Set the whole expression = to 0 and solve for x.
3x^(5/3) - 4x^(7/3) = 0. Factor out x^(5/3): x^(5/3) [3 - 4x^(2/3)] = 0
Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.
In the latter case, 4x^(2/3) = 3.
To solve this: mult. both sides by x^(-2/3). Then we have
4x^(2/3)x^(-2/3) = 3x^(-2/3), or 4 = 3x^(-2/3). It'd be easier to work with this if we rewrote it as
4 3
--- = --------------------
1 x^(+2/3)
Then
4
--- = x^(-2/3). Then, x^(2/3) = (3/4), and x = (3/4)^(3/2). According to my 3 calculator, that comes out to x = 0.65 (approx.)
Check this result! subst. 0.65 for x in the given equation. Is the equation then true?
My method here was a bit roundabout, and longer than it should have been. Can you think of a more elegant (and shorter) solution?
Answer:
112 in^2
Step-by-step explanation:
10 x 10 = 100
4 x 6 / 2 = 12
112 inches squared
Answer:
Step-by-step explanation:
The student currently has $50 and plans to save $15 every month.
Let x represent the number of months that the student will save enough money to buy the microscope.
Let y represent the amount that the student saves after x months.
The function that represents the amount y (in dollars) of money that the student saves after x months will be
y = 50 + 15x
The 50 remains constant because she has already saved it
False because to find a reciprocal u gotta divide that number by one (example: 1 divided by 8 is 1/8) there you go , so therefore the answer is false. :)
Q1. The answer is 4(2x - 3)(2x + 1)
16x² – 16x – 12 = 4 * 4x² - 4 * 4x - 4 * 3 =
= 4(4x² - 4x - 3) =
= 4(4x² + 2x - 6x - 3) =
= 4(2x * 2x + 2x - (2x * 3 + 3)) =
= 4(2x(2x + 1) - (3(2x + 1))) =
= 4((2x + 1)(2x - 3)) =
= 4(2x - 3)(2x + 1)
Q2. The answer is 3(x + 8)(x - 1)
3x² + 21x – 24 = 3 * x² + 3 * 7x - 3 * 8 =
= 3(x² + 7x - 8) =
= 3(x *x - x + 8x - 8) =
= 3((x(x - 1) + 8(x - 1)) =
= 3(x + 8)(x - 1)
