Solve for x over the real numbers:
-3 x^2 + 16 x + 12 = 0
The left hand side factors into a product with three terms:
-(x - 6) (3 x + 2) = 0
Multiply both sides by -1:
(x - 6) (3 x + 2) = 0
Split into two equations:
x - 6 = 0 or 3 x + 2 = 0
Add 6 to both sides:
x = 6 or 3 x + 2 = 0
Subtract 2 from both sides:
x = 6 or 3 x = -2
Divide both sides by 3:
Answer: | x = 6 or x = -2/3
You have to add the 2 yards together... 5,215 + 1,850 = 7,065. If 2 bags will cover 2,500 square feet, then 1 bag will cover 1,250. Divide 7,065 by 1,250 and you will need 6 bags of seed. For problem 2, add all the purchases together, which will be $250.50. This will get him a 30% discount. So his total price after the discount will be about $175.35. For problem 3, this is an exponential function. The $10,000 loan with 9% rate over 5 years is equal to 10,000(1+0.09)^5 which is about $15,500, so he will have to pay an additional $5,500.
The rate a computer works is 1/time. Working together, you add the rates.
Let new computer be x, old computer be y.
x = y - 7
Rounded to nearest tenth gives:
x = 23 hours
Answer:
Use the Triangle exterior angle theorem. The definition of this theorem, is that the exterior angle you are solving for is the sum of the two opposite interior angles. Set the equation:
80 + x = 3x - 22
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract x and add 22 to both sides.
80 (+22) + x (-x) = 3x (-x) - 22 (+22)
80 + 22 = 3x - x
Simplify.
102 = 2x
Isolate the variable, x. Divide 2 from both sides.
(102)/2 = (2x)/2
x = 102/2
x = 51
Check. Plug in 51 to the equation given.
80 + x = 3x - 22
80 + (51) = 3(51) - 22
131 = 153 - 22
131 = 131 (True).
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Area = length X width
A = L(12 ft) x W(9 ft) but since the cost of carpet is given in square yards not square feet we need to convert
A = (12 ft)(1 yd/3 ft) x (9 ft)(1 yd/3 ft) 1 yard = 3 feet so 1 foot = 1/3 yard
A = 4 yd x 3 yd divide by 3 ft which cancels the original ft and leaves yd's
A = 12 square yards
Cost = Area x price per yard
Cost = 12 sq yd X $35.00/ sq yd multiply and the sq yd's cancel leaving just cost in dollars
Cost = $420.00
