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3 years ago

Y-3=2(x-3) y+5=2(x+1)

Mathematics

1 answer:

bonufazy [111]3 years ago

8 0

Answer:

The same lines (answer)

Step-by-step explanation:

The equations can be written in slope-intercept form y = mx + c (where 'm' is slope and 'c' is the y-intecept) as,

y-3 = 2(x-3) .......(1) ; y + 5 = 2(x+1) ...........(2)

y = 2x - 6 + 3 ; y = 2x + 2 - 5

y = 2x -3 ; y = 2x - 3

Comparing with slope intercept form we have,

m1 = 2 ; m2 = 2

c1 = -3 ; c2 = -3

If the slopes are equal the lines are parallel and since y-intercepts are also equal means they are the same lines (overlapping)

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Initial salary = $50,000 .

Rate of raise = 5% each year.

Therefore, each next year salary would be 105% that is 1.05 times.

5% of 50,000 = 0.05 × 50000 = 2500.

Therefore raise is $2500 each year.

According to geometric sequence first term 50000 and common ratio 1.05.

Applying geometric sequence formula

$a_n = ar^{n-1}$

1) $a_n = 50000(1.05)^{n-1}$

2) In order to find salary in 5 years we need to plug n=5, we get

$a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4$

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3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.

$S_n = \frac{a(1-r^n}{1-r}$

Plugging n=10, a = 50000 and r= 1.05.

$S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}$

$S_10 = \frac{50000(0.050)^{10}}{0.05}$

= 628894.62678.

<h3>Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.</h3>

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3 years ago

The ratio of the angle measures in a triangle is 3 : 5 : 7. What are the measures of the angles of the triangle?

NeTakaya

Answer:

36, 60, 84

Step-by-step explanation:

3+5+7=15

180/15=12

12*3=36

12*5=60

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2 years ago

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10

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The approximate difference in the ages of the two cars, which depreciate to 60% of their respective original values, is 1.7 years.

<h3>What is depreciation?</h3>

Depreciation is to decrease in the value of a product in a period of time. This can be given as,

$FV=P\left(1-\dfrac{r}{100}\right)^n$

Here, (<em>P</em>) is the price of the product, (<em>r</em>) is the rate of annual depreciation and (<em>n</em>) is the number of years.

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%.

Suppose the original price of the first car is x dollars. Thus, the depreciation price of the car is 0.6x. Let the number of year is $n_1$ . Thus, by the above formula for the first car,

$0.6x=x\left(1-\dfrac{10}{100}\right)^{n_1}\\0.6=(1-0.1)^{n_1}\\0.6=(0.9)^{n_1}$

Take log both the sides as,

$\log 0.6=\log (0.9)^{n_1}\\\log 0.6={n_1}\log (0.9)\\n_1=\dfrac{\log 0.6}{\log 0.9}\\n_1\approx4.85$

Now, the second car depreciates at an annual rate of 15%. Suppose the original price of the second car is y dollars.

Thus, the depreciation price of the car is 0.6y. Let the number of year is $n_2$ . Thus, by the above formula for the second car,

$0.6y=y\left(1-\dfrac{15}{100}\right)^{n_2}\\0.6=(1-0.15)^{n_2}\\0.6=(0.85)^{n_2}$

Take log both the sides as,

$\log 0.6=\log (0.85)^{n_2}\\\log 0.6={n_2}\log (0.85)\\n_2=\dfrac{\log 0.6}{\log 0.85}\\n_2\approx3.14$

The difference in the ages of the two cars is,

$d=4.85-3.14\\d=1.71\rm years$

Thus, the approximate difference in the ages of the two cars, which depreciate to 60% of their respective original values, is 1.7 years.

Learn more about the depreciation here;

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Step-by-step explanation:

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