Answer:
g(x) = 1: 0
g(-2) = -3
Step-by-step explanation:
Just by looking at the graph, at the origin, <em>x</em><em> </em>is 0 and g(x)<em> </em>is 1. Now, look at where <em>x</em><em> </em>is -2. Below that, you see where g(-2) is because -2 REPLACED <em>x</em><em>.</em>
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Answer:
(b) Both vertical and horizontal reflection
Step-by-step explanation:
The figure will be a horizontal reflection of itself about any vertical line through two of the smaller 6-pointed stars.
The figure will be a vertical reflection of itself about any horizontal line through two of the smaller 6-pointed stars.
the pattern has both vertical and horizontal reflection
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<em>Additional comment</em>
A pattern will have horizontal reflection if there exists a vertical line about which the pattern can be reflected to itself. That is, there exists one (or more) vertical lines of symmetry.
Similarly, the pattern will have vertical reflection if there is a horizontal line about which the pattern can be reflected to itself. Such a line is a horizontal line of symmetry.
Answer: 2 1/2’ more pink then yellow
Step-by-step explanation:
Similar triangles so AC:BC=AE:DE
15+6=21 = AE
15:12.5=21:?
to get from 15 to 12.5 you divide by 15 and times by 12.5 so do this the to the other side
21/15=1.4
1.4 x 12.5=17.5
So DE=17.5
Answer:
Ok, we have a system of equations:
6*x + 3*y = 6*x*y
2*x + 4*y = 5*x*y
First, we want to isolate one of the variables,
As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:
(6*x + 3*y)/(2*x + 4*y) = 6/5
now we isolate one off the variables:
6*x + 3*y = (6/5)*(2*x + 4*y) = (12/5)*x + (24/5)*y
x*(6 - 12/5) = y*(24/5 - 3)
x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y
Now we can replace it in the first equation:
6*x + 3*y = 6*x*y
6*(0.5*y) + 3*y = 6*(0.5*y)*y
3*y + 3*y = 3*y^2
3*y^2 - 6*y = 0
Now we can find the solutions of that quadratic equation as:
So we have two solutions
y = 0
y = 2.
Suppose that we select the solution y = 0
Then, using one of the equations we can find the value of x:
2*x + 4*0 = 5*x*0
2*x = 0
x = 0
(0, 0) is a solution
if we select the other solution, y = 2.
2*x + 4*2 = 5*x*2
2*x + 8 = 10*x
8 = (10 - 2)*x = 8x
x = 1.
(1, 2) is other solution
