Find the equation of a line parallel to 4x-y=-3 that contains the point (-1,-2). Write the equation in slope-intercept form.
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Answer:
Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic.
According to Bleiler-Baxter & Pair [22], for a mathematician, a proof serves to convince or justify that a certain statement is true. But it also helps to increase the understanding of the result and the related concepts. That is why a proof also has the role of explanation.
There are many different ways to go about proving something, we'll discuss 3 methods: direct proof, proof by contradiction, proof by induction. We'll talk about what each of these proofs are, when and how they're used. Before diving in, we'll need to explain some terminology.
Although I will focus on proofs in mathematical education per the topic of the question, first and foremost proofs are so hard because they involve taking a hypothesis and attempting to prove or disprove it by finding a counterexample. There are many such hypotheses that have (had) serious monetary rewards available.
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference.
All mathematicians in the study considered proofs valuable for students because they offer students new methods, important concepts and exercise in logical reasoning needed in problem solving. The study shows that some mathematicians consider proving and problem solving almost as the same kind of activities.
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The roots of the given polynomials exist , and
.
For a quadratic equation of the form the solutions are
Therefore by using the formula we have
Let, a = 1, b = -16 and c = 54
Substitute the values in the above equation, and we get
simplifying the equation, we get
Therefore, the roots of the given polynomials are , and
.
To learn more about quadratic equations refer to:
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Answer:
1) x= 3i, x= - 3i
2) x= +i, x = - i
Step-by-step explanation:
1) x^2+9=0
(x+3i)(x-3i)=0
x= 3i, x=-3i
2) x^2-4=-11
x^2=-7
x= ±i
x= +i, x = - i
hope this helps!! :))