Sophie practices the piano 105 minutes in 1 week. If t represents the total time she practices for any number of days, d, write a proportional equation for t in terms of d that matches the context.

Step-by-step explanation:

You must first know that 1 week = 7days

If Sophie practices the piano 105 minutes in 1 week, this can be expressed as;

105 minutes = 7days

to calculate the total time t that she practices for any number of days, d, we will say;

t minutes = d days.

Solving both expression;

105 minutes = 7days

t minutes = d days.

Cross multiply;

7 * t = 105 * d

7t = 105d

Divide both sides by 7;

7t/7 = 105d/7

t = 15d

Hence a proportional equation for t in terms of d that matches the context is expressed as t = 15d

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

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option