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mylen [45]
2 years ago
7

For geometry:( will give brainist to the correct answer!!!

Mathematics
1 answer:
Pani-rosa [81]2 years ago
7 0

Answer:

y = ⅔x - 5

Step-by-step explanation:

The line that is parallel to 2x - 3y = 24, would have the same slope as the line, 2x - 3y = 24.

Rewrite;

2x - 3y = 24

-3y = -2x + 24

Divide both sides by -3

y = ⅔x - 8

Thus, the slope of 2x - 3y = 24 is ⅔.

Therefore the line that is parallel to 2x - 3y = 24, will have a slope (m) of ⅔.

Using point-slope form, we can generate an equation that passes through (-3, -7) and is parallel to 2x - 3y = 24.

Thus, substitute (a, b) = (-3, -7) and m = ⅔ into y - b = m(x - a)

Therefore:

y - (-7) = ⅔(x - (-3))

y + 7 = ⅔(x + 3)

Rewrite in slope-intercept form.

Multiply both sides by 3

3(y + 7) = 2(x + 3)

3y + 21 = 2x + 6

3y = 2x + 6 - 21

3y = 2x - 15

Divide both sides by 3

y = ⅔x - 5

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In 2000 the population of a country reached 1 ​billion, and in 2025 it is projected to be 1.2 billion. ​(a) Find values for C an
Mice21 [21]

Answer:

(a) The value of C is 1.

(b) In 2010, the population would be 1.07555 billions.

(c) In 2047, the population would be 1.4 billions.

Step-by-step explanation:

(a) Here, the given function that shows the population(in billions) of the country in year x,

P(x)=Ca^{x-2000}

So, the population in 2000,

P(2000)=Ca^{2000-2000}

=Ca^{0}

=C

According to the question,

P(2000)=1

\implies C=1

(b) Similarly,

The population in 2025,

P(2025)=Ca^{2025-2000}

=Ca^{25}

=a^{25}                    (∵ C = 1)

Again according to the question,

P(2025)=1.2

a^{25}=1.2

Taking ln both sides,

\ln a^{25}=\ln 1.2

25\ln a = \ln 1.2

\ln a = \frac{\ln 1.2}{25}\approx 0.00729

a=e^{0.00729}=1.00731

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P(x)=(1.00731)^{x-2000}     ...... (1)

The population in 2010,

P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555          

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(c) If population P(x) = 1.4 billion,

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1.4=(1.00731)^{x-2000}

\ln 1.4=(x-2000)\ln 1.00731

0.33647 = (x-2000)0.00728

0.33647 = 0.00728x-14.56682

0.33647 + 14.56682 = 0.00728x

14.90329 = 0.00728x

\implies x=\frac{14.90329}{0.00728}\approx 2047

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3 0
3 years ago
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bulgar [2K]

subtract 6.4 from 25 = 1.3c + 18.6

3 0
3 years ago
Help me with this I can’t figure it out
Stella [2.4K]

Answer:

y = 4x+6

The input is 11 when the output is 50

Step-by-step explanation:

We need to find the slope of this function using 2 points

(3,18) and (0,6) are two points

m = (y2-y1)/(x2-x1) is the formula for slope

  =(6-18)/(0-3)

  -12/-3

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We know the y intercept.  It is the value when x =0.  The y intercept is 6

We can use the slope intercept form of the equation

y = mx+b, where m is the slope and b is the y intercept.

y = 4x+6

We want to know the input when the output is 50 (or y=50)

50 = 4x+6

Subtract 6 from each side

50-6 = 4x+6-6

44 = 4x

Divide by 4

44/4 = 4x/4

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3 0
3 years ago
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Simplify 24 − (23 + 22).<br> HELP FAST
RSB [31]

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Step-by-step explanation:

23+22=45

45-24=21

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