you have two unknown variables, thus you need two equations
a = quantity of multiple choice questions
b = quantity of true and false questions
100 points = a*11 points/question + b*3 points/question
20 questions = a +b
using 2nd equation, find equation for 'a':
a = 20 - b
substitute this equation for 'a' into 1st equation:
100 = 11a + 3b
100 = 11(20 - b) + 3b
100 = 220 - 11b + 3b
100 - 220 = -8b
-120 = -8b
-120/-8 = b
15 = b
resolve 2nd equation now knowing value of 'b':
a = 20 - b
a = 20 - 15
a = 5
verify solution is correct by substituting values into first equation
11a + 3b = 100
11(5) + 3(15) = 100
55 + 45 = 100
100 = 100 [OK]
verify solution is correct by substituting values into second equation
a + b = 20
5 + 15 = 20
20 = 20 [OK]
Solve the system and the answer is 5 multiple choice questions.
x= -3 and
to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into
where a is the cube root of .
here this is 27 and the cube root of 27 is 3. so we write using the form:
set each factor to 0 and solve for x.
the quadratic expression does not factor and must be solved using the quadratic formula.
where a = 1, b=3, and c=9
this cubic has two complex roots.
the correct answer is b. negative exponential growth.
you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.
it is negative because the y-axis decreases as the x-axis increases.
therefore it is a negative exponential growth graph.
hope i !