What is the equation of the line that passes through the point (-3,7) and has a slope of 1/3

y = 1/3 x + 8.

or in standard form:

x - 3y = -24.

Step-by-step explanation:

To answer this we use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Here we have m = 1/3 and (x1, y1) = (-3, 7), so:

y - 7 = 1/3(x - (-3))

y - 7 = 1/3( x + 3)

y - 7 = 1/3 x + 1

y = 1/3 x + 8 .

This is the slope-intercept form of the equation.

Converting to standard form, we first multiply by 3:-

3y = x + 24

- x + 3y = 24

x - 3y = -24.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.