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A quadratic equation?

By graphing:

Standard form: ax^2+bx+c where a is vertical shift/stretch and c is the y-intercept

Intercept form: a(x-p)(x-q) where p and q are the roots of the equation and a is the vertical shift/stretch

Vertex form: a(x-h)^2+k where a is the vertical shift/stretch and h is the x value of the vertex and k is the y value of the vertex

h is also the horizontal sift and k is the vertical shift

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Thats right!

The question is from a youtube video, I think its from a Chinese TV show. I just saw it on youtube and saw how it was really intresting, it was like a tv show about 3rd graders solving math questions. 

So I would assume 3rd grade? (in China?)

We know that anything to the power of 0 is 1, but we are also taught that 0 to the power of anything is 0.

Because these two rules conflict, I would assume that it is undefined.

The commutative property of multiplication says that a*b = b*a.

Because of this, the answer is the 2nd one.

~~Hypotenuisance

To simplify this expression, first expand the four terms(in total) in the parantheses. When expanded, you get 14b - 12 - 10b + 15. Simplify this to get 4b + 3.

The simplified expression is 4b+3.

~~Hypotenuisance

So we can approach the problem by solving with "blocks".

WE put the boys in a single "block" and assume tht they are a single person.

Now there are four people since the boys are a block

We can do 4! 4*3*2*1 = 24 to find out how many ways to seat them all. But the boys can also switch in between themselves, so we get 24*2 = 48

We forgot rotational symmetry though so we have to divide by 4 (the number of people there are) since moving them around a table is considered the same rotation.

And then you get your final equation (4!*2!)/4

*The problem should be labled Combination not Permutation

When you did that, you were supposed to change the 2's symbol since there was a subtraction sign in front of the parentheses getting -3y+2=16

The first person who replied used substitution (and did it wrong), but here is it in elimination form and substitution

So in this problem it would be easier to substitute since it already gives us x

y-x=14

x=4y-2

To substitute it we can do y-(4y-2)=14

To get y = -4

We can then plug it into the X equation to get

x = -18

So the answer above is wrong

We can multiply the first sentence by 4 to get

4y-4x=56

We can then get the two equations:

4y-4x=56

4y-2=x

Then we can subtract these two equations from each other the eliminate the y.

Actually, the range is infinite, it should be (-inf, inf), since there is no "set" Y value. So the answer would be none of the above

So in order to solve this we can use two ways, complementary counting or how they had done it below (permutation)

Complementary counting starts with finding out the total amoutn of 3 digit whole numbers, in which we can use the Arithmatic Sequence.(1000-1/1)+1 = 999. 

We can then find how many numbers HAVE 9 or 7 as their digits. So we get 551 numbers that have 9 and 7 as digits. 

Using this information we can subtract 551 from 999, 999-551 = 448 Which is our answer.

ANSWER: 448

For the first one...

To calculate the first problem, first find the probability of getting one right. That is 1/2. Then, getting three right is the same as 1/8 probability. Likewise, getting three wrong is 1/8 probability. Multiplying these two fractions gets us 1/64 probability.

The probability of Karen getting three questions right and three questions wrong is 1/64.

~~Hypotenuisance