Answer:
The equation for the parallel line is: y = -4x - 20
The equation for the perpendicular line is: y = 1/4x + 11/2
Step-by-step explanation:
The given point is: (-6, 4)
The given equation is:
y = -4x + 8, note the slope m = -4.
A parallel line has the same slope. Use the point slope and substitute:
y - y1 = m(x - x1)
y - 4 = -4(x - (-6))
y - 4 = -4(x + 6)
y - 4 = -4x - 24
y = -4x - 20
Proof - find f(x) when x = -6:
f(x) = -4x - 20
f(-6) = -4(-6) - 20
f(-6) = 24 - 20 = 4, so the point is (-6, 4)
A perpendicular line has a slope that is negative and inverted so m = 1/4.
y - y1 = m(x - x1)
y - 4 = 1/4(x - (-6))
y - 4 = 1/4(x + 6)
y - 4 = 1/4x + 6/4
y - 4 = 1/4x + 3/2
y = 1/4x + 3/2 + 4
y = 1/4x + 3/2 + 8/2
y = 1/4x + 11/2
Proof - find f(x) when x = -6:
f(x) = 1/4x + 11/2
f(-6) = 1/4(-6) + 11/2
= -6/4 + 11/2
= -3/2 + 11/2
= 8/2 = 4, giving the point (-6, 4)
Answer:
14
Step-by-step explanation:
Let the original denominator be 2x.
The original numerator is x.
The original fraction is x/(2x).
The numerator is increased by 2, and the denominator is decreased by 2.
The new fraction is (x + 2)/(2x - 2).
The new fraction equals 3/4.
(x + 2)/(2x - 2) = 3/4
Cross multiply.
4(x + 2) = 3(2x - 2)
4x + 8 = 6x - 6
-2x = -14
x = 7
The original numerator was 7.
2x = 2(7) = 14
The original denominator was 14.
Take the 16 swimming caps and divide them by the s swimmers to get the expression 16/s.
Answer:
no
Step-by-step explanation:
We want to compare the pot holder hole dimension to the pot dimension. The hole diameter is the overall pot holder diameter less the wall thickness on either side:
hole diameter = (20 1/5) -2(1 2/7) = 20 -2(1) +1/5 -(2)(2/7)
= 18 +(1/5 -4/7) = 18 +(7 -20)/35 = 18 -13/35
= 17 22/35 . . . . cm
We want to compare this to 17 4/5. We can do that by using a common denominator for the fractions.
17 4/5 = 17 + (4/5)(7/7) = 17 28/35 . . . . cm
The pot has a diameter of 17 28/35 cm; the pot holder has a hole diameter of 17 22/35 cm, so <em>the hole is smaller than the pot</em>.
The pot will not fit into the plant pot holder.
_____
You can use your calculator to find the free space around the pot by computing ...
20 1/5 -2(1 2/7) -17 4/5 = free space = -6/35 . . . . cm
Negative space means the pot is larger than the hole.
