The width of a rectangle is 4 less than twice its length. if the area of the rectangle is 153 cm2, what is the length of the diagonal? give your answer to 2 decimal places. if anyone could explain this i would appreciate it, all the answers i kept getting on similar questions were a few numbers off and i don't know why.

  diagonal ≈ 18.43 cm

Step-by-step explanation:

Let L represent the length of the rectangle. Then the width is ...

  w = 2L -4 . . . . . . 4 less than twice the length

The area is ...

  A = wL = (2L -4)L = 2L² -4L

The area is said to be 153 cm², so we have ...

  2L² -4L = 153

  2L² -4L -153 = 0 . . . . . . subtract 153 to put into standard form

We can find the solution to this using the quadratic formula. It tells us the solution to ax²+bx+c=0 is given by ...

  x = (-b±√(b²-4ac))/(2a)

We have a=2, b=-4, c=-153, so our solution for L is ...

  L = (-(-4) ±√((-4)²-4(2)(-153)))/(2(2)) = (4±√1240)/4

Only the positive solution is of interest, so L = 1+√77.5.

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Now we know the rectangle is 1+√77.5 long and -2+2√77.5 wide. The diagonal (d) is the hypotenuse of a right triangle with these leg lengths. Its measure can be found from ...

  d² = w² +L² = (-2+2√77.5)² +(1+√77.5)²

It can work well to simply evaluate this using a calculator, or it can be simplified first.

  d² = 4 -8√77.5 +4·77.5 + 1 +2√77.5 +77.5 = 392.5 -6√77.5

Taking the square root gives the diagonal length:

  d = √(392.5 -6√77.5) ≈ 18.43 . . . . cm

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!

answer: b)

step-by-step explanation:

its a dot plot because since the score is not high numbers.

- r3ktforgood ☕