a = 4, b = -21, c = -18
to keep from getting "mixed up", evaluate the discriminant first ...
b<sup>2</sup> - 4ac = (-21)<sup>2</sup> - 4(4)(-18) = 729
sqrt(729) = 27
x = (21 +/- 27)/8
x = -3/4, x = 6
since the discriminant is a perfect square, the original quadratic will factor ...
4x<sup>2</sup> - 21x - 18 = 0
(4x + 3)(x - 6) = 0
x = -3/4, x = 6
Answer:
dy=9-y
dx=x
Step-by-step explanation:
Answer: 14 gallons of gasoline.
Step-by-step explanation:
given data:
25(x + 3) = 424
where x is the number of gallon of gasoline needed to purchase.
Solution.
25(x + 3) = 424
first we open the bracket
25x + 75 = 424
collect like terms
25x = 424 – 75
25x = 349
divide both sides by 25
25x/25 = 349/25
x = 13.96
x = 14
mathew needs to get 14 gallons of gasoline.
Let's say that the weight of the orange is x and the weight of the pineapple is y.
The weight of the pineapple is 7 times that of the orange, so
y = 7x.
Also, y = x + 870.
Therefore, 7x = x + 870.
If we take away x from both sides, we get 6x = 870
If we divide both sides by 6, we get x = 145.
Therefore, the weight of the orange is 145 g.
Also, 145 + 870 = 1015.
So the weight of the pineapple is 1015 g.
To convert grams into kilograms, they must be divided by 1000.
Therefore, the weight of the orange in kilograms is 145/1000 = 0.145 kg
And the weight of the pineapple is 1015/1000 = 1.015 kg.
Answers:
a. 145g for the orange and 1015g for the pineapple.
b. 0.145kg for the orange and 1.015kg for the pineapple.
