Write an equation of the straight line which is perpendicular
to the line 2x – 3y = 5 at the point (4,1).

3x + 2y = 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x - 3y = 5 into this form by subtracting 2x from both sides

- 3y = - 2x + 5 ( divide all terms by - 3 )

y = x - ← in slope- intercept form

with slope m =

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = - , thus

y = - x + c ← is the partial equation

To find c substitute (4, 1) into the partial equation

1 = - 6 + c ⇒ c = 1 + 6 = 7

y = - x + 7 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 14  ( add 3x to both sides )

3x + 2y = 14 ← in standard form

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: