An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c. Consider the trinomial 6x2 + 13x + 6. The value of ac is . The value of b is . The two numbers that have a product of ac and a sum of b are 4 and .

1. ac = 36

2. b = 13

3. 4 and 9

Step-by-step explanation:

Given

6x² + 13x + 6

Required

Fill in the gaps

Solving (1): The value of AC

The general form of an equation is:

ax² + bx + c

By comparison:

a = 6

b = 13

c = 6

So,

ac = a * c

ac = 6 * 6

ac = 36

Solving (2): The value of b

In (1) above, we showed that

b = 13

Solving (3): Two numbers that satisfy product ac and sum b

We have that.

ac = 36

If one of the numbers is 4, then the other number is

Other number = 36/4

Other number = 9

Alternatively, we have that.

b = 13

If one of the numbers is 4, then the other number would be:

Other number = 13 - 4

Other number = 9

The above answer is Perfect!

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.