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1 answer:
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Look at the picture.
We have the equation (1) 12x + 4y = 40.
We know, the sum of the acute angles in a right triangle is 90°.
Therefore we have the equation (2) (12x + 4y) + (17x - y) = 90
Substitute (1) to (2):
40 + 17x - y = 90 <em>subtract 40 from both sides</em>
17x - y = 50 (3)
We have the system of equations:
Substitute the value of x to (3)
Answer: x = 3 and y = 1.
Given:
The parent absolute function is
To find:
The new function if the parent function is translated up by 5 units and vertically stretched by a factor of 3.
Solution:
The translation is defined as
.... (1)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
Parent function is translated up by 5 units. So, b=5
It is vertically stretched by a factor of 3. So, k=3.
There is no horizontal shift. So, a=0.
Now, putting k=3, a=0 and b=5 in (1), we get
Therefore, the correct option is D.