For the linear function f(x)=mx+b, f(-2)=11 and f(3)=-9. find m and b

Step-by-step explanation:

Filling the given information into the equation gives two equations in two unknowns:

Subtracting the first equation from the second, we have ...

  (-9) -(11) = (3m +b) -(-2m +b)

  -20 = 5m . . . . . . simplify

  -4 = m  . . . . . . . . divide by the coefficient of m

Putting this value of m into the first equation above, we have ...

  11 = -2(-4) +b

  3 = b . . . . . . . . . subtract 8

The values of m and b are -4 and 3, respectively.

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