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Komok [63]
3 years ago
10

WILL GIVE 5 STARS

Mathematics
1 answer:
k0ka [10]3 years ago
3 0

Answer:

Step-by-step explanation:

to know:

-to be paralel the lines have to have the same slope

-to be perpendicular the slope has to be negative invers of thhe other

-to be neither has to be none of the above two

equation to compare to is

y=mx+b where m is the slope

if your equation does not have this form make it have this form

2y=3x+1 so divide by 2

y=\frac{3}{2} x+1 so here the slope is \frac{3}{2}

4x+6y=14 so subtract 4x and then divide by 6 to isolate y

6y= -4x+14

y=\frac{-4}{6}  x + \frac{14}{6}  symplify

y=\frac{-2}{3} x + \frac{7}{3}  so the slope here is \frac{-2}{3}

So if you compare the slopes you can see that are negative reciprocal of eachother so the lines are perpendicular

and so on...

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The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increas
Mazyrski [523]

Answer:

The population in 40 years will be 1220.

Step-by-step explanation:

The population of a town grows at a rate proportional to the population present at time t.

This means that:

P(t) = P(0)e^{rt}

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The initial population of 500 increases by 25% in 10 years.

This means that P(0) = 500, P(10) = 1.25*500 = 625

We apply this to the equation and find t.

P(t) = P(0)e^{rt}

625 = 500e^{10r}

e^{10r} = \frac{625}{500}

e^{10r} = 1.25

Applying ln to both sides

\ln{e^{10r}} = \ln{1.25}

10r = \ln{1.25}

r = \frac{\ln{1.25}}{10}

r = 0.0223

So

P(t) = 500e^{0.0223t}

What will be the population in 40 years

This is P(40).

P(t) = 500e^{0.0223t}

P(40) = 500e^{0.0223*40} = 1220

The population in 40 years will be 1220.

7 0
3 years ago
What is 1/5 + 1/4 + 1/10
ivolga24 [154]

Answer:0.55

Step-by-step explanation:

1/5 + 1/4 + 1/10

add them all together

adds up to 0.55

8 0
3 years ago
Read 2 more answers
A sequence is shown.
marin [14]

Answer:

Step-by-step explanation:

The given sequence of numbers is increasing in geometric progression. The consecutive terms differ by a common ratio, r

Common ratio = 6/3 = 12/6 = 2

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 3

r = 2

The function, f(n), representing the nth term of the sequence is

f(n) = 3 × 2^(n - 1)

6 0
3 years ago
Which is a factor of 91 multiple choice 7 20 4 or 12
ki77a [65]

Answer:

7

Step-by-step explanation:

Recall that a factor is a number that can divide a number and return a whole number as the quotient.

In this case, 91 / 7 = 13

So 7 is a factor

4 0
3 years ago
What is the area of the parallelogram?
Fed [463]

Answer:80cm^2

Step-by-step explanation:

Area of a parallelogram=base×height

In the above diagram we were given a base of 16cm and height of 5cm

Therefore area of the parallelogram=16×5 which is equal to 80cm^2

8 0
3 years ago
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