3x^3-24x^2=> this is the expression, find what they have in common: 3 and x^2
3x^2(x-8)=> so we took out 3x^2
I hope this helps you:)!
Answer:
A. 
B. 
Step-by-step explanation:
Consider the equation
A. This equation has no solutions when the coefficients at x are the same and the free coefficients are not the same.
First, use distributive property:
So, the equation is
This equation has no solutions when
B. The equation has infinitely many solutions when the coefficients at x are the same and the free coefficients are the same too.
So, the equation
has infinitely many solutions when
In other cases, the equation has a unique solution
Answer:
The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches
Step-by-step explanation:
we know that
<u>The Triangle Inequality Theorem</u>. states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
x -----> the possible lengths of the third side
Applying the Inequality Theorem
1) 12+8 > x
20 > x
Rewrite
x < 20 in
2) 8+x > 12
x> 12-8
x > 4 in
therefore
4 in < x < 20 in
The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches
vi is going in the positive direction (up). (That's my choice). a (acceleration) is going in the minus direction (down). The directions could be reversed.
Givens
vi = 160 ft/s
vf = 0 (the rocket stops at the maximum height.)
a = - 9.81 m/s
t = ????
Remark
YOu have 4 parameters between the givens and what you want to solve. Only 1 equation will relate those 4. Always always list your givens with these problems so you can pick the right equation.
Equation
a = (vf - vi)/t
Solve
- 32 = (0 - 160)/t Multiply both sides by t
-32 * t = - 160 Divide by -32
t = - 160/-32
t = 5
You will also need to solve for the height to answer part B
t = 5
vi = 160 m/s
a = - 32
d = ???
d = vi*t + 1/2 a t^2
d = 160*5 + 1/2 * - 32 * 5^2
d = 800 - 400
d = 400 feet
Part B
You are at the maximum height. vi is 0 this time because you are starting to descend.
vi = 0
a = 32 m/s^2
d = 400 feet
t = ??
formula
d = vi*t + 1/2 a t^2
400 = 0 + 1/2 * 32 * t^2
400 = 16 * t^2
400/16 = t^2
t^2 = 25
t = 5 sec
The free fall takes the same amount of time to come down as it did to go up. Sort of an amazing result.
What you can do is count all the shapes the put the number of blue with that into a fraction. Lets say that there are 24 shapes and 15 are blue the fraction would be 15/25
Hope this helped. If you post a pic I can help you more.
