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If she has to buy stickers with a single digit on each sticker, then she will have to buy 35 stickers with digit 3 on them, because you have 35 "threes", including repeats such as 133 and 233, between 101 and 250.

Angle QSR = 44 degrees.

The monic quartic is x^4 - 4x^3 - x^2 + 5x - 4 = 0.

You have 10 numbers that are being separated into 3 distinct groups. You have to move the 3 groups, in their ordered way, in 3! =6 ways. It is basically the same as moving 3 digits around, such as 123. You would have 3! =6 ways of arranging them: 123, 132, 213, 231, 312, 321. Place the 5 numbers 1, 2, 3, 4, 5 where 1 is if the 6 arrangements of 123. Then place 6, 7, 8 where 2 is. And finally, place 9, 10 where 3 is. Basically, you will have something like this: [12345678910], [12345910678], [67891012345], [67812345910], [91012345678], [91067812345]. 

Completing the square: a very useful technique. 
 

Hmm..that sounds like a good book title

Anyways, we know that circles are in the form (x−a)^2 + (y−b)^2 = r^2, so how do we get there? By completing the square! (Wow, that rhymes...)

We need to deal with both the x and y.

X: 

We see that x^2 - 18x is a fraction of a square. To find the last bit, we divide -18 by 2: this gives us -9. So, we need to take away 81 from 120. This leaves us with: (x−9)^2 + (y−b)^2 + 39 = 0.

Y: 

Again, our incomplete square is y^2 - 14y. Divide by 2: -7. Subtract 49: leaves us with -10. Which makes our equation: (x−9)^2 + (y−7)^2 - 10 = 0.

(x−9)^2 + (y−7)^2 - 10 = 0

(x−9)^2 + (y−7)^2 = 10

Therefore, the radius is sqrt(10)

:)

The delivery person can bring up 8 boxes at a time.

f(f(f(17))) = -4.

Let the lower number be n. Then

5*(n + n+ 2) = n*(n + 2) - 10      10n + 10 = n^2 +2n -10

Rearrange  

n^2 - 8n - 20 = 0

This factors as (n + 2)*(n - 10) = 0

I'll let you take it from here.

Let the amount invested at 10%     =M
Then, the amount invested at 14% =5,000 - M

0.10M + 0.14[5,000 - M] =620
0.10M + 700 - 0.14M      =620
- 0.04M = 620 - 700 =- 80
M = - 80 / - 0.04

M =$2,000 invested at 10%
$5,000 - $2,000 =$3,000 invested at 14%

This is just a fancy way of saying: Find cos(arctan(3/4)).                                                                                                                           
                                                                                                                 1

Like most things in math, there is a formula for it: cos(arctan(x)) = -----------------                                                                                                                                                                 

                                                                                                         sqrt(1 + x^2)   

So...what do we do? Well, we plug in 3/4.

            1                            1                 4  

---------------------- = -------------- = ------ 

 sqrt(1 + (3/4)^2)              5/4               5

After simplification, we realize two things:

1. The answer is 4/5

2. Typing fractions by hand is hard

:)

Don't worry. When the problem has eyes, I always get nervous

(get it? Eyes, i's? Haha, dad joke made from a "never-will-be" dad)

oh haha i guess i just overthought the problem thanks! :)

It's as simple as 66 + 57. (123)

All you have to do is plug the values in.

4 - 2i - 2(3 + 2i)

4 - 2i - 6 - 4i

-2 - 6i

There! 3 steps, and you are done.

:)

There are three ways to do this.

Method 1: Use a graph

Find the equation of the line passing through the points (-2,5) and (3/2, 2).  Express the answer in standard form.

It isn't a minimum of the original cubic function, it is the point of steepest negative slope.  It is where the changing slope has a minimum. Try plotting the function for a range of x values, and then plot the slope over the same range of x values ( say, from x = -2 to 2)  to see.

Point K is on line segment JL. Given KL = 2x – 2, JL = 4x + 9, andJK = 5x + 2, determine the numerical length of JL.

A is th point (4, 1) and B is the point (10, 15). Find the equation of the perpendicular bisector of the line AB.

1 / J  +  1 / K = 1 / 3

J = 4   and    K = 12

J = 6   and    K = 6

J = 12 and    K = 4

K = 4 + 6 + 12 = 22

7440 / 8 =930 mph - Plane's speed against the wind

3570 / 3 =1,190 mph - Plane's speed with the wind.

[930 + 1,190] / 2 =1,060 mph - Plane's speed in still air.

[1,190 - 930 ] / 2 =130 mph - wind speed.

Hi! i hear your paper is due tomorrow. im sorry but can you learn your topic, instead of giving your homework to us or whatever this is. i trust its much more effective!

The closer two numbers are when added together, the greater their product. Here is what I mean. 
 

Let's "shrink" this question a bit by changing rectangle to two lines, and change 60 into 10. Okay. So how would we get the largest value? We can do some guess and checking...assuming that you don't know the rule yet.

Comparing 1, 9 and 5, 5, we see that 5 * 5 is larger. Get what I mean now?

The same thing applies to 4 sides, and...that's about it. (BUT if we were talking about numbers, then it would go past the skies)

The closest the number can get to each other is 15 by 15. Simple enough, right? 

Therfore, the maximum area is 15 * 15 = 225

:)

Thanks Jenny, just another bug in the system (not being able to give likes I mean)