Answer:
see the explanation
Step-by-step explanation:
In this problem
I will assume that the total amount required for the trip is $1,200
so
Let
x ----> the number of weeks
we know that
The number of weeks multiplied by $75 plus $300 must be at least $1,200
In this context, the term "at least" means "greater than or equal to"
so
The linear inequality that represent this problem is
Solve for x
subtract 300 both sides
Divide by 75 both sides
therefore
The minimum number of weeks you need to save is 12
Join the centre O to the chord (let it be MN) & let OH be the perpendicular to the chord
OH bisects MN into 2 equal parts (each one is x/2)
OMH is a right triangle with one side =8, the second leg =x/2 & the hypotenuse = 12 (Radius)
Apply Pythagoras:
12² = 8² +(x/2)² ==>144=64 + x²/4 ==> x²=4(144-64) =320
x²=320==> x=√320 =17.88 ≈17.9
Answer:
(X=Y)=(3,6)
Step-by-step explanation:
5x-4(4x-6)=-9
x=3
y=4x3-6
y=6
Answer:
1.9 kg
Step-by-step explanation:
Empty container: 3/10 kg = 0.3 kg
Container half filled: 1 1/10 kg = 1.1 kg
Mass of water that fills it halfway: 1.1 kg - 0.3 kg = 0.8 kg
Mass of water that fills it completely: 2 * 0.8 kg = 1.6 kg
Mass of container completely filled with water: 0.3 kg + 1.6 kg = 1.9 kg
Answer:
BD = 35
Step-by-step explanation:
Calculate CD in right triangle ABC, then BD in right triangle BCD
Using Pythagoras' identity in both triangles.
The square on the hypotenuse is equal to the sum of the squares on the other two sides.
In Δ ADC
CD² + AD² = AC² , substitute values
CD² + 9² = 15²
CD² + 81 = 225 ( subtract 81 from both sides )
CD = 144 ( take the square root of both sides )
CD = 
= 12
----------------------------------------------------------------
In Δ BCD
BD² + CD² = BC² , substitute values
BD² + 12² = 37²
BD² + 144 = 1369 ( subtract 144 from both sides )
BD² = 1225 ( take the square root of both sides )
BD = 
= 35
