In order to solve for this question, let's assign a couple variables.
The variable 't' will represent the number of two-point questions, and the variable 's' will represent the number of six point questions.
From the given, we can already form two equations:
t + s = 36
("An exam... contains 36 questions")
2t + 6s = 148
("An exam worth 148 points... Some questions are worth 2 points, and the others are worth 6 points")
Before we begin calculating anything, we can simplify the second equation we made, since all the numbers are divisible by 2:
2t + 6s = 148
t + 3s = 74
Now let's refer back to the first equation. We can subtract both sides by 's' (you could also subtract both sides by 't', but I personally think that this will make solving the equation less difficult):
t + s = 36
t = 36 - s
This effectively gives us a value for the variable 't'. We can assign this value back into our first equation:
t + 3s = 74
(36 - s) + 3s = 74
36 + 2s = 74
2s = 38
s = 19
Input 's' into our second equation to solve for 't':
t = 36 - s
t = 36 - 19
t = 17
There are 17 two-point questions and 19 six-point questions
- T.B.
Answer:
Step-by-step explanation:
Simplifying
2x(3 + 4a) = -16x + 6x
(3 * 2x + 4a * 2x) = -16x + 6x
Reorder the terms:
(8ax + 6x) = -16x + 6x
(8ax + 6x) = -16x + 6x
Combine like terms: -16x + 6x = -10x
8ax + 6x = -10x
Solving
8ax + 6x = -10x
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-6x' to each side of the equation.
8ax + 6x + -6x = -10x + -6x
Combine like terms: 6x + -6x = 0
8ax + 0 = -10x + -6x
8ax = -10x + -6x
Combine like terms: -10x + -6x = -16x
8ax = -16x
Divide each side by '8x'.
a = -2
Simplifying
a = -2 <— answer
Answer:144 degrees
288 degrees
Step-by-step explanation:
