Line $l_1$ represents the graph of $3x + 4y = -14$. Line $l_2$ passes through the point $(-5,7)$, and is perpendicular to line $l_1$. If line $l_2$ represents the graph of $y=mx +b$, then find $m+b$. Please help fast!

  15

Step-by-step explanation:

The line perpendicular to ...

  3x +4y = -14

can be found by swapping the x- and y-coefficients, negating one of them:

  4x -3y = constant

The constant can be found by using the (x, y) values of the given point:

  4(-5) -3(7) = constant = -41

An equation of the line of interest is then ...

  4x -3y = -41

__

In the form ...

  y = mx +b

the value (m+b) is the y-value when x=1. Using x=1 in the equation of our line, we can solve for y:

  4(1) -3y = -41

  45 = 3y

  15 = y

The value of (m+b) is 15.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places