Answer: The correct option is figure (1).
Explanation:
Reason for correct option:
The figure (1) shows the reflection across the side XY followed by reflection across the side YT.
When we reflect the triangle XYZ across the side XY we get the triangle XYT as shown in below figure.
After that we reflect the triangle XYT across the side YT and we get the triangle PYT.
Therefore, only figure 1 shows the triangle pairs can be mapped to each other using two reflections.
Reason for incorrect options:
The figure (2) shows the rotation of 180 degree along the point y.
The figure (3) shows the reflection across the side XY followed by the translation.
The figure (4) shows the reflection, followed by rotation , followed by translation.
Answer:
probability the student plays both instruments is [ ]
students who play both instruments = total students - flute players - piano players - students who play neither instruments
students who play both instruments
→ 31 - 4 - 14 - 7
→ 6 students play both instruments.
probability:
<h2>→Answer:
When we have a rational function like:
The domain will be the set of all real numbers, such that the denominator is different than zero.
So the first step is to find the values of x such that the denominator (x^2 + 3) is equal to zero.
Then we need to solve:
x^2 + 3 = 0
x^2 = -3
x = √(-3)
This is the square root of a negative number, then this is a complex number.
This means that there is no real number such that x^2 + 3 is equal to zero, then if x can only be a real number, we will never have the denominator equal to zero, so the domain will be the set of all real numbers.
D: x ∈ R.
b) we want to find two different numbers x such that:
r(x) = 1/4
Then we need to solve:
We can multiply both sides by (x^2 + 3)
Now we can multiply both sides by 4:
Now we only need to solve the quadratic equation:
x^2 + 3 - 4*x - 4 = 0
x^2 - 4*x - 1 = 0
We can use the Bhaskara's formula to solve this, remember that for an equation like:
a*x^2 + b*x + c = 0
the solutions are:
here we have:
a = 1
b = -4
c = -1
Then in this case the solutions are:
x = (4 + 4.47)/2 = 4.235
x = (4 - 4.47)/2 = -0.235