Answer:
4/5
Step-by-step explanation:
rise over run boi or gerl
Note that when two lines have slopes of m₁ and m₂, then
(i) If m₁ = m₂, then the lines are parallel.
(ii) If m₁*m₂ = -1, then the lines are perpendicular.
Let us evaluate the given lines.
a. y = 4x - 1 and 12x = 3y + 7
y = 4x - 1 => m₁ = 4
Write the second equation in standard form.
3y = 12x - 7
y = 4x - 7/3 => m₂ = 4.
m₁ = m₂.
Answer: PARALLEL
b. x - 7y = 10 and 2x + 14y = 21
In standard form,
7y = x - 10 or y = (1/7)x - 10/7 => m₁ = 1/7
14y = - 2x + 21 or y = -1/7 + 3/2 => m₂ = -1/7
m₁ ≠ m₂ and m₁*m₂ ≠ -1.
Answer: NEITHER
c. 5x + 6y = 18 and 18x - 15y = 36
In standard form,
6y = -5x + 18 or y = -(5/6)x + 3 => m₁ = -5/6
15y = 18x - 36 or y = (6/5)x - 12/5 => m₂ = 6/5
m₁*m₂ = -1
Answer: PERPENDICULAR
d. x =1 and y = 1
x = 1 => m₁ is undefined
y = 1 => m₂ = 0
m₁ ≠ m₂ and m₁*m₂ ≠ -1
Answer: NEITHER
Answer:
the solution of the equation is: ![(-\infty,-3)\cup (2,7)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C-3%29%5Ccup%20%282%2C7%29)
Step-by-step explanation:
we are given the expression as ![\frac{x^2+x-6}{x-7}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%2Bx-6%7D%7Bx-7%7D%3C0)
=![\frac{(x-2)(x+3)}{(x-7)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-2%29%28x%2B3%29%7D%7B%28x-7%29%7D%3C0)
we will use the number line rule for inequalities(first by making the coefficients of x positive then taking the roots on the number line and depending on the sign in the equation we start taking alternate signs and depending on the inequality take the desired region)
we get
.
19/3 is the greater one because when you simplify it, it becomes 6.333........