The distance between -2 1/4 and 1 1/2

Find the equation of the line parallel to x+3y = 4 and passing through the point (2, 5)

dmitriy555 [2]

Answer:

The equation of the parallel line is x + 3y = 17

Step-by-step explanation:

Parallel lines have the same slopes and different y-intercept

The form of the equation y = m x + b, where

m is the slope of the line

b is the y-intercept

∵ The equation of the given line is x + 3y = 4

→ We must put it in the form above to find its slope

→ Subtract x from both sides to move x to the right side

∵ x - x + 3y = 4 - x

∴ 3y = 4 - x

→ Divide both sides by 3 to make the coefficient of y = 1

∴ $\frac{3y}{3}=\frac{4}{3}-\frac{1}{3}x$

∴ y = $\frac{4}{3}$ - $\frac{1}{3}$ x

→ Compare it with the form of the equation above

∴ m = $-\frac{1}{3}$

∵ Parallel lines have the same slopes

∴ The slope of the parallel line is $-\frac{1}{3}$

→ Put it in the form of the equation

∴ y = $-\frac{1}{3}$ x + b

→ To find b substitute x and y in the equation by the coordinates

of a point on the line

∵ The line passes through the point (2, 5)

∴ x = 2 and y = 5

→ Substitute them in the equation

∴ 5 = $-\frac{1}{3}$ (2) + b

∴ 5 = $-\frac{2}{3}$ + b

→ Add $\frac{2}{3}$ to both sides

∴ $\frac{17}{3}$ = b

→ Substitute it in the form of the equation above

∴ y = $-\frac{1}{3}$ x + $\frac{17}{3}$

→ Multiply each term by 3

∴ 3y = - x + 17

→ Add x to both sides

∴ x + 3y = 17

∴ The equation of the parallel line is x + 3y = 17

3 0

4 years ago

Read 2 more answers

A company has two packaging machines in a unit, each with a different daily capacity. The capacity of machine 1 is defined by th

ollegr [7]

Total capacity = sum of the individual production capacities.

Here,

Total capacity = sum of f(m) = (m + 4)^2 + 100 and g(m) = (m + 12)^2 − 50.

Then f(m) + g(m) = (m + 4)^2 + 100 + (m + 12)^2 − 50.

We must expand the binomial squares in order to combine like terms:

m^2 + 8 m + 16 + 100

+m^2 + 24m + 144 - 50

---------------------------------

Then f(m) + g(m) = 2m^2 + 32m + 160 + 50

f(m) + g(m) = 2m^2 + 32m + 210, where m is the number of

minutes during which the two machines operate.

6 0

3 years ago

The heights of adult men in the united states are approximately normally distributed with a mean of 70 inches and a standard dev

vodomira [7]

Answer:

Use the graphing calculator to graph the system of equations and find the solution where x is the total hats sold and y is the total t-shirts sold.

x + y = 152,

8.5x + 12y = 1,656

How many hats were sold?

hats

Step-by-step explanation:

3 0

2 years ago

Can someone please help me with business math

ale4655 [162]

Answer:

1721 $

1612.80

Step-by-step explanation:

Straight line depreciation means depreciation is the same spread over for all the years. The spread over amount is nothing but total cost of equipment - salvage value.

Here we have

Cost of equipment(Purchase cost) ... 18000

Shipping costs ... 620

Installation costs ... 590

Total cost of equipment ... 19210

Less: salvage value at the end ... 2000

Net cost of equipment for 10 years ... 17210

Depreciation per year = Net cost /number of years of life

= 17210/10 = 1721/-

Hence answer is 1721/- for all years and also hence for year 2.

--------------------

Peach tree has an average life of 12 years. First 3 years no benefit would arise, 4 to 8 would be peak and after that slowly decreasing.

Hence in 9th year there would be least value and least depreciation.

Hence answer is $1612.80

8 0

3 years ago

Which point is the image of B(3, 7) after a reflection in the x-axis?

galben [10]

option B is the answer.

B)B'(3,-7)

3 0

3 years ago

Read 2 more answers