1. A city map is laid out on a coordinate plane. Elm Street is described by the line x + 2y = -6. Oak street intersects Elm Street at an right angle. Which of the following could be the equation for Oak Street?
a. 2x + y = 5
b. -2x + y = 3
c. x + 2y = 4
d. -x - 2y = 8
My answer: d?
2. Which expression is NOT equivalent to 3/x-1?
a. (3x + 6)/(x^2 + x - 2)
b. (3x - 3)/(x^2 - 2x + 1)
c. (3x + 3)/(x^2 - 1)
d. (3x - 3)/(x - 1)
My answer: d?
1. the slope of x+2y = -6 is -1/2
so we are looking for a line with slope +2
so anything starting with 2x-y = .... or -2x + y = ... will do.
looks like b) to me
2.
They all factor and simplify
a) 3(x+2)/((x+2)(x-1)) = 3/(x-1) , x ≠ -2
b) 3(x-1)/((x-1)(x-1)) = 3/(x-1) , x ≠ 1
c) 3(x+1)/((x+1)(x-1) = 3/(x-1) , x≠ -1
so far they are all equal
so if there is an answer it must be d)
d) 3(x-1)(x-1) = 3 , which is not the same as 3/(x-1)
you were right with d)
1. To determine the equation for Oak Street, we need to find a line that intersects Elm Street at a right angle.
The equation for Elm Street is x + 2y = -6. We can rearrange this equation to solve for y:
2y = -x - 6
y = (-x - 6)/2
y = -0.5x - 3
For two lines to be perpendicular, their slopes must be negative reciprocals of each other. The slope of Elm Street is -0.5.
Let's examine the options given:
a. 2x + y = 5
The slope of this line is -2, which is not the negative reciprocal of -0.5. So, this is not the equation for Oak Street.
b. -2x + y = 3
The slope of this line is 2, which is the negative reciprocal of -0.5. So, this could be the equation for Oak Street.
c. x + 2y = 4
The slope of this line is -0.5, which is the same as Elm Street. So, this is not the equation for Oak Street.
d. -x - 2y = 8
The slope of this line is -0.5, which is the same as Elm Street. So, this is not the equation for Oak Street.
Based on this analysis, the equation that could be for Oak Street is b. -2x + y = 3. Therefore, your answer of d is incorrect.
2. To determine which expression is not equivalent to 3/x - 1, we can simplify each expression and see if we get the same result.
The given expression is 3/x - 1.
Let's examine the options given:
a. (3x + 6)/(x^2 + x - 2)
To simplify this, divide both the numerator and denominator by 3:
(1 + 2/(x^2 + x - 2))
This is not equivalent to 3/x - 1, so it is a possible answer.
b. (3x - 3)/(x^2 - 2x + 1)
To simplify this, divide both the numerator and denominator by 3:
(x - 1)/(x - 1)^2
Simplifying further, we get 1/(x - 1)
This is equivalent to 3/x - 1, so it is not the correct answer.
c. (3x + 3)/(x^2 - 1)
To simplify this, divide both the numerator and denominator by 3:
(x + 1)/(x^2 - 1)
Using difference of squares, we get (x + 1)/((x - 1)(x + 1))
Canceling out (x + 1), we are left with 1/(x - 1)
This is equivalent to 3/x - 1, so it is not the correct answer.
d. (3x - 3)/(x - 1)
To simplify this, divide both the numerator and denominator by 3:
(x - 1)/(x - 1)
This simplifies to 1
This is not equivalent to 3/x - 1, so it is a possible answer.
Based on this analysis, the expression that is not equivalent to 3/x - 1 is d. (3x - 3)/(x - 1). Therefore, your answer is correct.