wind, the same plane travels 5040 kilometers in 4 hours. This means that the total speed of the airplane would be (x + y) km/h. Therefore,
5040 = 4(x + y)
5040 = 4x + 4y - - - - - - - - - 2
Multiplying equation 1 by 4 and equation 2 by 5, it becomes
16000 = 20x - 20y
20160 = 20x + 20y
Subtracting, it becomes
- 4160 = - 40y
y = - 4160/-40
y = 104
Substituting y = 104 into equation 1, it becomes
4000 = 5x - 5 × 104
4000 = 5x - 520
5x = 4000 + 520
5x = 4520
x = 4520/5 = 904
Answer:
Volume of slice is 40 in³
Volume of the remaining cake is 197.014 in³
Step-by-step explanation:
hope this helps!!
brainliest please?
Answer:
See below.
Step-by-step explanation:
For item 2:
The Net Price Rate = 276 / 460 = 0.60 = 60 % (answer).
Item 3: Net Price Rate = 3247 * 100 / 3820 = 85% (answer).
Item 4 Net Price Rate = 675.11 / * 100 / 987 = 68.4%. (answer).
Item 5 Item's Net Price = 987 * 0.675 = $666.23 (answer).
Item 7 Net price Rate = 2945* 100 / 4750 = 62%. (answer).
Item 8: First find the list place $x:
0.90* 0.80 * 0.70x = 252 ( the 0.90 , 0.80 and 0.70 come from 100 - 10% = 1 - 0.10 = 0.90 and so on)
0.504 x = 252
x = $500
Answer is List Price = $500 and Net Price Rate = 50.4%.
Item 10 List price = 2890.65 / 0.35 = $8259. (answer)
Answer:
Given: In parallelogram ABCD, AC=BD
To prove : Parallelogram ABCD is rectangle.
Proof : in △ACB and △BDA
AC=BD ∣ Given
AB=BA ∣ Common
BC=AD ∣ Opposite sides of the parallelogram ABCD
△ACB ≅△BDA∣SSS Rule
∴∠ABC=∠BAD...(1) CPCT
Again AD ∥ ∣ Opposite sides of parallelogram ABCD
AD ∥BC and the traversal AB intersects them.
∴∠BAD+∠ABC=180∘ ...(2) _ Sum of consecutive interior angles on the same side of the transversal is
180∘
From (1) and (2) ,
∠BAD=∠ABC=90∘
∴∠A=90∘ and ∠C=90∘
Parallelogram ABCD is a rectangle.
