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3 years ago

Which properties of equality justify steps b and d?

Mathematics

1 answer:

Alik [6]3 years ago

6 0

<span>3. Subtraction Property of Equality; Multiplication Property of Equality
Subtracting seven from both sides is the justification for step b to get rid of the positive seven on both sides. Multiplying by 2 on both sides to get rid of the fraction on the left side of the equation is the justification for step d.
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What is the probability that all the roots of x2 + bx + c = 0 are real? [0,1]?

notsponge [240]

$x^2+bx+c$ will have real roots when the discriminant of the quadratic, $\Delta=b^2-4c$ , is non-negative, i.e.

$b^2-4c\ge0\implies b^2\ge4c$

Your question about probability is currently impossible to answer without knowing exactly what the experiment is. Are you picking $b,c$ at random from some interval? Is the choice of either distributed a certain way?

I'll assume the inclusion of "[0,1]" in your question is a suggestion that both $b,c$ are chosen indepently of one another from [0, 1]. Let $B,C$ denote the random variables that take on the values of $b,c$ , respectively. I'll assume $B,C$ are identical and follow the standard uniform distribution, i.e. they each have the same PDF and CDF as below:

$f_X(x)=\begin{cases}1&\text{for }0$

$F_X(x)=\begin{cases}0&\text{for }x$

where $X$ is either of $B,C$ .

Then the question is to find $P(B^2\ge4C)$ . We have

$P(B^2\ge4C)=P\left(C\le\dfrac{B^2}4\right)$

and we can condition the random variable $C$ on the event of $B=b$ by supposing

$P\left(C\le\dfrac{B^2}4\right)=P\left(\left(C\le\dfrac{B^2}4\right)\land(B=b)\right)=P\left(C\le\dfrac{B^2}4\mid B=b\right)\cdot P(B=b)$

then integrate over all possible values of $b$ .

$=\displaystyle\int_{-\infty}^\infty P\left(C\le\dfrac{b^2}4\right)f_B(b)\,\mathrm db$

$=\displaystyle\int_{-\infty}^\infty F_C\left(\dfrac{b^2}4\right)f_B(b)\,\mathrm db$

$=\displaystyle\int_0^1\dfrac{b^2}4\,\mathrm db=\frac1{12}$

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3 years ago

A photographer is arranging 3 puppies in a row for a photo. There is one black puppy (B), one tan puppy (T), and one white puppy

swat32

Btw, Twb, wtb, tbw, wbt,

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3 years ago

What number should be added to both sides of the equation to complete the square x^2+8x=4

Paraphin [41]

It would be half of the coefficient of x squared added to both sides:
So half of 8 ( the coefficient of 8x) is 4;
The number 4 squared is 16, so you would add that to both sides.

You do this so that you can easily factor the left side: x^2 + 8x + 16 = 4 + 16
(x + 4)(x+4) = 20

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4 years ago

Read 2 more answers

You invest $5000 in an account to save for college.

anyanavicka [17]

Answer:

5000 multiplied by 0.05 multiplied by 4

Step-by-step explanation:

you should get 1000. :D next you add 1000 to the orginal 5000 to get 6000!

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2 years ago

Anybody know the answer?

makvit [3.9K]

The first thing we need to do is take in all this information. We already know that the answer is between 0 and 7 because Line Segment AC is equal to 7. Second of all, it is recommended to solve this problem on paper to make it easier. You write the measurement under each individual Line Segment. Now we have to try to find a way how to subtract the Line Segments in order to get the measurement of Line Segment BC. If we were to write an equation. We would get mAB + mBC + mCD + mDE = mAE . We now try to think about the values that they give us to try to simplify it as much as possible. That's all that I can give you. I am sorry. This is a pretty tough and evil question.

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4 years ago