Answer:
x = 10, y = 20
Step-by-step explanation:
Because two sides of the rightmost triangle are congruent, the base angles would follow suit. This means 5x - 10 = 3x + 10. Simplifying this we get:
2x = 20
x = 10
Next, in the other triangle, we can say the same thing, the base angles would be congruent. From this we can say that the other base angle is 4y. Using the exterior angle theorem, we can say that the two angles with x terms add to 4y. This means 3x + 10 + 5x - 10 is 4y. We already know x is 10, so substituting that in we get:
80 = 4y
y = 20
Answer:
0.3429 is a decimal and 34.29/100 or 34.29% is the percentage for 12/35.
Answer:
b = 6 or b = -6 (non-zero vectors)
b = 0 (zero vector)
Step-by-step explanation:
Two vectors 
and 
are orthogonal if their dot product is equal to 0, or in other words
In your case,
Hence, if vectors a and b are orthogonal, then
Note, then if b = 0, then 
and zero-vector is orthogonal to any other vectors.
Thus, b = 6 or b = -6.
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
