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Natasha_Volkova [10]
3 years ago
6

I need to know the number of solutions and the descriminate value. I could figure it out if I had an equation for it. Any help?

I am offering a lot of points!

Mathematics
1 answer:
professor190 [17]3 years ago
3 0
The discriminant is the part of the quadratic formula under the radical, namely:



Two real and unequal roots. If is a perfect square, the roots are rational. Otherwise, they are irrational.
One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. The Fundamental Theorem of Algebra still holds because it allows counting roots up to the limits of their multiplicity.

A conjugate pair of complex roots of the form where is the imaginary number defined by

Terminology note: Rarely will you find a quadratic with purely imaginary roots. A quadratic that does not have real roots generally has complex number solutions which have a real part and an imaginary part. Hence, to say that a quadratic has "two different imaginary solutions" is almost always incorrect.

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Valentin [98]
13 factored out is 13x - 39 add 39 to both sides it equals 13x=78 and 78 divided by 13 is 6 the anwser is x=6
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2 years ago
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katovenus [111]

1. Let a and b be coefficients such that

\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}

Combining the fractions on the right gives

\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}

\implies 1 = (2a+b)x + 3a

\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23

so that

\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}

2. a. The given ODE is separable as

x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}

Using the result of part (1), integrating both sides gives

\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C

Given that y = 1 when x = 1, we find

\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)

so the particular solution to the ODE is

\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)

We can solve this explicitly for y :

\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)

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\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|

\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}

2. b. When x = 9, we get

y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}

8 0
2 years ago
State whether each situation has independent or paired​ (dependent) samples. a. A researcher wants to compare the hand–eye coord
Alex73 [517]

Answer:

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b. A researcher wants to know whether professors with tenure have fewer office hours than professors without tenure. She observes the number of office hours for professors with and without tenure. =  independent samples

Explanation:

Paired-samples t tests compare scores on two different variables but for the same group of cases; independent-samples t tests compare scores on the same variable but for two different groups of cases.

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3 years ago
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juin [17]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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