MrBillDoesMath!
Answer: 51,53,55,57
Discussion. By the triangle inequality the sum of the lengths of any two sides is greater than or equal to the third side. In our case, 3 + 54 = 57, so the third side must be less than or equal to 57.
MrB
Answer:
Take x = 10.2 in. or x = 10 in.
Step-by-step explanation:
Given :
Length = (2x+3) in.
Breadth = x in.
Also, the Area of Rectangle = 240 sq in.
We know that,
Area of Rectangle = length x breadth
240 = (2x+3) x
2x² + 3x = 240
2x² + 3x - 240 = 0
Solving 2x²+3x-240 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B²-4AC
x = ————————
2A
In our case, A = 2
B = 3
C = -240
Accordingly, B² - 4AC = 9 - (-1920) = 1929
Applying the quadratic formula :
-3 ± √ 1929
x = ——————
4
√ 1929 , rounded to 4 decimal digits, is 43.9204
So now we are looking at:
x = ( -3 ± 43.920 ) / 4
Two real solutions:
x =(-3+√1929)/4=10.230 ≈ 10
or
x =(-3-√1929)/4=-11.730
We'll take x = +ve value for calculation of length and breadth.
Therefore,
Length = [2(10.2) + 3 ]
L = 23.4 in.
Breadth = 10.2 in.
OR
Length = [2(10) + 3]
L = 23 in.
Breadth = 10 in.
Answer:
$863
Step-by-step explanation:
Given: Carla Arslanian is 55 years old. She wants to purchase a $100,000, 10-year term life insurance policy.
To find: What is her annual premium?
Solution: Insurance companies use mathematical calculation and statistics to calculate the number of insurance premiums they charge their clients.
Annual premium = face value x rate $100
Annual premium (for building) = $100,000 ÷ $1000 x 10 = $1000.
The sum of the annual premium is $863.
Combine the like terms
3b-5a
Or -5a+3b if keeping in a certain order
Let $k = the monthly base fee.
The variable cost is $0.30 per minute.
Let
C = total cost in a month
x = minutes used
September:
x = 120 minutes
C = $50
Therefore
k + (0.30)(120) = 50
k + 36 = 50
k = $14
October:
x = 165 minutes
The cost is
C = 14 + (0.3)(165)
C = $63.5
Answer: $63.50
