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3 years ago

WILL MARK BRANLIEST AND THANK! 10 POINTS, EASY QUESTION!!

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

4 0

Answer: 2±√3 and 1/(2±√3)

This might seem wrong, but you'll understand when you read the explanation.

Step-by-step explanation:

For this problem, you can write 2 equations to find the two numbers. Let's establish x for the first number and y for the second number.

Equation 1:

x+y=4

This equation comes from the problem that says the 2 numbers add up to 4.

Equation 2:

x*y=1

This equation comes from the part that says multiplies to 1.

Even if the problem states that the numbers can be negative, it is tricking us. We know in order for the product of 2 numbers to be positive, it has to be +*+ or -*-. Since the added numbers have to be +4, we know we cannot use -1 and 1 as our answer. What we can do is to use substitution to solve for x and y.

x+y=4 becomes y=4-x

We can substitute this into equation 2.

x(4-x)=1

4x-x²=1

4x-x²-1=0

-x²+4x-1=0

Since this equation is not factorable, we use the quadratic equation, $\frac{-b±\sqrt{b^2-4ac} }{2a}$ (Please ignore the weird looking A that's in front of the ± sign. I don't know what's wrong with the system, but it's not supposed to be there)

We plug our a, b, c into the equation and get x=2±√3.

Now that we know our x, we can plug it into any of the above equations.

(2±√3)(y)=1

y=1/(2±√3)

Our final 2 numbers are 2±√3 and 1/(2±√3)

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3 years ago

Consider Statement A and Statement B below:

wlad13 [49]

Answer:

These two statements are equivalent because statement A is the contrapositive of statement B.

Step-by-step explanation:

In logic, when we have an "if" statement we can have its contrapositive or its converse.

Given a "if p, then q" (p is the hypothesis and q is the conclusion), the converse is "if q, then p", in other words, we interchange the hypothesis and the conclusion.

Now, given a "if p, then q", the contrapositive is "if not q, then not p". In other words, we take the negation of both the hypothesis and the conclusion and then we interchange them.

Now, let's take a look at our statements:

If a and b are two real numbers, and if ab = 0, then either a = 0 or b = 0.

In this case:

p = a and b are two real numbers and ab=0

q = either a = 0 or b = 0

Now, let's take the negative of p and q:

The negative of p would be: a and b are two real numbers and their product is not zero.

The negative of q would be: neither of the two real numbers is zero

Now, given than the contrapositive is "if not q, then not p" we would have:

If neither of two real numbers is zero, then their product is not zero.

We can see that this last sentence is the contrapositive of the first one and thus:

These two statements are equivalent because statement A is the contrapositive of statement B.