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3 years ago

Consider the equation |(x-3)^2-4|=b. Determine the value of b so that the equation has no solution.

Mathematics

2 answers:

oee [108]3 years ago

3 0

As an absolute value makes any value positive, any negative value of b will cause the equation to be unsolvable.

saul85 [17]3 years ago

3 0

<span>|(x-3)^2-4|=b since this is an absolute value equation

b can have any value less than zero so that the above is never true, in interval notation:

b=(-oo,0)</span>

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Solve:<br><br> a.x3+x2-8x - 12x+2<br> b. x3-4x2-3x + 18x-3<br> c. x2 + 4x + 4<br> d. x2 - 6x + 9

NeTakaya

<h2>Steps:</h2>

So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\div \frac{x-3}{x+2}$

Next, remember that <u>dividing by a number is the same as multiplying by its reciprocal.</u> To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\times \frac{x+2}{x-3}$

Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:

$(\frac{f}{g})(x)=\frac{x^2+2x-3x-6}{1}\times \frac{x+2}{x-3}$

Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

$(\frac{f}{g})(x)=\frac{x(x+2)-3(x+2)}{1}\times \frac{x+2}{x-3}$

Now you can rewrite it as:

$(\frac{f}{g})(x)=\frac{(x-3)(x+2)}{1}\times \frac{x+2}{x-3}$

Next, multiply:

$(\frac{f}{g})(x)=\frac{(x-3)(x+2)^2}{x-3}$

Next, divide:

$(\frac{f}{g})(x)=(x+2)^2$

And lastly, simplify:

A good tip: $(x+y)^2=x^2+2xy+y^2$

$(\frac{f}{g})(x)=x^2+4x+4$

<h2>Answer:</h2>

<u>The correct option is C. x² + 4x + 4.</u>

7 0

3 years ago

In a wildlife park, there were 18 gray wolves. After three years, there were 27 gray wolves. What is the percent gain?

natulia [17]

27-18=9 (difference between)
9/18=0.5 (9 as a percentage of original as a decimal)
0.5x100=50 (as a percentage)

50% increase

4 0

3 years ago

Read 2 more answers

Rafael has a bag of marbles, there are 5 green marbles, 6 red marbles, and 4

yulyashka [42]

The probability of getting red marble from the consider withdrawal of a marble is 0.107 approximately.

<h3>How to calculate the probability of an event?</h3>

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

$P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}$

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Given that:

The bag contains:

5 green marbles,
6 red marbles,

45 white marbles.
Rafael draws one marble at random

Since he draws one marbel, thus, only one colored marble would come out.

Let we suppose we've to find P(red marble coming out).

Then, if we take:

E = event of Rafael drawing a red marble,

then E can be done in 6 ways as there are 6 red marbles to choose from.

Also, withdrawal of 1 marble (of any color) can be done in (5+6+45 = 56) 56 ways.

Thus, we get:

$P(E) = P(\text{Choosing a red marble}) = \dfrac{6}{56} = \dfrac{3}{28} \approx 0.107$

Thus, the probability of getting red marble from the consider withdrawal of a marble is 0.107 approximately.

Learn more about probability here:

brainly.com/question/1210781

#SPJ1

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2 years ago

PERSONAL QUESTION: Guys I just bought myself a brand new cart and well I've been charging the dab for 5 hours and it was green b

valkas [14]

<h2>Please ask maths questions next time </h2>

8 0

3 years ago

For the equation y=5+6x, what does y equal when x is 4?

xxTIMURxx [149]

Answer:

y=31

Step-by-step explanation:

we know that x=4

5+6(4) = y

5+24 = 31

y= 31

Hoped this helped

4 0

3 years ago

Read 2 more answers