Step-by-step explanation:
the area of a rectangle is
length × width
in our case
length × width = 70 m²
length = 3×width - 11
we can use this second equation in the first and get
(3×width - 11) × width = 70
3×width² - 11×width - 70 = 0
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 3
b = -11
c = -70
x = (11 ± sqrt((-11)² - 4×3×-70))/(2×3) =
= (11 ± sqrt(121 + 840))/6 =
= (11 ± sqrt(961))/6
x1 = (11 + 31)/6 = 42/6 = 7
x2 = (11 - 31)/6 = -20/6 = -10/3
the negative solution is not applicable for a length in an object.
so, only x1 = 7 m is our solution.
the width of the rectangle is 7 m.
the length = 3×width - 11 = 3×7 - 11 = 21-11 = 10 m
Answer:
8.25
Step-by-step explanation:
(5x^2-21x-20)/(5x^2-16x-16)
((x-5)(5x+4))/((x-4)(5x+4))
(x-5)/(x-4)
x² - 3 x - 54 = x² + 6 x - 9 x - 54 = x ( x + 6 ) - 9 ( x + 6 ) = ( x + 6 ) ( x - 9 )
x² - 18 x + 81 = ( x - 9 )²
x² + 12 x + 36 = ( x + 6 )²
... = ( x + 6 ) · ( x - 9 ) / ( x - 9 )² * ( x + 6 )² / ( x + 6 ) = ( after cancellation )
= ( x + 6 )² / ( x - 9 )
After solving the given problem, I’ve been able to get 3(x-2) / 2(x-3) as the simplified form of the given equation. I am hoping that this answer has satisfied your query and it will be able to help you, and if you would like, feel free to ask another question.
If I understand clearly, the expression is
(18st^4/52s^3t)(16s^3/9s^2t)
To simply the expression, we simply have to multiply the constants and reduce the product to the lowest terms and apply the laws on exponents to simplify the variables. So, the answer would be:
8t^2/13s
(40v^2)/(35v^4) / (20v^3)/(5v)
(8)/(7v^2) / (4v^2/1)
(8)/(7v^2) * (1 / 4v^2)
2/(7v^4)
20/15 simplified is:
how many times does 15 go into 20? 1
and how many leftovers are there? 5
so its 1 5/15
and you can simplify even more by 5 so it turns to 1 1/3
hope it helps :)
Answer: x = 29
Step-by-step explanation: take the total angle, which is 93, and subtract 35. that way, we have the total angle for the space that we're trying to work with. then, just divide that by 2. so, we can see that x = 29.
