Answer:
x = 20 cm
Step-by-step explanation:
The triangles given are similar triangles because they share the same angles. Because they are similar, their side lengths are in the same ratio, or proportion to one another. The left side of the larger triangle has a length of 121cm + 11cm = 132cm where the smaller triangle only has a length of 11 cm. We can put these lengths into a ratio:
Since the other side of the triangle would have to be in the same proportion, or ratio, we can set up the following proportion:
Use cross-multiplication: 5x + 20 = (10)(12) or 5x + 20 = 120
Subtract 20 from each side: 5x + 20 - 20 = 120 - 20 or 5x = 100
Divide and solve for 'x': 5x/5 = 100/5 or x = 20 cm
Solution:
The Preimage function is , F(x)=|x|
Consider a point (a,b) on the function, F(x)=|x|. it means
b=|a|-----(1) satisfies the function.
Now the function F(x)=|x| is vertically stretched by 5 units.It means
x=a , y= b+5
x=a, b=y-5
So, putting the value of a and b in equation (1).
y-5=|x|
y= |x| + 5 is vertical stretch of y= |x| by 5 units.
Answer:
Step-by-step explanation:
Substitute x=3 and y=-6 in the expression.
Evaluate.
Answer:
(x, y) ⇒ (2x, 2y)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Dilation is the increase or decrease in size of a figure. If a figure with point A(x, y) is dilated by a scale factor of k, the new location is at A'(kx, ky). If k > 1, it is an enlargement and if k < 1, it is a reduction.
Given that the inner circle has a radius of 1 r and the outer one has a radius of 2 r. To map the inner circle onto the outer circle, the inner circle would need to be enlarged. The scale factor is:
k = outer circle radius / inner circle radius = 2r / 1r = 2
A dilation with a scale factor of 2 would be needed to map the inner circle onto the outer circle.
That is:
(x, y) ⇒ (kx, ky)
