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3 years ago

Which of the following represents the set of possible rational roots for the

Mathematics

1 answer:

Marat540 [252]3 years ago

7 0

Answer:

is there an option for no solution? because when I solved there were no possible rational solutions

Step-by-step explanation:

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Given y = log3(x + 4), what is the range?

lora16 [44]

Answer:

The range is all real numbers.

The domain is all reals numbers that are greater than -4.

Step-by-step explanation:

$y=\log_3(x+4)$ only exists when $x+4$ is positive.

You can take the log of a negative or 0 number.

So $x+4>0$ implies $x>-4$ . (I just subtract 4 on both sides.)

So the domain is x>-4. You should see this also when you graph the curve that the curve only exist to the right of -4.

Now the range. The range is where the curve exist for the y-values.

The equivalent exponent form of $y=\log_3(x+4)$ is $3^{y}=x+4$

We can solve this for x be subtract 4 on both sides:

$x=3^y-4$

Now here y can be anything; there are no restrictions on the exponent.

Also if you look at the graph of $y=\log_3(x+4)$ you should see every y getting hit by the curve (look down to up; use the y-axis as a guide).

Let's think about the inverse I found above a little more (I'm going to swap x and y).

$y=3^x-4$ .

If we look at the domain and range of this we can just swap it to get the domain and range of $y=\log_3(x+4)$ .

$y=3^x-4$ is an exponential function of 3^x that has been moved down 4 units.

The range since it has been moved down 4 units is $(-4,\infty)$ .

The domain of an exponential function is all real numbers. There are no restrictions on what you can plug in for x.

So swapping these to find the domain and range of $y=\log_3(x+4)$ :

Domain: $(-4,\infty)$

Range : $(-\infty,\infty)$

4 0

3 years ago

The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width The peri

seraphim [82]

Answer:

160 yards

Step-by-step explanation:

P=2l+2w

P=2(3w-8)+2(w)

432=2(3w-8)+2(w)

432=6w-16+2w

432=8w-16

432+16=8w

448=8w

w=448/8

w=56yards

l=3(56)-8

l=168-8=160yards

4 0

3 years ago

Prompt: Data plays a crucial role in decision-making because it can reveal relationships between different quantities. We can of

Marina86 [1]

Answer:

You can run Design of experiments to quicky collect data and fine tune an analyze you data and information. Run the experiment multiple times to confirm the data. This will help you with trend analysis.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Avery paid a $5.00 entrance fee to the carnival

Anna007 [38]

Let’s start off by subtracting 5 from 10 leaving 5 dollars

if 6 tickets cost 3 dollars she can only buy 6 tickets because she will only have 2 dollars left

3 0

3 years ago

Graph the set on the number line.

Ratling [72]

Here’s the answer w explanation :)

8 0

3 years ago