Option C: The solution set is 
Explanation:
The expression is 
Now, let us find the solution set.
Switch sides, we get,
Dividing by 2 on both sides, we have,
Thus, 
Hence, the above expression becomes,
Simplifying, we get,
Applying the log rule, we get,
Simplifying, we have,
Applying the log rule, we have,
Thus, the solution set is
Hence, Option C is the correct answer.
Answer:
(a) B
(b) $2
Step-by-step explanation:
(a) Let's say the cost of a ticket is t and the cost of popcorn is p. Then we can write the two equations from the table:
12t + 8p = 184
9t + 6p = 138
We need to solve this, so let's use elimination. Multiply the first equation by 3 and the second equation by 4:
3 * (12t + 8p = 184)
4 * (9t + 6p = 138)
We get:
36t + 24p = 552
36t + 24p = 552
Subtract the second from the first:
36t + 24p = 552
- 36t + 24p = 552
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0 = 0
Since we get down to 0 = 0, which is always true, we know that we cannot determine the cost of each ticket because there is more than one solution (infinitely many, actually). The answer is B.
(b) Our equation from this, if we still use t and p, is:
5t + 4p = 82
Now, just choose any of the two equations from above. Let's just pick 9t + 6p = 138. Now, we have the system:
5t + 4p = 82
9t + 6p = 138
To solve, let's use elimination again. Multiply the first equation by 6 and the second one by 4:
6 * (5t + 4p = 82)
4 * (9t + 6p = 138)
We get:
30t + 24p = 492
36t + 24p = 552
Subtract the second from the first:
36t + 24p = 552
- 30t + 24p = 492
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6t + 0p = 60
So, t = 60/6 = $10. Plug this back into any of the equations to solve for p:
5t + 4p = 82
5 * 10 + 4p = 82
50 + 4p = 82
4p = 32
p = 32/4 = $8
So the ticket costs 10 - 8 = $2 more dollars than the popcorn.
The answer will be 37 yd. Hope it help!
Answer:
There is no solution of the system of equations.
Step-by-step explanation:
We are given two equations y = - 4 and y = 4 and are to find the solution to the equations.
Now, the straight line y = - 4 is parallel to the x-axis as the equation of straight lines that are parallel to the x-axis are given by y = c, where c is any constant value.
Again, the straight line y = 4 is parallel to the x-axis.
Therefore, y = - 4 and y = 4 two lines are parallel to each other and we know, parallel lines never intersect and hence there is no solution of the system of equations. (Answer)
(-3, 3) because it is the intersection point.
