Answer: point F is at <u> 0.6 </u> on the number line
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Explanation:
The ratio 2:3 scales up to 2x:3x for some positive real number x.
This means the distance from D to F is 2x units, and the distance from F to E is 3x units. Combine those two smaller distances to get 2x+3x = 5x to represent the full distance from D to E.
D is at -3 and E is at 6. This is a distance of 9 units since |-3-6| = |-9| = 9
Set this equal to the 5x from earlier and solve
5x = 9
x = 9/5
x = 1.8
This leads to 2x = 2*1.8 = 3.6
Therefore, we'll move 3.6 units from -3 to -3+3.6 = 0.6 which is the location of point F on the number line.
Notice that from 0.6 to 6 is 5.4 units and that 3x = 3*1.8 = 5.4 matches up to help confirm the answer.
Answer:
The constant of proportionality is 2
The equation is y=2x
Step-by-step explanation:
The unit price or unit rate is $2
Let y represent the price of tomatoes, then the price of x tomatoes is
dollars.
This represents a direct variation.
This equation is of the form 
, where k=2 is the constant of proportionality.
The division ➗ ÷ sign will make the expression correct if you correct the question!
Area of a rectangle: 2(L+W)
length: 4+W
Area: 2(4+W) + 2W = 96
8+2W+2W = 96
8+4W = 96
4W = 88
W= 22cm
Calculate for length: 2L + 2(22) = 96
2L + 44 = 96
2L = 52
L = 26cm
• The length is 26cm and width is 22 cm.
Answer:
We have to prove
sin(α+β)-sin(α-β)=2 cos α sin β
We will take the left hand side to prove it equal to right hand side
So,
=sin(α+β)-sin(α-β) Eqn 1
We will use the following identities:
sin(α+β)=sin α cos β+cos α sin β
and
sin(α-β)=sin α cos β-cos α sin β
Putting the identities in eqn 1
=sin(α+β)-sin(α-β)
=[ sin α cos β+cos α sin β ]-[sin α cos β-cos α sin β ]
=sin α cos β+cos α sin β- sinα cos β+cos α sin β
sinα cosβ will be cancelled.
=cos α sin β+ cos α sin β
=2 cos α sin β
Hence,
sin(α+β)-sin(α-β)=2 cos α sin β
