Answer:
a ≈ 21.8
Step-by-step explanation:
We require the third angle in the triangle
Subtract the sum of the 2 angles from 180
third angle = 180° - (75 + 31.8)° = 180° - 106.8° = 73.2°
Using the Sine rule, that is
=
( cross- multiply )
a × sin75° = 22 × sin73.2° ( divide both sides by sin75° )
a = ≈ 21.8 ( to the nearest tenth )
Answer: The scale factor of the dilation is 0.5.
Explanation:
It is given that ABCD is polygon which is reflected and dilated , then we get PQRS.
The vertices of ABCD are (2, 2), (6, 8), (12, 8), and (16, 2) respectively. The vertices of image PQRS are (11, 15),(9, 12), (6, 12), and (4, 15) respectively.
The reflection affects the coordinates but does not affect the length of the sides.
But when we talk about dilation it affects the length of sides according to the scale factor or a constant factor.
If a line segment AB is dilated by scale factor k then length of A'B' is k times length of AB.
.... (1)
So we have to find any side length of preimage and the side length of that side in image. it means we have to find AB and PQ.
Use distance formula to find the side length.
It is noticed that the size of side in preimage is and the size of same side in image is
.
Using equation (1), we get
Hence, the value of scale factor is 0.5.
Answer:
Step-by-step explanation:
The first equation is
The second equation is
When we graph these two equations, <em>they will meet at a point which represent the solution of the two equations</em>.
We can solve the two equations simultaneously to determine their point of intersection.
Let us substitute the second equation into the first equation to get;
Multiply through by 2 to get;
Group similar terms to obtain;
Simplify;
Divide both sides by 3;
Put into the second equation;
Therefore the graphs of the two functions intersect at (2,3)
See graph in attachment.
