An exam worth 388 points contains 65 questions. Some questions are worth 4 points and the others are worth 8 points. How many 4 point questions are on the test?

33 questions.

Step-by-step explanation:

Let x = 4 points questions.

Let y = 8 points questions.

Translating the word problem into an algebraic equation;

For the total number of questions;

.........equation 1

For the total number of points;

..........equation 2

Given the following data;

Total number of questions = 65

Total number of points = 333

Solving the linear equation by using the substitution method;

Making x the subject in equation 1:

.......equation 3

Substituting "x" into equation 2;

Simplifying the equation, we have;

Rearranging the equation, we have;

y = 32 (For the 8 points question).

Substituting "y" into equation 3;

x = 33 (For the 4 points question).

Therefore, the number of 4 point questions on the test are 33 questions.

which expression represents the approximate length of bc?

step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11