Let n be an integer. What is the product of five times the integer added to to times the next consecutive integer?
1 answer:
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V1=(-2,4)=(x1,y1)→x1=-2, y1=4
V2=(4,0)=(x2,y2)→x2=4, y2=0
V3=(2,-3)=(x3,y3)→x3=2, y3=-3
V4=(x4,y4)→x4=?, y4=?
V1-V2
dx=x2-x1=4-(-2)=4+2→dx=6
dy=y2-y1=0-4→dy=-4
V4-V3
dx=x3-x4→6=2-x4
Solving for x4:
6=2-x4→6-2=2-x4-2→4=-x4→(-1)(4=-x4)→-4=x4→x4=-4
dy=y3-y4→-4=-3-y4
Solving for y4:
-4=-3-y4→-4+3=-3-y4+3→-1=-y4→(-1)(-1=-y4)→1=y4→y4=1
V4=(x4, y4)→V4=(-4, 1)
Answer: The coordinates of the fourth vertex are (-4,1)
V2=(4,0)=(x2,y2)→x2=4, y2=0
V3=(2,-3)=(x3,y3)→x3=2, y3=-3
V4=(x4,y4)→x4=?, y4=?
V1-V2
dx=x2-x1=4-(-2)=4+2→dx=6
dy=y2-y1=0-4→dy=-4
V4-V3
dx=x3-x4→6=2-x4
Solving for x4:
6=2-x4→6-2=2-x4-2→4=-x4→(-1)(4=-x4)→-4=x4→x4=-4
dy=y3-y4→-4=-3-y4
Solving for y4:
-4=-3-y4→-4+3=-3-y4+3→-1=-y4→(-1)(-1=-y4)→1=y4→y4=1
V4=(x4, y4)→V4=(-4, 1)
Answer: The coordinates of the fourth vertex are (-4,1)
Answer:
a. $18.36 for 3 pizzas : k = 6.12
b. $4.17 for 3 pounds of bananas . k = 1.39
c. $16.48 for 4 pounds of potatoes . k = 4.12
d. 2 cups of flour to make 24 cookie . k = 12
Step-by-step explanation:
PROPORTIONALITY:
Two quantities x and y are said to proportional to each other
if for x ∝ y , x = y k.
Here, k is called the PROPORTIONALITY CONSTANT.
⇒
Now, for the given quantities:
a. $18.36 for 3 pizzas [box]
Here,
So, the proportionality constant is 6.12.
b. $4.17 for 3 pounds of bananas [box]
Here,
So, the proportionality constant is 1.39.
c. $16.48 for 4 pounds of potatoes [box]
Here,
So, the proportionality constant is 4.12.
d. 2 cups of flour to make 24 cookies
Here,
So, the proportionality constant is 12.