The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)
Step-by-step explanation:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
- If the equation of a line is ax + by = k is dilated, with center origin and scale factor k, then the equation of the image of the line is kax + kby = kc
- The line and its image are parallel
- The coordinates of a general point on the image is (kx , ky)
Line L is mapped onto the line T by a dilation centered at the origin and a scale factor of 3.
That means lint T is the image of line L after dilation
∵ The equation of line L is 2x - y = 7
∵ Line L is dilated by scale factor 3 and centered at origin
- That means multiply the equation of line L by 3 to find the
equation of line t
∵ Line T is the image of line L after dilation
∴ The equation of line T is (3)(2x) - (3)(y) = (3)(7)
∴ The equation of line T is 6x - 3y = 21
<em>Very important note:</em>
The equation of line T is the same with equation of line L but multiplied by the scale factor 3 ⇒ L and T are coincide lines (same line)
That means the equation of lines T and L is 2x - y = 7
The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)
Learn more:
You can learn more about dilation in brainly.com/question/2480897
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Answer:
10 minutes
Step-by-step explanation:
First, find how much higher the airplane has to travel:
35,000 - 30,000
= 5,000
To fine how long it will take, divide 5000 by 500
5000/500
= 10
So, it will take 10 minutes to get above 35,000 feet
Answer:
Neither
Step-by-step explanation:
knowing that the system are y=-x+6 and y=x+2, then: x+2=-x+6; x+x=6-2; 2x=4; x=2, and replacing x in y we have: y=-2+6=4 and y=2+2=4, finally tha solution to sistem is (2,4)
Answer: On the 29th day
Step-by-step explanation:
According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.
On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.
The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are 
lilypads on the 30th, and 
lilypads on the 29th. This can be deduced multiplying succesively by 2.
Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π → C = π - (A + B)
→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))
→ sin C = sin (A + B) cos C = - cos(A + B)
Use the following Sum to Product Identity:
sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]
cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]
Use the following Double Angle Identity:
sin 2A = 2 sin A · cos A
<u>Proof LHS → RHS</u>
LHS: (sin 2A + sin 2B) + sin 2C
![\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D%5Cqquad%20%5Cqquad%20%5Cqquad%202%5Csin%20C%5Ccdot%20%5B%5Ccos%20%28A-B%29%2B%5Ccos%20%28A%2BB%29%5D)
LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C 
