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3 years ago

Are the lines below parallel, perpendicular, or neither?

Mathematics

2 answers:

I am Lyosha [343]3 years ago

8 0

Answer:

Neither

Step-by-step explanation:

<u>Given lines</u>

2y=3x-4 ⇒ y = 3/2x - 4
y= 2/3x - 3

The lines have different slope so they intersect but they are not perpendicular as perpendicular lines have negative reciprocal slopes

So the answer choice is neither

levacccp [35]3 years ago

5 0

Answer:

<h2>Neither </h2><h2></h2>

2y = 3x - 4

y = 2/3x - 3

Step-by-step explanation:

Parallel means the lines never cross. These two lines cross. Perpendicular means they cross and form a 90° angle.

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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

In 2012, the population of a city was 6.38million. The exponential growth rate was 2.38% per year.

Aleksandr-060686 [28]

The exponential growth function is P(t) = 6.38 million x (1.0238^t).

The population of the city in 2018 is 7.35 million.

The year the population would be 9 million is 14.46 years.

The doubling time is 29.12 years.

<h3>What is the exponential growth function?</h3>

FV = P (1 + r)^n

FV = Future population
P = Present population
R = rate of growth
N = number of years

6.38 million x (1.0238^t)

Population in 2018 = 6.38 million x (1.0238^6) = 7.35 million

Number of years when population would be 9 million : (In FV / PV) / r

(In 9 / 6.38) / 0.0238 = 14.46 years

Doubling time = In 2 / 0.0238 = 29.12 years

To learn more about exponential functions, please check: brainly.com/question/18760477

#SPJ1

5 0

2 years ago

Which is the height of the triangle 12 times 27

kykrilka [37]

<span> 4.24 height is the answer</span>

3 0

4 years ago

Please help! 20 PTS!<br> v<br> the picture down below l

telo118 [61]

Step-by-step explanation:

the answer is in the pic

hope it helps

4 0

2 years ago

Read 2 more answers

The sunrise café gets tea bags of 1,000. If the café charges $1.75 for each cup of tea, and each cup of tea gets 1 tea bag, how

Setler [38]

Answer:

You would do $1.75 x 1,000. That would be 1$,750. Then, you would take away that $95 because they spent buying the box of tea bags, and their total would be $1,750 - $95 = $1,655.

5 0

3 years ago