Classify the following lines as either parallel, intersecting, coincident, or skew. in each case find the measure of the acute angle between them?

The lines are parallel with an acute angle of 0 degrees.

Missing Information:

The equations of lines are missing which are as follows:

Line 1:

x = 1 - 2t , y = 8 + t, z = 5

Line 2:

x = 2 + 4s , y = -1 -2s, z = 3

Step-by-step explanation:

First, we need to find the direction vectors of both the line, we can write them as:

Direction Vector of line 1 == -2u + 1v + 0w

Direction Vector of line 2= =4u -2v+0w

As we can see,

=-2

such that:

4u -2v+0w= -2(-2u + 1v + 0w)

Since,

=-2

So the lines are parallel such that θ= 0 degrees. (Which is the acute angle between them)

All the points on line 1 have z-coordinate as 5 (z=5),

All the points on line 2 have z-coordinate as 3 (z=3),

Since the z-coordinate do not match , so the lines are not coincident.

Also as the lines are parallel so they are not intersecting.

third choice down

step-by-step explanation:

the first inequality is based on the number of adults and campers, and the second inequality is based on the cost of feeding both the adult and the camper.

we know that there is room for 525 people max.   it's ok to have less than 525, but it's not ok to have more than 525, so the inequality is less than or equal to.   the number combination of adults (x) and campers (y) cannot exceed this 525 max.   therefore:

x + y ≤ 525

now we talk about cost.   it costs $9 to feed one adult, so depending upon the number of adults you have (x) depends upon how much it will cost to feed that number of adults.   same with the campers, who cost $5 to feed.   the adults can be represented by 9x and the campers can be represented by 5y.   since the budget cannot exceed 1,200, the second inequality is:

9x + 5y ≤ 1200