First we must change these numbers to improper fractions:
So then we set it up:
÷
When we divide fractions like this, we must flip the second fraction and change the sign from division to multiplication like so:
Then we solve:
Then if we divide the numerator and the denominator by 9, we get:
or, in mixed-number form,
.
Answer:
m<E =
Step-by-step explanation:
From the diagram, ΔACE and ΔBDE are similar. So that comparing its angles, we have;
(8x + 4) = (9x - 5)
8x + 4 = 9x - 5
5 + 4 = 9x - 8x
x = 9
Thus,
(8x + 4) = 8(9) + 4 = 76
(9x - 5) = 9(9) - 5 = 76
3x = 3(9) = 27
From ΔACE,
3x + (8x + 4) + m<E = 180 (sum of angles in a triangle)
27 + 76 + m<E = 180
m<E = 180 - 103
m<E =
Answer:
16.5 square units
Step-by-step explanation:
You are expected to integrate the function between x=1 and x=4:
__
<em>Additional comment</em>
If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.
The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.
This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...
area = 4.5 +3×4 = 16.5 . . . square units
