Noah is writing an exam for his 8th grade students. the exam is worth 100 points and noah wants 35 questions on the exam. he plans to mix short answer questions, worth 3 points, with multiple choice questions worth 2 points. create a system of equations to tell us how many of each type of question noah can have on the test. let x= the number of short answer questions and y= the number of multiple choice questions

the system of equations are

x + y = 35

3x + 2y = 100

Step-by-step explanation:

Let x= the number of short answer questions.

Let y= the number of multiple choice questions.

Noah wants 35 questions on the exam. This means that

x + y = 35

He plans to mix short answer questions, worth 3 points, with multiple choice questions worth 2 points. This means that x short answer questions will give 3x points and y multiple choice questions will give 2y points

Since the exam is worth 100 points, then,

3x + 2y = 100 - - - - - - - -1

Substituting x = 35 - y into equation 1, it becomes

3(35 - y) + 2y = 100

105 - 3y + 2y = 100

y = 105 - 100 = 5

x = 35 - y = 35 - 5

x = 30

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752