Students are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. there are 15 questions on the test, and students are given 51 minutes to take it.

the system of equations shown can be used to find the number of multiple-choice questions, m, and the number of free-response questions, f, on the test.

m + f = 15

3m + 5f = 51

how many multiple-choice questions are on the test?
3
5
12
14

option C is correct.

12 multiple-choice questions are on the test

Step-by-step explanation:

Given: The system of equation :

m + f = 15            ......[1]

3m + 5f =51         .......[2]

where m is the number of multiple choice questions and f is the number of free response questions.

Now, multiply 3 to both sides of an equation in [1];

Simplify:

3m + 3f = 45  

Now, subtract 3f to both sides of an equation:

3m + 3f -3f = 45 -3f

Simplify:

3m = 45 -3f             ......[3]

Substitute the equation [3] in [2];

45 -3f +5f = 51

Combine like terms;

45 + 2f = 51

Subtract 45 to both sides of an equation we get;

45+ 2f -45 =51-45

Simplify:

2f = 6

Divide by 2 to both sides of an equation:

Simplify:

f = 3

Substitute the value of f = 3 in equation [1] solve for m;

m + 3 = 15

Subtracting 3 from both sides we get

m + 3 -3  = 15 - 3

Simplify:

m = 12

Therefore, the number of multiple-choice questions are on the test is; 12

i'm assuming it's looking for the missing length, which should be 4cm

hope this !

19.side- angle- side

20. angle- side- angle

step-by-step explanation: