Let f(x)= 100 / −10+ e^ −0.1x . What is f(−6) ?
Enter your answer, rounded to the nearest tenth, in the box.

The value of f(-6) is -12.2

Explanation:

Given that the function

We need to determine the value of f(-6)

The value of f(-6) can be determined by substituting the value for in the function and simplify the function.

Hence, let us substitute in the function, we get,

Let us apply the rule , we get,

Multiplying the numbers, we get,

The value of

Substituting the value of , we get,

Subtracting the denominator, we have,

Dividing, we have,

Rounding off to the nearest tenth, we have,

Thus, the value of f(-6) is -12.2

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form