Answer: (9ab^2+c^3)(9ab^2-c^3)
Step-by-step explanation:
81a^2b^4-c^6
(9ab^2)^2-(c^3)^2
(9ab^2+c^3)(9ab^2-c^3)
Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! As well as a great Superbowl Weekend! :-)
- Cutiepatutie ☺❀❤
Answer:
6sqrt2(cos(-5pie/4)+isin(-5pie/5))
Step-by-step explanation:
Answer:
i believe that it is 45
Step-by-step explanation:
Let x=ab=ac, and y=bc, and z=ad.
Since the perimeter of the triangle abc is 36, you have:
Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36
The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.
Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).
The perimeter of the triangle abd is 30:
Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60
So, we have two equations on x, y and z:
(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60
Substitute 2x + y by 36 from (eq.1) in (eq.2):
(eq.2') 36 + 2z = 60
And solve for z:
36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12
The measure of ad is 12.
If you prefer a less algebraic reasoning:
- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).
- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:
ad = 30 - (36/2) = 30 - 18 = 12
Answer:
a) Table and graph showed
b) The distance will be 231 miles
c) Yes
Step-by-step explanation:
We know the van gets 22 mi/gal, so the distance D in miles traveled by the van can be expressed as
D(g)=22g, being g the number of gallons of gas used
a) The graph of the function D and its corresponding table of values is shown below.
b) If the van used g=10.5 gallons of gas, the distance would be:
D(10.5)=22 x 10.5 = 231 miles
c) The values of g are real in nature because they represent the amount of gas consumed by the van and it can be any real positive number. Being D a linear function of g, it also happens to take positive real values. Then it makes sense to connect the points with lines.
