Answer: X = 27
Step-by-step explanation: If we observe very closely, we have two similar triangles in the diagram. The first one is ABC and the other triangle is EDC. Also take note that angle ACB in the first triangle is equal in measurement to angle ECD (45 degrees) in the other triangle, (Opposite angles).
Hence in triangle ECD, we have identified two angles so far which are angle 2x + 10 and angle 45. Same applies to triangle ABC, we already have two angles which are, 3x - 10 and 45.
However angle D in the second triangle is equal in measurement to angle B in the first triangle
(Alternate angles).
Hence we have a third angle in triangle ABC which is
Angle B = 2x + 10.
Therefore 3x - 10 + (2x + 10) + 45 = 180
(Sum of angles in a triangle)
3x - 10 + 2x + 10 + 45 = 180
By collecting like terms we now have
3x + 2x = 180 + 10 - 10 - 45
5x = 135
Divide both sides by 5,
x = 27
Find the first derivatives:
.
Solve the system
:
. The second equation has solutions
and then
and you have two points
.
Find the first derivatives:
and calculate
.
Since
and
,
is a point of maximum and
.
Since
and
,
is a point of minimum and
.
Answer:
CD=66
Step-by-step explanation:
12x-30=6x+18
6x=48
x=8
12(8)-30=66
CD=66
Answer:
4399.98 ft per min
Step-by-step explanation:
- Divide 50 mi by 60 min = 0.83333
- Multiply this by 5280 = 4399.9824 ft per min
Answer:
x = 3 and y = -18
Step-by-step explanation:
y = -6x
y = -8x + 6
Both equations are equal to y. So,
y = -6x = -8x + 6
Solve for x first.
-6x = -8x + 6
Add 8x to both sides.
2x = 6
x = 3
Substitute x = 3 into y = -6x
y = -6 * 3
y = -18
Now, double check to see if this is correct.
y = -8x + 6
-18 = -8 * 3 + 6
-18 = -24 + 6
-18 = -18
x = 3 and y = -18 are correct.
I hope this helps! Feel free to ask any questions!