Answer:
.
Step-by-step explanation:
Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to 
. Make use of the power rule to find the following:
.
.
The question states that the graphs of 
and 
touch at 
, such that 
. Therefore:
.
On the other hand, since the graph of and coincide at , 
(otherwise, the two graphs would not even touch at that point.) Therefore:
.
Solve this system of two equations for 
and 
:
.
Therefore, 
whereas 
.
Substitute these two values back into the expression for and :
.
.
Evaluate either expression at to find the 
-coordinate of the intersection. For example, 
. Similarly, 
.
Therefore, the intersection of these two graphs would be at .
The percent of the jerseys :
6 : 800 = 0,75%
Answer: x=8
Step-by-step explanation:
Hope this helps
The interpretation is that we are 95% confident that the true population proportion p is somewhere between 0.58 and 0.64
The population proportion p in this case refers to the proportion of people who feel that race relations in this country are generally bad.
Something like 0.58 converts to 58% when you move the decimal point 2 spots to the right.
Answer:
x = 8 units, measure of angle AFE = 60 degrees, measure of angle CFD = 60 degrees
Step-by-step explanation:
Finding x:
You know all three of the given measures add up to 180 because they are on the same side of the line. Write an equation and solve for x.
6x + 2 + 8x + 6 + 7x + 4 = 180
21x = 168 --> x = 8
Angle AFE:
Substitute the value of x in the given measure.
7x + 4 = 7*8 + 4 = 56 + 4 = 60
Measure of angle CFD:
Angle AFE is it's vertical angle, so their measures (60 degrees) are equal.
