Given the graph of y = 2x² is transformed into y = -2x² + 3.
For any function y = f(x), the transformation y' = -y = -f(x) reflects the graph across x-axis.
So it means that y = -2x² is the reflection of y = 2x² across the x-axis.
For any graph y = g(x), the transformation y' = y + k = g(x) + k shifts the graph 'k' units upward for all value of 'k' > 0.
So it means that y = -2x² + 3 is the shifted version of y = -2x² by '"3 units up".
Hence, option B and C are correct i.e. "reflection across x-axis" and "shift of 3 units up".
1) Since these triangles are congruent, then we can write out the following for congruent triangles have congruent sides:
2) Still based on that principle, we can plug v=2 into any of those formulas to get the measure of QS and TV. So let's pick the simpler one:
As we can see these segments are congruent.
Answer:
Step-by-step explanation:
We want to verify the identity:
Let us take the LHS and simplify to get the LHS.
Express everything in terms of the cosine and sine function.
Collect LCM
We simplify the RHS to get:
We rationalize to get:
We expand to get:
Factor negative one in the denominator:
Apply the Pythagoras Property to get:
Simplify to get:
Or
Divide both the numerator and denominator by sin x
This finally gives:
By definition of complement,
Pr[not P | G and T] = 1 - Pr[P | G and T]
and by definition of conditional probability,
Pr[not P | G and T] = 1 - Pr[P and G and T] / Pr[G and T]
Pr[not P | G and T] = 1 - (16/100) / (33/100)
Pr[not P | G and T] = 1 - 16/33
Pr[not P | G and T] = 17/33
Answer:
Valid
Step-by-step explanation:The term "valid" generally refers to a property of particular statements and deductive arguments. This term is used to describe an argument or proof that is logically correct. That is, its conclusion stems from its assumptions or premises.
A valid argument is one that the conclusion necessarily follows from the premises. That is, if the premises are true, the conclusion will also be true.
Suppose you are presented with two true premises. If you accept that both are true, then you will have to accept that the conclusion is also true, because there is no possibility that the conclusion is false in this case.