When you think of the situation as a whole, you may notice that the lines in the problem actually form a triangle. First, the man driving 10 miles east forms a bottom leg of the triangle 10 units long. When he drives the 2 miles north, he adds another leg of 2 units length. When the place of work is connected to the starting position through a line, a third and final line is drawn which creates the triangle.
So, how can we find the direct distance from his place of work to his home? We can use the Pythagorean Theorem (
, where
and
are the lengths of the legs of the triangle and
is the length of the hypotenuse). We know that the lengths of the legs are 10 and 2, which we can use in the formula, as shown below:

Now, we can solve this equation for
:


The distance would be √104 miles, or approximately 10.2 miles.
Answer:
(0, 33) : Yes
(4.8, 30.5) : Yes
Step-by-step explanation:
height of at least 24 ft : y >= 24
horizontal distance of no more than 10 ft. : 0 <= x <= 10
The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.:
y >= 3x and y <= 33
So Constraints:
24 <= y <= 33
y >= 3x
0 <= x <= 10
Now check to see if those coordinate points meet all the constraints
(0, 33) : Yes
(4.8, 30.5) : Yes
(9, 26) : No (because 26 is less than (3 * 9) = 27)
(4, 36)
: No (because 36 > 33, must be 24 <= y <= 33)
(2, 22): No (because 22 <24, must be 24 <= y <= 33)
Density

is given by

where m is the mass of the object
V is the Volume of the object
let m1 be the mass of the smaller cube
let m2 be the mass of the larger cube
you know that the larger cube has twice the mass of the smaller cube
or m2=2*m1
so apply this information into the density equation and you can determine the volume of the larger cube
Plug -8 in for x:
4(-8) + 5
solve:
-32 + 5
-27
Answer: The volume of container that holds 460 grams of oil is 500 cm³.
Step-by-step explanation:
Density of olive oil is 
An olive farmer wants to sell bottles that contain 460 grams of oil.
Therefore
Mass of oil = 460 grams
As we know

Hence, the volume of container that holds 460 grams of oil is 500 cm³.