Answer:
Step-by-step explanation:
A triangle with angles of 30-60-90 will always have sides that measure in the following proportions:
The side opposite the 30* angle = a
The side opposite the 60* angle = 
The side opposite the 90* angle = 2a
(I used "a" here because your question uses "x" and I don't want to confuse things, but usually people use "x" rather than "a")
They gave us that the hypotenuse (the side opposite the 90* angle) is 10, from there we can figure out the other sides:
Since the side opposite 90* is 2a, and 2a = 10, divide 10 by 2 and you get a = 5.
Once we know what "a" is, we can fill in the rest:
30* = 5
60* =
90* = 10
<h3>
Answers:</h3><h3>
x = 12</h3><h3>
Angle B = 45 degrees</h3>
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Explanation:
Angles A and B are alternate exterior angles.
Due to the parallel lines, alternate exterior angles are congruent
A = B
5x-15 = 2x+21
5x-2x = 21+15
3x = 36
x = 36/3
x = 12
Use this x value to find the measure of angle B
angle B = 2x+21
angle B = 2*12+21
angle B = 24+21
angle B = 45 degrees
As a check,
angle A = 5x-15
angle A = 5*12+15
angle A = 60-15
angle A = 45 degrees
Since A and B are both 45 degrees, this confirms the correct x value
Yay, derivitives
I'mma ignore that x is the shorter side because I don't know which one has to be shorter yet
we need to find the max area
but with 3 sides
area=LW
let's say the sides are z and y
zy=area
and the relatiionship between them is
hmm,
z+2y=1200
because one side has no fencing
so
z+2y=1200
solve for z
z=1200-2y
sub for z in other
(1200-2y)(y)=area
expand
1200y-2y²=area
take derivitive
1200-4y=dy/dx area
max is where dy/dx goes from positive to negative
solve for where dy/dx=0
1200-4y=0
1200=4y
300=y
at y<300, dy/dx<0
at y>300, dy/dx>0
so at y=300, that is the max
then
z=1200-2y
z=1200-2(300)
z=1200-600
z=600
so then
z=600
y=300
300<600
so the shorter side would be y
so then we see our choices and noticed that
erm
I think it is f(x)=1200x-2x²
takind the derivitive yeilds none of the others
so ya, you are right
Answer:
20/5=number in each group. It can also be S/5
Step-by-step explanation:
Answer:
Step-by-step explanation:
Her base salary is $1900 ,
and she makes an additional $70 for every copy =N
total pay = P
P= 1900 + 70 N
Plug N=29
