Assuming the equation is 3x-2y+4=0 then the equation of the line, solving for y in terms of x, gives y=3/2x+2 the slope of this line is 3/2 then the slope of a line that is perpendicular is -2/3 .An easy way to see this is to draw the line. By definition the slope, m=tan(α) where α is the angle the line makes with the x axis. Let L=slope of the perpendicular line then L=tan(β) but the two lines with the x axis form a right triangle hence α+π-β=π/2 so β=π/2+α and L=tan(β)=tan(π/2+α)=-cot(α) = -1/tan(α)=-1/m.In our problem m=3/2 so L=-2/3.The geometry becomes clear if you make a sketch of the two lines. Hope this helps
Answer:
d = 13 and n = 52
Step-by-step explanation:
Number of dimes: d
Number of nickels: n
Then d + n = 65, and n = 4d
Substituting 4d for n in the first equation, we get:
d + 4d = 65, or 5d = 65. Then d = 13 and n = 52
Answer:
John paid $72
Step-by-step explanation:
To find the discount, we take the regular price and multiply it by the discount percentage
Discount = 90 * .2
= $18
The new price is the regular price minus the discount
New price = 90 -18
= $72
Answer:
15
Step-by-step explanation:
You want to find n such that ...
n×(2/3 mi) = 10 mi
Divide by 2/3 mi:
n = (10 mi)/(2/3 mi) = 10·3/2 = 15
You would have to bike the path 15 times to bike 10 miles.
Answer:
x ≤ -27
Step-by-step explanation:
-6(x + 7) ≥ 120
multiply -6 by x and by 7 so...
-6x - 42 ≥ 120
then you will add 42 to both sides...
-6x - 42 ≥ 120
+42 +42
-6x ≥ 162
then divide -6 by both sides (Hint: flip the sign since you are dividing a negative)
>>> x ≤ -27 <<<
