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11111nata11111 [884]
3 years ago
6

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

Mathematics
1 answer:
Ratling [72]3 years ago
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!
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I need help with these three
Ludmilka [50]
A. The relationship of <7 and <8 are that they are vertical angles, and are congruent.

B. Since vertical angles are congruent, you can form an equation where the two measurements equal each other. 

C. 5y-29=3y+19       then plug y into your equation: 5*24-29=91
    2y=48                   and so: <7 = 180-91=89 (and since <8 is congruent)
    y=24                     <8 also equals 89

Your second problem: 
complementary are two angles that add up to 90 degrees.
<B=x, <A=2x
2x+x=90
3x=90
x=30       so: <B=30 degrees, <A=60 degrees

Your third problem:
1. Since A and B are parallel, angle 3x+7 and angle 4x+5 are same-sided exterior angles. That means that they both add up to 180 degrees. So if you should add the two and make it equal 180
2. 3x+7+4x+5=180
    7x+12=180
    7x=168
    x=24
3. <6 is a corresponding angle with angle 3x+7, meaning that they are congruent. So plug x into 3x+7: 3*24+7=79 and since <6 is congruent to 3x+7, <6=79 degrees
6 0
3 years ago
Read 2 more answers
How many 1/16 pound servings of chocolate are in a 1/2 pound chocolate bar
Keith_Richards [23]
1/2 = 8/16 . . . so there are (<u><em>8</em></u>) - 1/16 pounds servings of chocolate in a 1/2 pound chocolate bar
6 0
3 years ago
If there are 400 ounces in 25 pounds, how many ounces are in 8 pounds
ladessa [460]
The answer is:  " 128 oz. " . 
_________________________________________________________
There are:  " 128 oz. " (in " 8 lbs." ) .
_________________________________________________________
Explanation:
________________________________________________________
Set up a proportion;  as a fraction; as follows:
________________________________________________________

 400/ 25  = x / 8 ; 

in which:  "x" = the number of "ounces [oz.] there are in "8 lbs." ;
________________________________________________________
We shall solve for "x" , the answer to the problem:

Cross-factor multiply:

25x = (400) * 8 ; 

→ 25x = 3200 ; 

Divide each side of the equation by "25" ; to isolate "x" on one side of the equation; & to solve for "x" ; 

→ 25x / 25 = 3200 / 25 ; 

→  x = 128 .
_________________________________________________________
Answer:  " 128 oz. " . 
_________________________________________________________
There are:  " 128 oz. " (in " 8 lbs." ) .
_________________________________________________________

Note of interest:  " 16 oz. =  1 lb. " (exact conversion). 

So;  "8 lbs.  <span>=  ?</span>  oz. " ; 

→  " 8 lbs. * (16 oz/ 1 lb)  =   ( 8 * 16) oz.  =  128 oz. ;  →  which is our answer!
_________________________________________________________
3 0
2 years ago
Read 2 more answers
Question 4 (3 points)
katovenus [111]

Answer:

The vertical one is the y axis and the horizontal one is the x axis.

Step-by-step explanation:

3 0
3 years ago
The question is in the picture please help
ahrayia [7]

Answer:

Claim 2

Step-by-step explanation:

The Inscribed Angle Theorem* tells you ...

... ∠RPQ = 1/2·∠ROQ

The multiplication property of equality tells you that multiplying both sides of this equation by 2 does not change the equality relationship.

... 2·∠RPQ = ∠ROQ

The symmetric property of equality says you can rearrange this to ...

... ∠ROQ = 2·∠RPQ . . . . the measure of ∠ROQ is twice the measure of ∠RPQ

_____

* You can prove the Inscribed Angle Theorem by drawing diameter POX and considering the relationship of angles XOQ and OPQ. The same consideration should be applied to angles XOR and OPR. In each case, you find the former is twice the latter, so the sum of angles XOR and XOQ will be twice the sum of angles OPR and OPQ. That is, angle ROQ is twice angle RPQ.

You can get to the required relationship by considering the sum of angles in a triangle and the sum of linear angles. As a shortcut, you can use the fact that an external angle is the sum of opposite internal angles of a triangle. Of course, triangles OPQ and OPR are both isosceles.

4 0
3 years ago
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