What is (6 + 3e)4 - 5e and 3(x - 5) + 7(x + 2) ?
1 answer:
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Answer:
The inequality describing the situation is:
Step-by-step explanation:
Joe works as a busboy at the rate of = $7 per hour
Let the number of hours he works as a bus boy this month be = hours
∴ Amount Joe would make this month working as a busboy =
Joe works as a theater usher at the rate of = $9 per hour
Let the number of hours he works as a theater usher this month be = hours
∴ Amount Joe would make this month working as a theater usher =
Total amount Joe would make this month =
His goal is earn more than $1500 this month.
∴ The situation can be represented in the following inequality:
In the given figure we can determine the coordinate of point M from the graph, we get:
We can also determine the coordinates of point N as:
Now, to determine the length of segment MN, we need to subtract the x-coordinate of M from the coordinates of N, we get:
Subtracting the fractions we get:
Now, to obtain the length of AB we need to subtract the x-coordinate of A from the x-coordinate of B.
The coordinates of A are determined from the graph:
The coordinates of B are:
Therefore, the length of segment AB is:
Now we do the same procedure to determine the segment of CD. The coordinates of C are:
The coordinates of D are:
Therefore, CD is:
Now, we determine MN as half the sum of the bases. The bases are AB and CD, therefore:
Therefore, we have proven that the median of a trapezoid equals half the sum of its bases.