Let
be the line given by the vector equation
.
First, we use the director vectors of the lines L1 and L2 to get the
vector equation of the plane containing them, which we denote by
. This is,

We observe that
. Therefore, the vector equation of
defines a plane and
is a normal vector to 
Finally, the vector equation for the wanted plane, which we denote by
, is
Thus, if
, then
and since
is parallel to
, then it is perpendicular to
.
A) Tonya bought 3 games at X price, so 3X would be total amount.
B) Tony's cost was 0.50 less than X, so x-0.50, he bought 4 games, so he spent 4(x-0.50).
C) Set those to equal to solve for x:
3x = 4(x-0.50)
D) Solve:
3x = 4(x-0.50)
Distribute:
3x = 4x - 2
Subtract 4x from both sides:
-X = -2
Multiply both sides by -1:
X = 2
E) Since X is the amount Tonya paid per game, Tony paid X - 0.50, so Tony paid 2 - 0.50 = $1.50 per game.
Check:
Tonya: 3x = 3(2) = $6 total
Tony: 4(x-0.50) = 4(2.00 - 0.50) = 4(1.50) = $6 total
Answer:
2.5 m
Step-by-step explanation:
Consider the ramp, the ground and the back of the lorry to form a right triangle where the ramp is the hypotenuse and the distance from the back of the lorry is the adjacent side, x
Using the cosine ratio in the right triangle
cos32° =
= 
Multiply both sides by 3
3 × cos32° = x, hence
x ≈2.5 m
Answer: SECOND OPTION
Step-by-step explanation:
You must find the ratio of the sides of the triangle, as following:

Therefore, the ratio of the areas is:

Now you must multiply the area of the larger triangle by the ratio obtained above, therefore, you have that the result is:
≈
Answer:
Step-by-step explanation:
The answer to this problem is C