Answer:
110 degrees
Step-by-step explanation:
The measures of the two base angles of an isosceles triangle are the same so 180 - 2(35) = 110 which is the vertex angle.
464 inches. Hope this helped! :)
Answer:
The area is growing at a rate of 
Step-by-step explanation:
<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>
We identify that the info given on the increasing rate of the circle's radius is 3
and we identify such as the following differential rate:

Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find
.
So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):

We now apply the derivative operator with respect to time (
) to this equation, and use chain rule as we find the quadratic form of the radius:
![\frac{d}{dt} [A=\pi\,r^2]\\\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5BA%3D%5Cpi%5C%2Cr%5E2%5D%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%5Cpi%5C%2C%2A2%2Ar%2A%5Cfrac%7Bdr%7D%7Bdt%7D)
Now we replace the known values of the rate at which the radius is growing (
), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :

which we can round to one decimal place as:

Answer:
the exponent of x is 4
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
__

<span>pennies = 0.01 $
nickels = 0.05 $
dimes = 0.1 $
quarters = 0.25 $
We must write the system of equations that best suits this problem and solve it:
Let:
x = pennies
y = nickels
z = dimes
w = quarters
Writing the equations
0.01x + 0.05y + 0.1z + 0.25w = 3.71
I have twice as many dimes as nickels
z = 2y
two more nickels than quarters
y = w + 2
three fewer pennies than three times the number of nickels
x = 3y-3.
Solving the system of equations:
x = 21
y = 8
z = 16
w = 6
answer
He has
21 pennies
8 nickels
16 dimes
6 quarters
</span>