Tracey is looking at two different travel agencies to plan her vacation. ABC Travel offers a plane ticket for $295 and a rental car for $39 per day. M & N Travel offers a plane ticket for $350 and a rental car for $33 per day. What is the minimum number of days that Shirley’s vacation should be for M & N Travel to have the better deal?

10 days.

Step-by-step explanation:

Let d represent number of days.

We have been given that ABC Travel offers a plane ticket for $295 and a rental car for $39 per day. The total cost of travelling x days using ABC travel company would be .  

We have been given that M and N Travel offers a plane ticket for $350 and a rental car for $33 per day. The total cost of travelling x days using M and N travel company would be .

To make M and N travel the better deal, we will set an inequality, where total cost of x days using ABC travels is greater than M and N travels as:

Since the closest integer to 9.1677 is 10, therefore, for a vacation of 10 days using M and N travels will be the better deal.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this