We have: x + y < 40 

=> \(x+y\le39\)

=> \(\left(x+y\right)^2\le1521\)

=> \(x^2+2xy+y^2\le1521\)

=> \(xy\le\dfrac{1521-x^2-y^2}{2}\)

The book has the number of page is: 

480 x 600 = 288000 (pages)

So it takes her the number of minutes is: 

288000 : 240 = 1200 (mins) = 20 (hrs)

Call the number of miles Peter rode on the first day is a

We have: 

The sum of five days Peter rode is:

a + ( a + 10 ) + ( a + 10 + 10 ) + ( a + 10 + 10 + 10 ) + ( a + 10 + 10 + 10 + 10 ) = 5a + 100 = 500 (miles)

=> 5a = 400 

=> a = 80 ( miles)

=> a + 10 + 10 + 10 + 10 = 120 ( miles) 

So he rode 120 miles on just the fifth day.

Call the length of a rectangular room is a

its width is b

We have:

\(\dfrac{a}{b}=\dfrac{5}{3}\Leftrightarrow\dfrac{a}{5}=\dfrac{b}{3}\)

Put \(\dfrac{a}{5}=\dfrac{b}{3}=k\left(k\in Z^+\right)\)

\(\Rightarrow\left\{{}\begin{matrix}a=5k\\b=3k\end{matrix}\right.\)

We also have:

( a + b ) x 2 = 48 (ft)

=> 5k + 3k = 24

=> 8k = 24

=> k = 3

\(\Rightarrow\left\{{}\begin{matrix}a=5.3=15\left(ft\right)\\b=3.3=9\left(ft\right)\end{matrix}\right.\)

So the room's area is: 15 x 9 = 135 (ft^2)

Call the length ò a side of the square is a 

According to the title, we have:

\(4a=a^2\)

\(\Leftrightarrow4=a\)(because a>0)

No, b just be: 2 - ( -8 ) = 10 and the product is -80, Oh :( 

Call two integers is a and b ( \(a,b\in Z\))

Because a and b have the same role, suppose a > b

So we have:

a - b = -18

a + b = 2 

=> a = ( -18 + 2) / 2 = -8

=> b = -8 -2 = -10

So their product is: -8 x (-10) = 80 

We have: 1000 = \(2^3.5^3\)\(=20.2.5^2⋮20\)

=> 1000 : 2 \(⋮\) 20

1000 : 5 \(⋮\) 20

1000 : 2 x 5 \(⋮\) 20

1000 : \(\left(2.5^2\right)⋮\) 20

So there are 5 factors of 1000 can be divided by 20 without a remainder.

Each day, all three plant produce the number of cars is:

100 + 80 + 70 = 250 (cars)

So, need the number of full days to produce 1600 cars is :

1600 : 250 = 6,2 days 

So need 7 full days to produce 1600 cars

When Simba left, the distance from Simba and Mary is 55 miles.

Simba travel faster than Mary the number of mph is:

65-55 = 10 (mph)

So the time Simba catches up to Mary is:

55 : 10 = 5,5 ( hours)

Or 14 : 30 from the beginning

Call three two-digit prime number is a, b and c.

Suppose: a < b < c

We have: \(\left\{{}\begin{matrix}c=43\\b-a=10\end{matrix}\right.\)

But a + b + c = 79 => a + b = 36.

=> b = ( 36 + 10 ) : 2 = 23 

=> a = 23 - 10 = 13 

=> a x b x c = 23 x 13 x 43 = 12857 

We have the recipe:

\(x_n=\left(n-1\right).d+x_1\)

with d = distance.

According to the recipe, we have:

\(x_{2011}=\left(2011-1\right).3+\left(-4\right)=2010.3-4=6026\)

\(\left\{{}\begin{matrix}2a+b=19\left(1\right)\\2c+d=37\left(2\right)\end{matrix}\right.\)

Put (1) + (2) we have:

\(2a+b+2c+d=56\)

\(\Rightarrow2a+2c=32\) (because b + d = 24 ) 

\(\Rightarrow a+c=16\)

So a + b + c + d = 24 + 16 = 40

We have: 

\(a+b=29\Rightarrow\left(a+b\right)^2=841\)

\(\Leftrightarrow a^2+2ab+b^2=841\)(1)

Other way:

\(ab=204\Rightarrow2ab=408\) (2)

Put (1)-(2) we have: 

\(a^2+b^2=841-408=431\)

For a = 15 and b = 6.

=> a # \(b=15.6+15^2+6^2=90+225+36=375\)

(a#b)@a = \(\dfrac{375}{3}\)- a = 125 - 15 = 110 

The name occurs 12 alphabet letter.

The alphabet has 26 alphabet letter.

The probability is: \(\dfrac{12}{26}=\dfrac{6}{13}\)

Problem: A and B have 88 marbles, B has 23 marbles. How many marbles does A have?

Solution: A has the number of marbles is: 88 - 23 = 65 ( marbles)

Answer: 65 marbles 

Oh, no, the last unit must be miles, not gallons, oh sr ^^

If we want the UAV to arrive back home with a fuel reserve of 0,5 hour, the gallons must be left is 3 x 0,5 = 1,5 (gallons)

The gallons have it burns is: 45 - 1,5 = 43,5 (gallons)

The length that location X be is: 43,5 : 2 x 160 = 3480 (gallons)

When flying in the area for 1h, it burns 3 gallons. So it has left: 42 gallons

If you want to have the greatest number of miles away from the UAV's launching point can location X then it must burns the maximum gallons.

Specifically, it burns 2y gallons from its lauching point to X and flies back.

Max 2y = 42 => y = 21 ( gallons)

So the greatest number of miles away from the UAV's launching point can location X be: 21 x 160 = 3360 (miles)