Answer:
x = 4
Step-by-step explanation:
Given
2(3x - 5) = 2x + 6 ( divide both sides by 2 )
3x - 5 = x + 3 ( subtract x from both sides )
2x - 5 = 3 ( add 5 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
Before we do any solving, we need to simplify both sides.
On the left, we can simplify -2x + 3x - 5 to x - 5.
On the right, we can simplify 6 - 21 to -16.
So we have x - 5 = -16.
Solving from here, we add 5 to both sides to get x = -11.
Answer: a) It will be a right triangle with a hypotenuse of 75 and a vertical leg that is 62.
b) The length of the kite string is 75 (given in the problem). However, I believe you are looking for the distance from the spot on the ground beneath the kite to Janet. That is about 42.2 m.
To find the missing distance in the right triangle. You have to use the Pythagorean Theorem. I set it up and solve it below.
a^2 + b^2 = c^2
x^2 + 62^2 = 75^2
x^2 + 3844 = 5625
x^2 = 1781
x = 42.2 (about)
Answer:
B (second table in list)
Step-by-step explanation:
The function is a quadratic with vertex and y-intercept at (0,-2). The parabola opens up meaning only y - values above -2 are a part of the function. Since range is the set of all y values, then the range is 
.
The domain is not restricted and it is all real numbers.
The inverse of the function is where x and y are switched. So the range becomes the domain and vice verse.
This means the domain of the inverse is 
and the range of the inverse is all real numbers.
