A videotape can record 2 hours on short play, 4 hours on long play, or 6 hours on extra long play. After recording 32 minutes on short play and 44 minutes on long play, how many minutes can it record on extra-long play

It can record 198 mintues on extra-long play

Step-by-step explanation:

The full battery(100%) of the videotape is:

2 hours(120 minutes) on short play

4 hours(240 minutes) on long play

6 hours(360 minutes) on extra long play.

32 minutes on short play

It used 32/120 = 0.2667 of the battery

44 minutes on long play

it used 44/240 = 0.1833 of the battery

Battery used:

0.2667 + 0.1833 = 0.45

Battery remaining

1 - 0.45 = 0.55

Out of 6 hours(360) on long play

0.55*360 = 198

It can record 198 mintues on extra-long play

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d