Which graph represents the solution to the system of inequalities?

x + y ≥ 4

2x + 3y < 12

Solution:

we are given with the system of equation:

x + y ≥ 4

2x + 3y < 12

we have been asked to find the graph representing the solution of the given system of equation.

To find the the solution of the given system of inequalities, we can draw the graph using a graphing calculator and thereafter , the point of intersection will give the solution of the given system of equation.

As we can see, the graph is intersecting at only one point at (0,4).

The given system of inequalities will have infinite number of solutions and it will fall in the region shaded with green.

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .

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