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apply the Pythagorean Theorem 

I'm assuming that you mean "all real constants k"

First add the two equations together. 

\(4(x+y)=k(x+y)\). k = 4

Then subtract the two. 

\(-2(x-y)=k(x-y)\). k = -2.

So our two solutions are k = 4, -2

For this problem the "three-dimensional" Pythagorean Theorem states:

             x² + x² + x²  =  20²  

b) Hint: Find the possibilities by first finding the fraction then convert to a percent to compare.(same thingcfor (c))

If the equation is in vertex form:

1)  If the vertex is on the x-axis, there is one root (a double root)

2)  If the vertex is above the x-axis and the parabola rises, there are no real roots.

3)  If the vertex is above the x-axis and the parabola falls, there are two real roots.

4)  If the vertex is below the x-axis and the parabola rises, there are two real roots.

5)  If the vertex is below the x-axis and the parabola falls, there are no real roots.

a) 3 because the possibility to draw a 3 is 80% and 80%>20%

b) What is the expected value of the number shown if we add one additional 9 to the bag?

c) What is the expected value of the number shown if we add two additional 9's (instead of just one) to the bag?

Forgot the numbers sorry

If we use guess and check with positive numbers, it looks like the only pairs are (1, 7) and (7, 1).

thank you that was correct!!!!

Everything is 20$ off its original price, so each item is 80% of its original price. This $112 MP3 player is 80$ of its original cost.

\(\frac{80}{100}x=112\\ 80x=11200\\ x=140\)

Its original cost is $140. 30% off would leave 70% of $140$, which is

\(\frac{7}{10}\cdot140\\ =98\)

Therefore the MP3 player would be $98.

There aren't that many cases because of the \(a \le b \le c \le d\) restriction, so we don't have to worry about permutations. 

Using casework we find:

Case 1: 3 ones (36 as 1 factor)

1*1*1*36

Case 2: 2 ones (36 as 2 factors)

1*1*2*18

1*1*3*12

1*1*4*9

1*1*6*6

Case 3: 1 one (36 as 3 factors)

1*2*3*6

1*2*2*9

1*3*3*4

Case 4: 0 ones (36 as 4 factors)

2*2*3*3

Counting them up, we find that there are 9.

tHe hint guest gave i already knew  but it is a great start! 

Hint: Try to factoring out (t+1)

I think it's 45...

The largest is 15*16 = 240.

Since the question states thta x and y are positive integers, the smallest value is 1*30 = 30

No, you're not dumb!

So, the time elapsed from 9:40 am to 1:20 pm is 3 hours 40 minutes.

In 3 hours 40 min = 220 min, she drove 165 miles.

165 miles / 220 min = 33 miles / 44 minutes.

Try turning that fraction into x miles / 60 minutes!

that's not the only way... 

I need the full answer and solution

To find the volume of the water in the basement you multiply \(24 \space \text {ft} \times 32 \space \text {ft} \times 18 \space \text {in}\).

Then using the formula: \(\frac {24 \space \text {ft} \times 32 \space \text {ft} \times 18 \space \text {in}} {\frac{1}{8} \times 3}\) 

Figure out the rest yourself. 

There's:

1 * 2 * 3 * 6

How do I solve it?

do you get it from https://artofproblemsolving.com/class/2193-prealgebra2/alcumus ?

please fix your latex because i can not see your latex.