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4 years ago

Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer

Mathematics

1 answer:

m_a_m_a [10]4 years ago

8 0

Answer:

After 20 months the total amount paid would be same for both

The amount is $5500

Step-by-step explanation:

* Lets explain how to solve the problem

- Kenya plans to make a down payment plus monthly payments in

order to buy a motorcycle

- There are two dealer

# 1st : she would pay $2,500 down and $150 each month

# 2nd : she would pay $3,000 down and $125 each month

- We need to know after how many months the total amount paid

would be the same for both dealers

* Lets change the two dealer to two equations

- Let f(x) represents the total amount of the motorcycle in x months

∴ f(x) = 2500 + 150 x ⇒ 1st dealer

∴ f(x) = 3000 + 125 x ⇒ 2nd dealer

- Equate the two equations

∴ 2500 + 150 x = 3000 + 125 x

- Subtract 125 x from both sides and 2500 from both sides

∴ 150 x - 125 x = 3000 - 2500

∴ 25 x = 500

- Divide both sides by 25

∴ x = 20

* After 20 months the total amount paid would be same for both

- To find the amount substitute the value of x in one of the

two equation

∵ f(x) = 2500 + 150 x

∵ x = 20

∴ f(x) = 2500 + 150 (20)

∴ f(x) = 2500 + 3000

∴ f(x) = 5500

∵ f(x) represents the total amount of the motorcycle

* The amount is $5500

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The equations of three lines are given below. Line 1: y = - 3/4 x + 3 Line 2/8 x - 6y = 2 Line 3/- 3y = 4x + 7 For each pair of

Maru [420]

Answer:

No parallel lines

Lines 1 and 3 are perpendicular

Step-by-step explanation:

Given:

$Line\ 1:y = -\frac{3}{4}x + 3$

$Line\ 2: \frac{2}{8}x -6y = 2$

$Line\ 3: 3y = 4x + 7$

Required

Determine if they are parallel, perpendicular or not

The slope intercept of a line has the form:

$y = mx + b$

Where

$m = slope$

First, we calculate the slope of each lines

$Line\ 1:y = -\frac{3}{4}x + 3$

Compare the above to $y = mx + b$

$m_1 = -\frac{3}{4}$

$Line\ 2: \frac{2}{8}x -6y = 2$

$\frac{2}{8}x -6y = 2$

Make -6y the subject

$-6y = 2 - \frac{2}{8}x$

Divide through by -6

$y = -\frac{2}{6} + \frac{2}{8*6}x$

$y = -\frac{1}{3} + \frac{1}{8*3}x$

$y = -\frac{1}{3} + \frac{1}{24}x$

$y = \frac{1}{24}x-\frac{1}{3}$

Compare the above to $y = mx + b$

$m_2 = \frac{1}{24}$

$Line\ 3: 3y = 4x + 7$

$3y = 4x + 7$

Divide through by 3

$y = \frac{4}{3}x + \frac{7}{3}$

Compare the above to $y = mx + b$

$m_3 = \frac{4}{3}$

So, we have:

$m_1 = -\frac{3}{4}$

$m_2 = \frac{1}{24}$

$m_3 = \frac{4}{3}$

None of the slopes are the same, so none of the lines are parallel.

However, lines 1 and 3 are perpendicular.

This is shown below

When the slope of two lines satisfy the following condition, then they are perpendicular.

$m_1 = -\frac{1}{m_3}$

This gives:

$-\frac{3}{4} = -\frac{1}{4/3}$

$-\frac{3}{4} = -1/\frac{4}{3}$

Convert / to *

$-\frac{3}{4} = -1*\frac{3}{4}$

$-\frac{3}{4} = -\frac{3}{4}$

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