Answer:
Step-by-step explanation:
I can't make specific statements about the proof because the midpoint is missing.
Givens
There are two right angles created by where the perpendicular bisector meats MN. Both are 90 degrees.
MN is bisected by the point on MN where the perpendicular meets MN
The Perpendicular Bisector is is common to both triangles.
Therefore the two triangles are congruent by SAS
PM = PN Parts contained in Congruent triangles are congruent.
Answer:
16
Step-by-step explanation:
6.9-(-5)+4.1
When we subtract negatives, it is like adding positives
6.9 +(5)+4.1
11.9 + 4.1
16
Answer: 15e^5x
Step - by - step
y=3e^5x - 2
By the sum rule, the derivative of 3e^5x - 2 with respect to x is d/dx [ 3e^5x ] + d/dx [-2].
d/dx [ 3e^5x ] + d/dx [ -2 ]
Evalute d/dx [ 3e^5x ]
Since 3 is constant with respect to x , the derivative of 3e^5x with respect to x is
3 d/dx [ e^5x ].
3 d/dx [ e^5x ] + d/dx [ -2 ]
Differentiate using the chain rule, which states that d/dx [ f(g(x))] is f' (g(x)) g' (x) where f(x) = e^x and g(x) = 5x.
To apply the Chain Rule, set u as 5x.
3 ( d/du [ e^u] d/dx [5x] ) + d/dx [ -2]
Differentiate using the Exponential rule which states that d/du [ a^u ] is a^u ln(a) where a=e.
3( e^u d/dx[5x] ) + d/dx [ -2 ]
Replace
3(e^5x d/dx [5x] ) + d/dx [ -2 ]
3(e^5x( 5 d/dx [x] )) + d/dx [ -2 ]
Diffentiate using the Power Rule which states that d/dx [x^n] is nx^n-1 where n=1.
3(e^5x(5*1)) + d/dx [-2]
3 ( e^5x * 5 ) + d/dx [-2]
Multiply 5 by 3
15e^5x + d/dx [-2]
Since -2 is constant with respect to x, the derivative of -2 with respect to x is 0.
15e^5x + 0
15e^5x
Answer:
The numbers 
such that the average value of 
on the interval [0, b] is equal to 8 are 
and 
.
Step-by-step explanation:
The mean value of function within a given interval is given by the following integral:
If , 
, 
and 
, then:
The roots of this polynomial are determined by the Quadratic Formula:
and .
The numbers such that the average value of on the interval [0, b] is equal to 8 are and .
Answer:
XY is 4 units.
Step-by-step explanation:
We are given the following in the question:
Right triangle ABC is similar to triangle XYZ.
AB = 20.8 units
BC = 36.4 units
YZ = 7 units
We have to find the length of side XY.
Since the given triangles are similar, they have the following property:
The ratio of corresponding sides of similar triangles are equal.
We can write,
Putting the given values, we have,
Thus, the length of XY is 4 units.
