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3 years ago

Write an equation, in point-slope form, for the line that goes through points (4,4) and (-4,-1).

Mathematics

1 answer:

Soloha48 [4]3 years ago

3 0

Answer:

C.) Y= 5/8x + 1 1/2

Step-by-step explanation:

To write the equation of a line, calculate the slope between points (4,4) and (-4,-1). After, substitute the slope and a point into the point slope form.

$m = \frac{y_2-y_1}{x_2-x_1} = \frac{4--1}{4--4}= \frac{5}{8}$

Substitute m = 5/8 and the point (4,4) into the point slope form.

$y - y_1 = m(x-x_1)\\y -4 = \frac{5}{8}(x-4)\\y-4 = \frac{5}{8}x - \frac{20}{8} \\\y = \frac{5}{8}x - 2{1}{2} + 4 \\ y = \frac{5}{8}x + 1\frac{1}{2}$

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The information given below was extracted from the accounting records of Sunray Traders, a partnership business with Sunny and R

Crank

The preparation of the Profit and Loss Appropriation Account for the year ended February 28, 2022, is as follows:

<h3>What is the Profit and Loss Appropriation Account?</h3>

A profit and loss appropriation account is a special account prepared for the distribution of the partnership's profit and loss for the period.

For Sunray Traders Partnership, the profit and loss appropriation account is detailed below.

<h3>Profit and Loss Appropriation Account</h3>

For the year ended February 28, 2022

Sunny Raymond Total

Net Profit for the year R900,000

Interest on capital R84,000 R24,000 (R108,000)

Annual Salaries R307,500 R246,000 (R553,500)

Share of profits R119,250 R119,250 (R238,500)

<h3>Question Completion:</h3>

Sunny R25 000 Raymond R20 000

Note: The salaries of the partners were increased by 10% with effect from 01 December 2021.

d) The balance of the profit and loss must be shared equally between Sunny and Raymond.

Prepare the Profit and Loss Appropriation Account for the year ended February 28m 2022.

<h3>Data and Calculations:</h3>

DEBIT CREDIT

Capital: Sunny R1 000 000

Capital: Raymond 600 000

Current a/c: Sunny (01 March 2021) 40 000

Current a/c: Raymond (01 March 2021) 60 000

Drawings: Sunny R300 000

Drawings: Raymond 400 000

Net profit = R900 000

Sunny's Salaries = R307,500 (R25,000 x 9 + R25,000 x 1.1 x 3)

Raymond Salaries = R246,000 (R20,000 x 9 + R20,000 x 1.1 x 3)

<h3>Capital Accounts Balances:</h3>

Sunny Raymond Total

Capital accounts R1 000 000 R600 000 R1 600 000

Drawings accounts 300 000 400 000 700 000

Net Capital accounts R700 000 R200 000 R900 000

Interest on capital R 84 000 R24 000 R108 000

Thus, the profit and loss of Sunray Traders Partnership are shared equally as agreed.

Learn more about partnership accounts at brainly.com/question/22693552

#SPJ1

3 0

2 years ago

A sea bird is 28 meters above the surface of the ocean.What is its elevation?

Citrus2011 [14]

Answer:

91.8 ft above sea level

Step-by-step explanation:

Note that 1 meter is approx. 3.28 feet.

Converting 28 meters to feet is accomplished by multiplying 28 m by the conversion factor 3.28 ft / 1 m:

28 m 3.28 ft

-------- * ----------- = 91.8 ft above sea level

1 1 m

4 0

3 years ago

Why are the factors in your multiplication sentences in a different order

Diano4ka-milaya [45]

In multiplication, the order doesn't matter.

2 rows of 7 and 7 rows of 2 is the same.

If you have seven 2's, that's the same as two 7's.

See here:

2 + 2 + 2 + 2 + 2 + 2 + 2 = 14

7 + 7 = 14

Or:

2 * 7 = 7 * 2 = 14

5 0

3 years ago

You find out that you get a 20% off on your favorite sweater, and you also get an additional 30% off. Does the store apply the d

Marta_Voda [28]

Answer:

Apply them sequentially.

Step-by-step explanation:

The store would apply the discounts sequentially because it gives less of a discount compared to if they did it all at once.

8 0

3 years ago

Read 2 more answers

A. Do some research and find a city that has experienced population growth.

horrorfan [7]

A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation $N_{t} =N _{0}e^{rt}$
where:
$N(t)$ is the population after $t$ years
$N_{0}$ is the initial population
$t$ is the time in years
$r$ is the growth rate in decimal form
$e$ is the Euler's constant
We now for our investigation that $N(t)=238300$ , $N_{0} =192157$ , and $t=10$ ; lets replace those values in our equation to find $r$ :
$238300=192157e^{10r}$
$e^{10r} = \frac{238300}{192157}$
$ln(e^{10r} )=ln( \frac{238300}{192157} )$
$r= \frac{ln( \frac{238300}{192157}) }{10}$
$r=0.022$
Now lets multiply $r$ by 100% to obtain our growth rate as a percentage:
$(0.022)(100)$ =2.2%
We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
Population in 2000: 951,307
Population in 2010: 713,777
We know from our investigation that $N(t)=713777$ , $N_{0} =951307$ , and $t=10$ . Just like before, lets replace those values into our equation to find $r$ :
$713777=951307e^{10r}$
$e^{10r} = \frac{713777}{951307}$
$ln(e^{10r} )=ln( \frac{713777}{951307} )$
$r= \frac{ln( \frac{713777}{951307}) }{10}$
$r=-0.029$
$(-0.029)(100)$ = -2.9%.
We just show that Detroit's population has been declining at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

C. Final equation from point A: $N(t)=192157e^{0.022t}$ .
Final equation from point B: $N(t)=951307e^{-0.029t}$
Similarities: Both have an initial population and use the same Euler's constant.
Differences: In the equation from point A the exponent is positive, which means that the function is growing; whereas, in equation from point B the exponent is negative, which means that the functions is decaying.

D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations $N(t)=192157e^{0.022t}$ and $N(t)=951307e^{-0.029t}$ and solve for t:
$192157e^{0.022t} =951307e^{-0.029t}$
$\frac{192157e^{0.022t} }{951307e^{-0.029t} } =1$
$e^{0.051t} = \frac{951307}{192157}$
$ln(e^{0.051t})=ln( \frac{951307}{192157})$
$t= \frac{ln( \frac{951307}{192157}) }{0.051}$
$t=31.36$
We can conclude that if Orlando's population keeps growing at the same rate and Detroit's keeps declining at the same rate, after 31.36 years in May of 2031 Orlando's population will surpass Detroit's population.

E. Since we know that the population of Detroit as 2000 is 951307, twice that population will be $2(951307)=1902614$ . Now we can rewrite our equation as: $N(t)=1902614e^{-0.029t}$ . The last thing we need to do is equate our Orlando's population growth equation with this new one and solve for t:
$192157e^{0.022t} =1902614e^{-0.029t}$
$\frac{192157e^{0.022t} }{1902614e^{-0.029t} } =1$
$e^{0.051t} = \frac{1902614}{192157}$
$ln(e^{0.051t} )=ln( \frac{1902614}{192157} )$
$t= \frac{ln( \frac{1902614}{192157}) }{0.051}$
$t=44.95$
We can conclude that after 45 years in 2045 the population of Orlando will exceed twice the population of Detroit.

8 0

4 years ago