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Let the original price be x. With what we know, we can say:

0.85x = 34

We isolate the "x" by dividing by 0.85:

x = 34/0.85 = $40

We now need to check our work:

40 * 0.85 = 34.

And, we solved the problem in the matter of thirty seconds!

have a lovely discounted dress i got for you:

it's a russian one from the 1717...isn't history super sophisticated?

:)

Something is missing from your question, please check again.

Since the line is dotted, it can only be y < __x - __ or y > __x - __.

The slope is -3/2x and the intercept -2. The shaded area is below the line so the second answer is correct.

Let the distance to the Park = D
Let the time it took them to cycle to the Park = T
8T = D.............................(1)
D + 4 =7[T+1]..................(2), solve for D, T

T = 3 - hours - time it took them to get to the Park.
3 + 1 = 4 - hours - time it took them to return home.
3 + 4 = 7 - hours they spent cycling.

D = 24 - miles - distance to the Park.
24 + 4 = 28 miles - distance they cycled home.
24 + 28 =52 miles - total distance they cycled to the Park and back home.

S = (n - 2) * 180

n = S/180 + 2  

~~~~~~~~~~~~~~~~~~~~~~~~

If you are not sure what to do, use the real numbers:

S = (n -2) * 180                   S = 360       n = 4

360 = (4 - 2) * 180

4 = 360/180 + 2

4 = 4

Let the number of nickels = N

The number of quarters    =N + 7

0.05N + 0.25[N + 7] = 3.55

0.05N + 0.25N +  1.75 = 3.55

0.3N = 3.55 - 1.75

0.3N = 1.8

N = 1.8 / 0.3

N = 6 - number of nickels

6 + 7 = 13 - Number of quarters

Check: [6 x 0.05] + [ 13 x 0.25] =0.30 + 3.25 =$3.55

We can write -4 in exponential notation as 4e^(pi*i), so the equation is z^4 = 4e^(pi*i).

By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4).  Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i.  Then the other roots work out as

4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,

4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and

4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.

2 a - 10 = b
2 b - 10 = c
2 c - 10 = 0 for a, b, c

a =$8.75  What he started with.

b =$7.50  What he had left at the 2nd store

c =$5.00  What he had left at the 3rd store.

1500/100 = 15

The smallest "a" that I can think of is a = 757, so that:

2015 + 757 = 2772, which is also a palindrome.

The quadratic is 2x^2 - 12x + 16.

The correct roots of the quadratic are 2 and -7.

(x,y) = (4,-22).

Because z^4, your answers should read:

y = +or- sqrt(3), and

y = +or- 1

x is bigger than y        should be:  (9/5, 8/5) 

S = (n - 2) x 180

S/180 = n - 2

Its pretty obvious from here...

the latex is glitched.

the "less than" symbol does not show up..

the top part is if a is less than b

As you said, a=8/5 and b = 9/5. Then ab = 72/25.

Amy, Ben, Carl, and Debbie each have some coins. Ben has three times the number of coins that Amy has and a third of the number of coins that Carl has, and Debbie has two-thirds the number of coins that Carl has. The number of coins that Amy has, multiplied by the number of coins that Ben has, multiplied by the number of coins that Carl has, multiplied by the number of coins that Debbie has, is . How many coins do the four children have all together? 

So, this is an extremely long problem, and hence we must turn it into words. 

A = Amy

B = Ben

C= Carl

D= Debbie

B = 3A

3B = C

3D = 2C

ABCD = NOT STATED

A+B+C+D = x (we want x)

Please state what them all multiplied together is.

In square ABCD, point P is in the square, such that triangle CDP is equilateral.  What is angle CPB?   

I don't think it can be drawn to those description, BUT...

If angle CPB is an internal angle of an equilateral triangle, then it's 60^o no matter where the triangle is. 

_.

A little complex:

Area geometry:

So, we are given that the radius of the total area is 4, and the calculation for the total area = 4²π = 16π

Then we are also given that the side length of the square is 4 sqrt(2). The preffered area is 8

Hence, it will be (8)/(16π) = (1)/(2π) = 0.16

What is the range of possible sizes for side x?

Hello Guest!

\(x \in \{\mathbb{R}\ |0.8 < x < 16.8 \}\)

  !

I beg to differ.

I see where you have an error in your calculations. What I believe you may have done is you overlooked the fact that a negative number divided by a positive number carries a negative result. Aside from that, there is a slight error in your understanding of the inequality. 

-8>m does not mean that it is at most -8, as it is not less than OR equal to, but is rather only less than.

These small errors have caused me to believe your answer is wrong, but then again, I could be the wrong one.

1 million = 1,000,000

1.8=1.8

This means that 1.8 million is the same as 1.8*1,000,000.

Multiply it out: 1.8*1,000,000 = 1,800,000.