The local amusement park is a popular field trip destination. this year the senior class at high school a and the senior class of highscool b both planned trips there. the senior class at highschool a rented and filled 12 vans and 13 busses with 672 students. highschool b rented and filled 14 vans and 13 busses with 706 students. each van and bus carried the same number of students. how many students can a van carry? how many students can a bus carry?

A van can carry 17 students and a bus can carry 36 students.  

Step-by-step explanation:

To solve for two different variables, in this case 'v' = the number of vans and 'b' = the number of buses, we can set up a system of equations and use elimination to solve.  Our first equation would be 12v + 13b = 672 and our second equation would be 14v + 13b = 706.  In order to use elimination, I first need to multiply one of the equations by -1 in order to eliminate the 'b' variable.  If I multiply the entire first equation by -1, I get -12v - 13b = -672.  I then add the first and second equation together to get 2v =34, or v = 17.  Now that I know that number of vans, I can put 17 into my equation for 'v' and solve for 'b'.  12x17 + 13b = 672, 204 + 13b = 672 (subtract 204 from both sides), 13b = 468 (divide both sides by 13), b =36.

13

Step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

$5.41

step-by-step explanation:

$20 - $14.51 = $5.49.