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Drupady [299]
3 years ago
10

Use the discriminant to determine the nature of the roots of the following equation.

Mathematics
1 answer:
kvv77 [185]3 years ago
4 0

Discussion

The discriminate is b^2 - 4*a*c

The general equation for a quadratic is ax^2 + bx + c

In this equation's case

a = 1

b= -5

c = - 3

Solve

(-5)^2 - 4*(1)*(-3)

25 - (-12)

25 + 12

37

Note

Since the discriminate is > 0, the roots are real and different. The roots do exist and there are 2 of them.

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Which zero pair could be added to the function f(x)=x^2+12x+6 so that the function can be written in vertex form?
andrew11 [14]
<span>f(x) = x</span>² <span>+ 12x + 6  </span>→ y = x² + 12x + 6<span>

Let us convert the standard form into vertex form.

1) Complete the squares. Isolate x</span>² and x terms.
<span>y - 6 = x</span>² + 12x
<span>
2) Create the perfect square trinomial. Whatever number is added on one side must also be added on the other side. 

y - 6 + 36 = x</span>² + 12x + 36<span>
y + 30 = (x + 6)</span>²
<span>y = (x + 6)</span>² - 30  ← Vertex form
<span>
To check:

y = (x + 6) (x + 6) - 30
y = x</span>² + 6x + 6x + 36 - 30
<span>y = x</span>² + 12x + 6<span>

The zero that could be added to the given function is 36, -36</span>
4 0
3 years ago
Greatest common factor of 7 and 49
valina [46]

Answer:

7

Step-by-step explanation:

The greatest common factor or GCF of 7 and 49 is 7 because 7 is the highest number that can go into both numbers 7 and 49. No other number can go into those numbers except 7.

3 0
3 years ago
Asap help please on this question thanks
Rina8888 [55]
90-30=60 Hoped this helped
3 0
3 years ago
Please help me solve ​
IgorLugansk [536]
Here’s the answer
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3 0
3 years ago
Assume that different groups of couples use the XSORT method of gender selection and each couple gives birth to one baby. The XS
olganol [36]

Answer:

Mean and Standard deviation for the numbers of girls in groups of 36 births are 18 and 3 respectively.

Step-by-step explanation:

We are given that he X SORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.

Now consider a group consisting of 36 couples.

The above situation can be represented through binomial distribution;

P(X=r)=\binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x=0,1,2,3,.....

where, n = number of trials (samples) taken = 36 couples

            r = number of success

            p = probability of success which in our question is probability

                   of a girl, i.e.; p = 0.5

<em><u>Let X = Numbers of girls in groups of 36 births </u></em>

So, X ~ Binom(n = 36, p = 0.5)

Now, mean for the numbers of girls in groups of 36 births is given by;

         <u>Mean</u>, E(X) = n \times p = 36 \times 0.5 = 18

Also, standard deviation for the numbers of girls in groups of 36 births is given by;

        <u>Standard deviation</u>, S.D.(X) =  \sqrt{n\times p\times (1-p)}

                                                      =  \sqrt{36\times 0.5\times (1-0.5)}

                                                      =  3

3 0
3 years ago
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