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Iteru [2.4K]
3 years ago
15

Find the solutions to the equation below check all that apply

Mathematics
2 answers:
jek_recluse [69]3 years ago
7 0

Answer:

C. x=-1/2  and F. x=-3

Step-by-step explanation:

We can solve this by factoring.  We will look for factors of a*c, 2*3, that sum to b, 7.  Factors of 6 are:

1 and 6; these sum to 7.

2 and 3; these do not sum to 7.

We will use 1 and 6.  We will split bx, 7x, into 1x and 6x:

2x²+1x+6x+3 = 0

We will group the first two and the last two terms together:

(2x²+1x)+(6x+3) = 0

We will factor out the GCF of each group.  The GCF of the first group is 1x:

1x(2x+1)+(6x+3) = 0

The GCF of the second group is 3:

1x(2x+1)+3(2x+1) = 0

The GCF of the two terms remaining is (2x+1); factoring this out,

(2x+1)(1x+3) = 0

Using the zero product property,

2x+1 = 0 or 1x+3 = 0

To solve the first equation, subtract 1 from each side:

2x+1-1 = 0-1

2x = -1

Divide both sides by 2:

2x/2 = -1/2

x = -1/2

To solve the second equation, subtract 3 from each side:

1x+3-3 = 0-3

x = -3

Harman [31]3 years ago
4 0

2x^2+7x+3=0:    x=-1/2 and x=-3   c and F

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Step-by-step explanation:

These are the answers because:

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a. The water in the second tank decreases at a faster rate than the water in the first tank. The initial water level in the first tank is greater than the initial water level in the second tank.

Step-by-step explanation:

Step 1:

It is given that the time remaining in first tank is given by the equation y = -10x + 80. We can get the total water in the tank by substituting x = 0 in the equation. The total volume of water in first tank is 80 litres.

Step 2:

The value of y in the equation y = -10x + 80 will be 0 when the tank is fully empty. When y = 0 , 10x = 80, so x = 8. We can conclude that the first tank empties fully in 8 minutes.

In 8 minutes 80 litres of water is emptied from first tank. So the water in the first tank decreases at  rate of 80 / 8 = 10 litres per minute

Step 3:

As per the given table for the second tank, 60 litres of water remains when x =0. So the total volume of water in the second tank = 60 litres.

Step 4:

As per the given table for the second tank, the volume becomes 0 in 5 minutes. In 5 minutes 60 litres of water is emptied from second tank. So the water in  second tank decreases at rate of 60 / 5 = 12 litres per minute.

Step 5:

The initial volume of water in first tank is higher. The water in  second tank decreases at a faster rate than the first tank.

Step 6:

The only correct option is:

a. The water in  second tank decreases at a faster rate than the water in the first tank. The initial water level in  first tank is greater than the initial water level in the second tank.

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