Question

PLEASE HELP ME
Medal will be awarded

y varies directly as the square of x. When x = 1, y = 3. What is the value of y when x = 3?

1

9

27

81



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At a specialty nut store, almonds cost $4.30 per pound and walnuts are priced at $3.75 per pound. How many pounds of walnuts are in a 12-pound mixture priced at $47.75?

4

5

6

7
What is the fourth term in the expansion of (x – 4)6?

–1280x3

–256x4

256x4

1280x3

Answer 1

The second one is a Guess, Check, and Revise problem. You have to think of two addends that will add to 12 pounds.

So at first I tried out how much will the price be if there are 6 pounds of almonds and 6 pounds of walnuts. But then I figured out that the price was too much than required. Then I tried decreasing the amount of almond by one pound (which is 5 pounds) and keeping the amount of walnuts the same. So what I did is ($4.30x5)+($3.75x6)=$47.75.

Answer 2

direct variation of thing 1 with thing 2 means that thing1 = k * thing 2, where k is a constant.

so, if y varies directly with the square of x, that means \(y = kx^2\) Plug in the known data to find \(k\) and update the equation to find the other point.

\[3=k(1)^2\]\[3=k\]
\[y = 3x^2\]\[y = (3)^2 = 9\]

Answer 3

Sorry about the first question. I figured out that y has to be squared. So since y=9, the answer will be 81 because 9x9=81.

Answer 4

You can guess and check for the second problem, or write the equations and solve.

A is amount of almonds
W is amount of walnuts

A+W = 12
4.3A + 3.75W = 47.75

Solve by substitution or elimination.
To substitute, solve the first equation for one of the variables in terms of the other, then plug into the second and solve:
A+W = 12
A = 12-W
4.3(12-W) +3.75W = 47.75
51.6 - 4.3W + 3.75W = 47.75
W = 7
A = 12-W = 12-7 = 5

To eliminate, multiply each equation by a number that will cause one of the coefficients to be equal in magnitude, then add or subtract as appropriate.

A + W = 12
4.3A + 3.75 W = 47.75

multiply first eq by -4.3
-4.3A -4.3W = -51.6
4.3 A + 3.75 W = 47.75
-------------------
-0.55 W = -3.85
W = 7

Answer 5

For the 3rd problem, I would use the binomial theorem.

Answer 6

But isn't this a question related to variables?

Answer 7

I meant for the second question.

Answer 8

what are A and W if not variables? well, okay, a fast food joint :-)

Answer 9

@calculusxy "So since y=9, the answer will be 81 because 9x9=81."
where are you getting that y = 9?

Answer 10

So what is number 3

Answer 11

@magbak do you know the binomial theorem?

Answer 12

Also is number 1 p

Answer 13

IS number 1 y=9

Answer 14

sorry, I missed a 3 on my answer to #1

we found k = 3, so the equation is \(y = 3x^2\) and we want to find \(y\) when \(x=3\) so that gives us \(y=3(3)^2 = 3*9 = 27\)

Answer 15

What is number 3 please.

Answer 16

you didn't answer my question about the binomial theorem...do you know it?

Answer 17

Yes.

Answer 18

okay, that's what I would use to find the answer.

What is the fourth term in the expansion of \((x – 4)^6\)?

We have \(a = x, b = -4, n = 6\) and we want to find the 4th term

Answer 19

Yes. But I believe pascals triangle will be the easiest.

Answer 20

okay, the race is on :-)

Answer 21

OK

Answer 22

-6144x that is the 6th term.

Answer 23

but we want the 4th term...

Answer 24

you are correct about the 6th term, however I am unable to award extra credit :-)

Answer 25

I mean -1280x^3

Answer 26

Our answer is going to be
\[\binom{6}{3}a^{3}b^{6-3} = \frac{6!}{3!3!} (x)^3(-4)^3 = \frac{6*5*4*3*2*1}{3*2*1*3*2*1}x^3(-64) \]\[= 20(-64)x^3 = -1280x^3\]

Answer 27

Is the fourth trem

Answer 28

agreed.

Answer 29

Yep thank you. Got to go. Thank you so much.

Answer 30

you're welcome!