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3 years ago

How many real solutions does this system of equations have? xy = 9 y = 3x - 1

Mathematics

1 answer:

tekilochka [14]3 years ago

6 0

Answer:

two real, unequal roots

Step-by-step explanation:

y is definied as y = 3x - 1. Substitute 3x - 1 for y in xy = 9, obtaining:

x(3x - 1) = 9. Then:

3x^2 - x - 9 = 0. In this quadratic, the coefficients are a = 3, b = -1 and c = -9.

Calculating the discriminant b^2 - 4ac, we get (-1)^2 - 4(3)(-9), or 1 + 108, or 109. Because the discriminant is positive, we have two real, unequal roots.

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2 years ago

Sven got money for his birthday. He spent $12 of the money and now has $28 left. Write and solve an equation to find out how muc

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3 years ago

Read 2 more answers

What is the slope between these two points? (6,10) (8,3)

cricket20 [7]

Answer:

the slope of the two points is $-\frac{7}{2}$

Step-by-step explanation:

to find the slope of two points you have to subtract them (x1,y1), (x2,y2)

Steps:

$(X_1,Y_1) (X_2, Y_2)$

$\frac{3 - 10}{8 - 7} = -\frac{7}{2}$

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3 years ago

What is the length of the unknown side of the right triangle?

DerKrebs [107]

Answer:

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem

$a^2+b^2=c^2$

where a and b are the legs and c is the hypotenuse.

We know that the legs are 5 and 12. We also know the hypotenuse is x, or unknown.

Substitute 5 in for a, 12 for b, and x for c.

$5^2+12^2=x^2$

Evaluate the exponents.

5^2 is the same as 5*5, which is 25.

12^2 is the same as 12*12, which is 144.

$25+144=x^2$

Add 25 and 144

$169=x^2$

We are trying to find out what x is. In order to do this, we have to get x alone. Since x is being squared, take the square root of both sides. The exponent and square root will cancel, leaving x by itself.

$\sqrt{169} =\sqrt{x^2} \\\\\sqrt{169}=x\\13=x$