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3 years ago

Which number line represents the solution set for the inequality 1x24?

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

5 0

Answer:

answer b

Step-by-step explanation:

1. First solve the in equality as if it was an equallity.

-1/2x = 4

that is true for x = -8

By that knowledge alone, you can eleminate two of the four answers. The possible candidates for a good answer are now only answers b an d since the start with -8 on the number line.

2. Now carefully interpret the sign in the inequality. It says for what x values in -1/2x is the outcome BIGGER or equal then 4. From point 1 we established already that it is equal at x = -8 so try for one easy value of x.

With that I mean, substitute that easy value of x in the inequality and that will give you a true or false statement.

3. If the inequality results in a TRUE statement, then that will give you a deffinitive indication about which of the two remaining candidate answers is the right one, and you will have found your answer.

My choice for subsrituting an easy number is x = 0.

Just substitute x= 0 in -1/2x >= 4 and you get

( -1/2 * 0 ) >= 4

0>= 4

Because zero is NOT bigger then 4, the resulting statement is FALSE.

At this moment you know that the point x = 0 is NOT a member of the solution on the number line, which excludes solution d.

Now the only remaining solution is answer b which must be the right answer.

EXTRA

Although you have deduced beyond any certainty, that answer b must be the right answer, you still can check your findings 'to be sure' by substituting a number on the numberline of answer b.

BE CAREFUL, ONLY DO THIS IF YOU HAVE ENOUGH TIME. Again, you already know the right answer, and this is "just to confirm", so what is the harm in that?

By double checking yourself, it will sort of "undermine" your confidence in your chosen aproach. Basically you are doing something which is strictly not nessasary any more. So I urge you, to basically step over the urge to check yourself, and stick to your found answer.

However, if can not resit the temptation of checking, to see if you actually found the right answer, you could test for x = -10 and then you see:

( -1/2 * -10 ) >= 4

( 5 ) >= 4

Because five is BIGGER then 4 this is a true statement, which confirms that answer b is indeed the right answer.

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Which polynomial identity will prove that 49-4=45

goldfiish [28.3K]

Consider the polynomial identity (difference of squares):
(x+y)(x-y) = x² - y²

Set x =7 and y = 2 to obtain
(7+2)*(7-2) = 7² - 2²
9*5 = 49 - 4
45 = 49 - 4
This is the result required, obtained by using difference of squares.

Answer: Difference of squares.

3 0

3 years ago

What is the equation of the line?

spin [16.1K]

Answer:

y=1/2x+2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(0,2) and (-4,0).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (-4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m= 0 - 2-4 - 0 or... m= -2-4 or... m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,2). When x of the line is 0, y of the line must be 2.

(-4,0). When x of the line is -4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (-4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,2). y=mx+b or 2=1/2 × 0+b, or solving for b: b=2-(1/2)(0). b=2.

(-4,0). y=mx+b or 0=1/2 × -4+b, or solving for b: b=0-(1/2)(-4). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,2) and (-4,0)

y=1/2x+2

4 0

3 years ago

a number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and1. How ma

NeX [460]

Answer: