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tensa zangetsu [6.8K]
2 years ago
15

Graph the set {x|x≤-5} on the number line. Then, write the set using interval notation.

Mathematics
1 answer:
GaryK [48]2 years ago
3 0

The interval notation that defines this set is: (-∞, -5]

And the graph can be seen below.

<h3 /><h3>How to graph the inequality?</h3>

Here we want to graph the inequality:

x ≤ -5

This refers to all the values of x equal or smaller than -5.

To graph this, we need to graph a closed circle at -5, and we need to draw an arrow that points to the left (values smaller than -5). The graph is the one that you can see below.

The interval notation that defines this set is: (-∞, -5]

The first end is open, and the second is closed (because of the symbol ≤).

If you want to learn more about inequalities:

brainly.com/question/18881247

#SPJ1

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Here

Step-by-step explanation:

Irrational exponents are non repeating or infinite decimals while rational exponents are rational numbers. The value of an irrational exponent when calculated is approximate in nature while the value of rational exponent is exact.

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Read 2 more answers
PLEASE HELP!!! BRAINLIEST TO CORRECT COMPLETE ANSWER!
notka56 [123]

Answer:

y=16x+1

Step-by-step explanation:

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

(1,17) and (2,33).

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, (1,17), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=17.

Also, let's call the second point you gave, (2,33), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=2 and y2=33.

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

m=  

33 - 17/  2 - 1

or...

m=  16/ 1

or...

m=16

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=16x+b

Now, what about b, the y-intercept?

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

(1,17). When x of the line is 1, y of the line must be 17.

(2,33). When x of the line is 2, y of the line must be 33.

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

Now, look at our line's equation so far: y=16x+b. b is what we want, the 16 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 (1,17) and (2,33).

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:

(1,17). y=mx+b or 17=16 × 1+b, or solving for b: b=17-(16)(1). b=1.

(2,33). y=mx+b or 33=16 × 2+b, or solving for b: b=33-(16)(2). b=1.

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

(1,17) and (2,33)  is   y=16x+1

4 0
2 years ago
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