Answer:
Step-by-step explanation:
<u>Equation Solving</u>
We are given the equation:
![\displaystyle x=\sqrt[3]{\frac{3y+16}{2y+9}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3y%2B16%7D%7B2y%2B9%7D%7D)
i)
To make y as a subject, we need to isolate y, that is, leaving it alone in the left side of the equation, and an expression with no y's to the right side.
We have to make it in steps like follows.
Cube both sides:
![\displaystyle x^3=\left(\sqrt[3]{\frac{3y+16}{2y+9}}\right)^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E3%3D%5Cleft%28%5Csqrt%5B3%5D%7B%5Cfrac%7B3y%2B16%7D%7B2y%2B9%7D%7D%5Cright%29%5E3)
Simplify the radical with the cube:
Multiply by 2y+9
Simplify:
Operate the parentheses:
Subtract 3y and 
:
Factor y out of the left side:
Divide by 
:
ii) To find y when x=2, substitute:
Jayden ran 1/5 of his total distance in 1 minute. His total distance is 6/5 of a kilometer. He ran 6/25 of a kilometer in 1 minute or 3/5 of a lap.
Answer:
There is a whole range of speeds at which you are allowed to drive, not just one. In cases like this where there is more than one correct answer, we use inequalities, not equations, to represent the situation.
Inequalities are mathematical statements that define a range of values. They are easily recognizable because they contain the symbols <, ≤,>, or ≥.
By the converse of the Pythagorean Theorem, if 8.6 ^2 = 8.1 ^2 + 2.6 ^2 , then the triangle is right. 73.96 is not equal to 72.37 so the triangle is not a right triangle.
8.6^2 is greater than (8.1^2 + 2.6^2) which means that the triangle is obtuse.
The obtuse angle is opposite the 8.6 side.
Answer:
y = -2x + 1.
Step-by-step explanation:
2y = x - 1
y = 1/2y - 1/2
If line X is perpendicular to line Y (the line where y = 1/2y - 1/2), the slope will be the negative reciprocal of line Y. That means that there will be a negative sign instead of positive, and the 1/2 will be flipped to become 2/1, which is 2.
So, the slope will be -2.
We now have y = -2x + c.
To find c, simply put in -1 for x and 3 for y.
3 = -2 * -1 + c
c + 2 * 1 = 3
c + 2 = 3
c = 1
So, the equation of the line is y = -2x + 1.
Hope this helps!
