Tara has ridden her bike .5 miles and rides 10 miles per hour. Felipe has
ridden his bike .25 miles and rides 15
miles per hour. For what number of
hours will-Tara have ridden less miles
than Felipe?

0.5 hours

Step-by-step explanation:

Given that Tara has covered 0.50 miles and  rides with a speed of 10 miles/hour. Felipe has  covered bike 0.25 miles and rides with a speed of 15  miles/hour.

Tara has covered more distance while the speed of Felipe is more than the speed of Tara.

Assuming that in time t hour, Felipe reaches Tara, then Tara left behind as Felipe has faster speed.

So, after t hour, Felipe will be ahead of Tara and Tara will cover lesser miles than Felipe .

As distance = speed x time, so

So, the distance covered by Tara in hour = 10t miles and she already has covered 0.5 miles, so total distance covered by Tara miles.

Similarly, the distance covered by Felipe in hour = 15t miles and he already has covered 0.25 miles, so the total distance covered by Tara miles.

Therefore, at the time then Felipe reached Tara, both have covered the same distance, i.e

hour

Hence, after 0.5 hours Tara will cover lesser miles than Felipe .

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

step-by-step explanation:

10.50 + taxes which added up to 11.50