Answer:
The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis. ⇒ False
The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis. ⇒ False
Step-by-step explanation:
<em>Let us explain the reflection about the axes</em>
- If a graph is reflected about the x-axis, then the y-coordinates of all points on it will opposite in sign
Ex: if a point (2, -3) is on the graph of f(x), and f(x) is reflected about the x-axis, then the point will change to (2, 3)
- That means reflection about the x-axis change the sign of y
- y = f(x) → reflection about x-axis → y = -f(x)
- If a graph is reflected about the y-axis, then the x-coordinates of all points on it will opposite in sign
Ex: if a point (-2, -5) is on the graph of f(x), and f(x) is reflected about the y-axis, then the point will change to (2, -5)
- That means reflection about the y-axis change the sign of x
- y = f(x) → reflection about y-axis → y = f(-x)
<em>Now let us answer our question</em>
The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis.
It is False because reflection about x-axis change sign of y
The graph of y = -f(x) is a reflection of the graph of y = f(x) in the x-axis
The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis.
It is False because reflection about y-axis change sign of x
The graph of y = f(-x) is a reflection of the graph of y = f(x) in the y-axis
SOLUTION
Let us use a simple diagram to interprete the question
In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.
So we will use the right-angled triangle formed to find h
As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA
So we have
Hence the answer is 104.9 feet to the nearest tenth
The perimeter of the triangle, namely the sum of all its 3 sides, is 110.
now, the three sides are in a 6:7:9 ratio, namely, if we divide 110 by (6+7+9), it will give us hmmm 110/22, a quotient of 22 equal pieces, namely how many times 22 would go into 110.
now, the small side, takes 6 of those pieces, the medium side takes 7 of them and the largest takes 9 of those pieces.
110/22 = 5
the small side is then 6(5).
the medium side is 7(5).
and the largest side is 9(5).
add them up, and you'd get the perimeter, 110 inches.
(4x - 8) = 80/2
4x - 8 = 40
4x = 48
x = 12
answer
x = 12
Answer:
-4
Step-by-step explanation:
3x-2(6-x)=7x+2(5+x)-6
First, distribute.
3x+ −12+ 2x = 7x + 10 + 2x −6
Combine like terms on each side.
5x − 12= 9x + 4
To solve for x, pick a side to solve. I will solve the right x.
5x - 12 = 9x + 4
-5x -5x
-12 = 4x + 4
Subtract 4 to isolate the variable.
-16 = 4x
Divide 4.
-4 = x
