Stephen currently has 300 songs on his phone. he downloads 25 additional sans per month. his sister stephanie has 200 songs on her phone and downloads 50 per month. how long will it take for steven and stephanie they have the same amount of sans on their phones? how many songs is this? who will have 1000 songs on their phone first?

Step-by-step explanation:

stephen : 300 + 25m

stephanie : 200 + 50m

when will they have the same amount when will they be equalso set them equal and solve for m, the number of months

300 + 25m = 200 + 50m

300 - 200 = 50m - 25m

100 = 25m

100/25 = m

4 = m < they will have the same amount in 4 months

how many songs is this...

300 + 25m                                          200 + 50m

300 + 25(4) =                                       200 + 50(4)

300 + 100 = 400 songs                       200 + 200 = 400 songs

they will both have 400 songs <===

who will have 1000 songs first ?

stephen :                                          stephanie :

300 + 25m = 1000                      200 + 50m = 1000

25m = 1000 - 300                       50m = 1000 - 200

25m = 700                                   50m = 800

m = 700/25                                  m = 800/50

m = 28 months                            m = 16 months

so stephanie will have 1000 songs first <===

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.

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step-by-step explanation: