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3 years ago

Write the equation of the line that passes through the given points.

Mathematics

1 answer:

ozzi3 years ago

6 0

Answer:

Step-by-step explanation:

Going from (15/8,0) to (17/8,1/2), we see that x (the 'run') increases by 2/8, or 1/4, and that y (the 'rise') increases by 1/2. Thus, the slope of this line through the given points is m = rise / run = (1/2) / (1/4) = 2.

Using the point-slope formula for the equation of a line, we obtain:

y - 0 = 2(x - 15/8), or

y = 2(x - 15/8) (simplest form), or

8y = 2x - 15/4, or

2x - 8y = 15/4, or

8x - 32y = 15

All of these are correct; they are 'equivalent.'

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Assume the exponential growth model A(t)equals=Upper A 0 e Superscript ktA0ekt and a world population of 5.95.9 billion in 2006

Whitepunk [10]

Answer:

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Step-by-step explanation:

We are given the following in the question:

The exponential growth model is given by:

$A(t) = A_0e^{kt}$

where k is the growth rate, t is time in years and $A_0$ is constant.

The world population is 5.9 billion in 2006.

Thus, t = 0 for 2006

$A_0 = 5.9\text{ billions}$

We have to find the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Putting these values in the growth model, we have,

$24 = 5.9e^{100k}\\\\k = \dfrac{1}{100}\ln \bigg(\dfrac{24}{5.9}\bigg)\\\\k = 0.01403\\k = 0.01403\times 100\% = 1.4\%$

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

8 0

3 years ago

Last year there were 221 students and 13 teachers at Hillard School. This year there are 272 students. The principal wants to ke

weeeeeb [17]

221 / 13 = 272 / x

Hope this helps.

4 0

3 years ago

Read 2 more answers

Okay, help me out here!!

luda_lava [24]

Answer:

65.8

Step-by-step explanation:

(2.6*4.7)/2=6.11

11*4.7=51.7

(4.7(17-(2.6+11)))/2=7.99

6.11+51.7+7.99=65.8

3 0

3 years ago

Where do you find the solution to a system of liner equations??

oksano4ka [1.4K]

Answer:

The intersection of both lines.

7 0

3 years ago

Read 2 more answers

Find the value of a and of b for which<br>(a) the solution of x2 + ax < b is<br>-2<x < 4

KengaRu [80]

Answer: $a = -2$

$b = 8$

Step-by-step explanation:

Given :

$x^{2} +ax$

re - writing the equation , we have

$x^{2} +ax-b$

we need to find the value of a and b for which -2<x < 4 , this means that the roots of the quadratic equation are -2<x < 4.

The formula for finding the quadratic equation when the roots are known is :

$x^{2}$ - sum of roots(x) + product of root = 0

sum of roots = -2 + 4 = 2

product of roots = -2 x 4 = -8

substituting into the formula , we have:

$x^{2} -2x-8=0$ , which could be written in inequality form as

$x^{2} -2x-8$

comparing with $x^{2} +ax-b$ , it means that :

$a = -2$

$b = 8$

3 0

3 years ago