Cedric completed the square for the quadratic expression 5x^2−40x+15 in order to determine the minimum value of the expression, as shown.
Step 1: 5(x^2−8x+3)
Step 2: 5(x^2−8x+16−16+3)
Step 3: 5((x+4)^2−16+3)
Step 4: 5((x+4)^2−13)
Step 5: 5(x+4)^2−65
What mistake, if any, did Cedric make?

Step 3 is not correct (should be , not

Step-by-step explanation:

The expression that we have to simplify is:

We proceed step-by-step, in order to find the mistake did by Cedric:

1) First, we factorize the 5 outside:

--> this step is correct

2) We add +16 and -16 inside the brackets:

--> this step is correct

3) We rewrite the term as the square of a bynomial, which is , so the expression becomes

--> we notice that this step is wrong: in fact, Cedric wrote , which is not correct.

4) Now we continue: we rewrite -16+3 as -13,

5) Finally, we multiply the 5 by the terms in the bracket:

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%

answer: 80,000

step-by-step explanation:

the population doubles every day.

10,000*2=20,000 day 4

20,000*2=40,000 day 5

40,000*2=80,000 day 6