Answer:
Step-by-step explanation:
The ratio of the number of fiction books is 9:4
the difference between the number of fiction and nonfictionn is 245
so if the number of fiction books = 9x
then the number of nonfiction books = 4x
then difference = 9x-4x = 5x
the difference is given 245
then 5x= 245
x=
=49
number of fiction books =49×9=441
number of nonfiction books =49×4=196
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Answer:
The dimensions of the rectangle are 22cm of length and 15cm of width
Step-by-step explanation:
To solve this we first have to know the formula to calculate the area of a rectangle
a = area = 330 cm²
L = length =
w = width = L - 7cm
a = l * w
we replace with the known values
330 cm² = L * (l - 7cm)
330 cm² = L² - 7Lcm
0 = L² - 7Lcm - 330 cm²
when we have an equation like this we can use bhaskara
a = 1
b = -7Lcm
c = -330cm²
ax² + bx + c = 0
x = -b(±)√(b² - 4ac)/2a
we replace with the known values
L = -(-7cm)(±)√(7² - 4(1)(-330cm²)) / 2(1)
L = 7cm(±)√(49 + 1320cm²)) / 2
L = 7cm(±)√(1369cm²)) / 2
L1 = (7cm + 37cm) / 2
L1 = 44cm / 2 = 22cm
L2 = (7cm - 37cm) / 2
L2 = -30cm / 2 = -15cm
The positive represents the unknown with which we work (L) and the negative with which we do not work (W)
The dimensions of the rectangle are 22cm of length and 15cm of width
Answer:
are there any options? if not then i think it's 360 ( sorry if i'm wrong)
Answer:
- f^-1(x) = (3/8)(x +1) . . . . as written
- f^-1(x) = (x +5)/(3x -1) . . . with appropriate parentheses
Step-by-step explanation:
The inverse function can be found by solving for y:
x = f(y)
x = y + 5/3y -1 . . . . . . . . . . y +(5/3)y -1 . . . per order of operations
x+1 = 8/3y . . . . . . . . . . add 1
(3/8)(x +1) = y . . . . . . . . multiply by 3/8
f^-1(x) = (3/8)(x +1) . . . . . inverse of the function as written
_____
Perhaps you intend f(x) = (x+5)/(3x-1). The inverse is found the same way.
x = (y +5)/(3y -1)
x(3y -1) = y +5
3xy -x = y +5 . . . . . eliminate parentheses
3xy -y = x + 5 . . . . . add x-y
y(3x -1) = x +5 . . . . . factor out y
y = (x +5)/(3x -1) . . . divide by the coefficient of y
f^-1(x) = (x +5)/(3x -1) . . . . inverse of rational function
