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3 years ago

Solve the inequality and write down the solution in interval notation x(x-3)(x+1)<0

1 answer:

8 0

Since it's so nicely grouped, we can work with it! For the equation to equal 0, x=0, 3, or -1 (since x-3 and x+1 equal 0 when plugged in with 3 and -1 respectively). All we have to do is plug in numbers before, between, and after these numbers and apply it to the rest of them. Since -1 is the smallest number of the group, we can plug in a number below that (for this example, -5) and plug it in to get -8*-5*-4= something negative since it contains an odd number of negative numbers. Therefore, anything less than 1 is negative. For between -1 and 0, we get x=-0.5 equals -0.5*-3.5*0.5=something positive (since it has an even amount of negative numbers), proving that everything between -1 and 0 here is positive. For something between 0 and 3, we can plug 1 in to get 1*-2*2= something negative. Do you see a pattern here? It's negative, then positive, etc.. Therefore, if the number is greater than 3 it is positive. Reviewing a bit, we can see that (-inf, -1) is negative as well as (0,3), making the interval notation (-inf, -1) U (0, 3) since when you plug -1, 0, and 3 in it is 0, not less than 0!

You might be interested in

Evaluate: Four To The Third Power write the numerical answer only

Alja [10]

The answer is 4^3 and I believe that this is right

7 0

2 years ago

I don’t understand how to proof Cpctc or answer the questions

n200080 [17]

I think that first you need to understand what CPCTC is used for.

Let's start with the definition of congruent triangles.

Definition of congruent triangles
Two triangles are congruent if each side of one triangle is congruent to a corresponding side of the other triangle and each angle of one triangle is congruent to a corresponding angle of the other triangle.

A definition works two ways.
1) If you are told the sides and angles of one triangle are congruent to the corresponding sides and angle of a second triangle, then you can conclude the triangles are congruent.
2) If you are told the triangles are congruent, then you can conclude 6 statements of congruence, 3 for sides and 3 for angles.

Now let's see what CPCTC is and how it works.
CPCTC stands for "corresponding parts of congruent triangles are congruent."
The way it works is this. You can prove triangles congruent by knowing fewer that 6 statements of congruence. You can use ASA, SAS, AAS, SSS, etc. Once you prove two triangles congruent, then by the definition of congruent triangles, there are 6 congruent statements. That is where CPCTC comes in. Once you prove the triangles congruent, then you can conclude two corresponding sides or two corresponding angles are congruent by CPCTC. These two corresponding parts were not involved in proving the triangles congruent.

Problem 1.

Statements                                        Reasons
1. Seg. AD perp. seg. BC               1. Given
2. <ADB & <ADC are right angles     2. Def. of perp. lines
3. <ADB is congr. <ADC                 3. All right angles are congruent
4. Seg. BD is congr. seg CD           4. Given
5. Seg. AD is congr. seg. AD        5. Congruence of segments is reflexive
6. Tr. ABD is congr. tr. ACD           6. SAS
7. Seg. AB is congr. seg. AC        7. CPCTC

4 0

3 years ago

It would take Delia 3 hours longer to re tile their bathroom by herself than it would for kari to retile on her own. If they wor

max2010maxim [7]

Answer:

6hours

Step-by-step explanation:

From the given information:

Suppose it took Karl x hours to retile her bathroom,

Then it will take Della 3 hours longer i.e (3+x) hours

If Della and Karl work together or will take them 2 hours

The objective is to determine how long it will take Delia to retile the bathroom alone?

∴

$\dfrac{1}{x}+\dfrac{1}{3+x}= \dfrac{1}{2}$

$\dfrac{x+3+x}{x(3+x)}= \dfrac{1}{2}$

$\dfrac{2x+3}{3x+x^2}= \dfrac{1}{2}$

By cross multiplying, we have:

2(2x+3) = 3x+x²

4x + 6 = 3x + x²

3x + x² - 4x - 6

x² - x - 6 = 0

Using quadratic equation

x² -3x +2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x +2) (x - 3) = 0

x + 2 = 0 or x - 3 = 0

x = -2 or x = 3

Since we are concerned about the positive integer,

Then, Karl = x = 3 hours while Della which is (3+x) = 3+3 = 6hours

6 0

3 years ago

A line passes through the point (-4,7) and has a slope of 5/2.

hoa [83]

Answer:

(9,20)

Step-by-step explanation:

9 and 20 together... (9,20)

8 0

2 years ago

The number of employees for a certain company has been decreasing each year by 3%. If the company currently has 810 employees an

8090 [49]

Answer:

219 employees

Step-by-step explanation:

3% of decreasing rate of employees per year is calculated thus:

$3\% \: of \: 810 \: employees$

$= \frac{3}{100} \times 810$

$= 24.3 \: employees \: per \: year$

In 9 years,

$= 24.3 \times 9$

$= 218.7 = 219 \: employees$

Therefore, the number of employees for a certain company where decreasing rate of employees is 3% and continued to decrease for 9 years; and 810 employees are currently working is 219 employees. By implication, 810 + 219 = 1029 employees were working in the company 9 years ago.

6 0

3 years ago